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Measurement and applications of dynamic nuclear polarization
229
Advances in Molecular Relaxation Processes Elsevier Publishing Company, Amsterdam.
MEASUREMENT
AND
P r i n t e d in t h e N e t h e r l a n d s
APPLICATIONS
OF
DYNAMIC
NUCLEAR
POLARIZATION
JOSEPH POTENZA
School o f Chemistry, Rutgers University, N e w Brunswick, N.J. 08903 (U.S.A.)
CONTENTS 1. I n t r o d u c t i o n
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230
II. T h e o r y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. The single resonance experiment . . . . . . . . . . . . . . . . . . . . . . 1. S o m e f u n d a m e n t a l p r o p e r t i e s o f n u c l e i . . . . . . . . . . . . . . . . . . 2. S p i n s t a t e s in a m a g n e t i c field . . . . . . . . . . . . . . . . . . . . . . 3. B o l t z m a n n t h e r m a l e q u i l i b r i u m p o p u l a t i o n d i s t r i b u t i o n . . . . . . . . . . . 4. S a t u r a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. R e l a x a t i o n t r a n s i t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . B. T h e d o u b l e r e s o n a n c e e x p e r i m e n t . . . . . . . . . . . . . . . . . . . . . C. S y s t e m s w i t h s h o r t - l i v e d i n t e r m e d i a t e s - ¢ior~P . . . . . . . . . . . . . . . . 1. B a s i c o b s e r v a t i o n s - c h e m i c a l p u m p i n g . . . . . . . . . . . . . . . . . . 2. T h e m u l t i p l e t effect . . . . . . . . . . . . . . . . . . . . . . . . . . 3. F i e l d d e p e n d e n c e o f ¢IDNP s p e c t r a - " z e r o - f i e l d p o l a r i z a t i o n " . . . . . . . . III. I n s t r u m e n t a t i o n a n d e x p e r i m e n t a l a s p e c t s o f DNP A. Electronically induced oNP . . . . . . . . . . . . . . . . . . . . . . . . 1. E x t r a p o l a t e d e n h a n c e m e n t s . . . . . . . . . . . . . . . . . . . . . . . 2. S a m p l e p r e p a r a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . 3. R a d i c a l s u s e d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. I n s t r u m e n t a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. CIDNP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. Q u a n t i t a t i v e CIDNP e n h a n c e m e n t s . . . . . . . . . . . . . . . . . . . . 2. H i g h - f i e l d p o s i t i v e e n h a n c e m e n t s . . . . . . . . . . . . . . . . . . . . . 3. R a d i c a l l i f e t i m e c o n s i d e r a t i o n s . . . . . . . . . . . . . . . . . . . . . 4. R e a c t i o n c o n d i t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . .
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IV. E x p e r i m e n t a l r e s u l t s a n d c h e m i c a l a p p l i c a t i o n s - DNP . . . . . . . . . . . . . . A. Physical factors affecting enhancement . . . . . . . . . . . . . . . . . . . 1. S p e c t r a l d e n s i t y c u r v e s - d i p o l a r vs. s c a l a r c o u p l i n g . . . . . . . . . . . . 2. E f f e c t o f v i s c o s i t y . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. E f f e c t o f t e m p e r a t u r e v a r i a t i o n . . . . . . . . . . . . . . . . . . . . . 4. P h y s i c a l p a r a m e t e r s o b t a i n a b l e f r o m DNP m e a s u r e m e n t s . . . . . . . . . . B. E x p e r i m e n t a l r e s u l t s f o r p r o t o n s . . . . . . . . . . . . . . . . . . . . . . 1. L o w - f i e l d m e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . 2. H i g h - a n d m u l t i f i e l d m e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . 3. E x c e p t i o n s to t h e r u l e - s c a l a r c o u p l i n g f o r p r o t o n s . . . . . . . . . . . . C. E x p e r i m e n t a l r e s u l t s f o r f l u o r i n e n u c l e i . . . . . . . . . . . . . . . . . . . 1. L o w - f i e l d m e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . 2. P o s s i b l e i n t e r p r e t a t i o n s f o r s c a l a r c o u p l i n g . . . . . . . . . . . . . . . . 3. M u l t i f i e l d m e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . D. Experimental results for phosphorus nuclei . . . . . . . . . . . . . . . . . 1. L o w - f i e l d r e s u l t s . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. H i g h - f i e l d m e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . E. E x p e r i m e n t a l r e s u l t s f o r c a r b o n n u c l e i . . . . . . . . . . . . . . . . . . .
232 232 232 235 237 239 241 244 254 254 258 270 273 273 273 275 276 280 289 290 291 291 292 292 293 293 296 297 298 298 298 300 302 304 304 306 309 313 313 318 321
Advan. MoL Relaxation Processes, 4 ( 1 9 7 2 ) 2 2 9 - 3 5 4
230
J. POTENZA
V. E x p e r i m e n t a l r e s u l t s - CIDNP A. Alkyl and aryl radicals . . . . . . . . . . . . . . . . . . . . . . . . . . B. P h o t o c h e m i c a l a p p l i c a t i o n s - t e s t s o f t h e K a p t e i n - C l o s s t h e o r y . . . . . . . . C. Chain reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Reactions involving lithium alkyls - characterization of radical intermediates . . E. R a d i c a l p a i r i n t e r m e d i a t e s in r e a r r a n g e m e n t r e a c t i o n s . . . . . . . . . . . . . F. Nuclei other than protons . . . . . . . . . . . . . . . . . . . . . . . . . G . G a s p h a s e CIDNP? .
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Appendix
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324 324 329 338 339 345 347 349
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349
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
350
I. I N T R O D U C T I O N
The subject to be discussed in this review is called by a variety of names. It is called the Overhauser effectI, after the author who first predicted it in 1953; it is called nuclear-electron double resonance 2, in analogy with electron-nuclear double resonance (eNDOR); and it is called dynamic nuclear polarization 3 (DNP), the notation we shall use. Whatever the name, ONV is a double magnetic resonance technique, and, as such, requires the presence of two non-identical spins. Basically, the population distribution of one type of spin is changed while that of the other is observed. Under these conditions, the magnitude of the resonance signal of the second spin is increased. Thus, if in a solution containing protons and unpaired electrons, the EPR signal is stimulated by light, an increase in the size of the NMR signal, known as an enhancement, is observed. Enhanced NMRsignals may be several hundred times larger than unenhanced signals and may be either positive or negative. In addition, the sign, magnitude and structure of the enhanced signal is extremely sensitive to the chemical composition of the system and the type of reactions occurring. Therein lies its chemical utility. The following historical abstract of work in the field will serve to demonstrate the type of information obtainable by DNV and the interest it has for chemists. In 1953, Overhauser predicted 1 that by stimulating the conducting electrons in a metal, it should be possible to increase the size of the NMR signal. This was verified experimentally a year later by Carver and Slichter4 who showed that appreciable nuclear polarizations could be achieved for lithium, sodium and hydrogen nuclei. Since that time, a variety of enhanced NMR signals has been observed in materials as diverse as chars 5, tars 6, metals 7-9, solutions containing transition metal ions 1°-~2, and solid free radicals t3-t5. Most of these systems have been investigated from a physical point of view with the aim of understanding spin-spin interactions. The first mention of chemical applications for DNV was by Richards and White16, J v. In a series of papers beginning in 1962, they suggested the possibility Advan. Mol. Relaxation Processes, 4 ( 1 9 7 2 ) 2 2 9 - 3 5 4
DYNAMIC
NUCLEAR
231
POLARIZATION
of using DNP tO increase the size of unobservable NMR signals, and to determine mean distances between and association times for species in solution. Simultaneously, other groups, including those of Miiller-Warmuth 18 and Poindexter 6 were using DNP as an experimental means for investigating molecular motions and collision dynamics in liquids. The greatest chemical possibilities for DNP have emerged in the last few years, and these have been in two distinct areas: solutions containing stable free radicals and systems with short-lived radical intermediates. With stable systems, ordinary, or electronically induced DNP, has been used for studying weak molecular complex formation 19' 20, as between two aromatic molecules, as a probe for stereo-specific collisions in liquids 21, as a probe for aromaticity in non-benzenoid compounds 22, and to measure NMR signals which cannot ordinarily be seen with a high resolution NMR spectrometer 23. In this area, DNP has the promise of contributing to the understanding of liquids on a microscopic level. Applications of DNP important to organic chemistry began in 1967 with the discovery of chemically induced dynamic nuclear polarization (CIDNV) by Bargon et al. 24' 25, and by Ward and Lawler 26' 27. Using only a high resolution NMR spectrometer, they observed that certain systems, such as organic peroxides and azo compounds, which are known to decompose via free-radical intermediates (refs. 28, 29), gave rise to transient NMR emission signals, whose magnitude changed as the reaction proceeded. With the same systems, no EPR signal from the radical intermediates could be observed. During the past few years, CIDNP has been used routinely to test for the presence of short-lived radical intermediates in several reactions including: (1) The rearrangement of a benzyne adduct to N,N-dimethyl benzylamine 3° (2) The reaction of gem-dihalocyclopropanes with alkyllithium compounds
(ref. 31). (3) The sigmatropic rearrangement of I to II (ref. 32) N N I
1I
In all these cases, enhanced NMR signals were observed and the presence of radical intermediates was ascertained. For the organic chemist, then, CIONP provides a powerful, routine, experimentally simple test for the presence of radical pair intermediates. Further, it has recently been shown 33 that CIDNP is capable of determining the spin multiplicity (singlet or triplet) of radical intermediates. Thus, the decomposition of an acyclic azo compound known to proceed via the singlet state gave an enhanced NMR spectrum predictably distinct from that of the same reaction product formed via a triplet intermediate in a different reaction. As Advan. Mol. Relaxation Processes, 4 (1972) 2 2 9 - 3 5 4
232
J. POTENZA
more reactions are studied and their spectra interpreted in detail, it is expected that additional insight concerning radical reactions will be gained. The purpose of this review is to introduce organic chemists to the principles and experimental techniques underlying DNP. No previous knowledge of magnetic resonance is assumed except for some familiarity with chemical shifts and coupling constants. For the sake of brevity, some items are not treated rigorously. Wherever possible, the reader is referred to standard textbooks and articles for a more complete treatment. In the theory section to follow, electronically induced DNP, applicable primarily to systems containing stable free radicals, is treated in some detail because of its intrinsic interest and because many of the concepts developed pertain also to CIDNP.
II. T H E O R Y
A. The single resonance experiment 1. Some fundamental properties o f nuclei
Fundamental particles such as electrons and protons have certain intrinsic properties, including charge, mass and spin. However, a spinning charge creates a magnetic field and so these particles also have associated with them a magnetic moment; that is, they behave like tiny magnets whose strength is described by a magnetic moment p, also an intrinsic property. The magnetic moment is a vector quantity proportional to the spin angular momentum of the particle (hi) and is given by
(1)
la = 7hi
where ~, the magnetogyro ratio, is the constant of proportionality. Figure 1 shows
N
p ((1)
(b)
Fig. 1. Relationship between spin angular momentum and magnetic moment for a particle with (a) positive, (b) negative gyromagnetic ratio. Advan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
233
POLARIZATION
the relationship between the spin angular momentum and the magnetic moment for particles with positive and negative magnetogyro ratios. Figure 1(a) depicts a positive rotating charge and corresponds to most nuclei. Figure I (b) shows a net negative circulating charge as found for the electron, neutron and certain nuclei. North and south poles are also shown for the magnetic moments. The magnetic moment is also given by the expression (2)
la = g i l l
Here # is a dimensionless constant called the nuclear # factor for nuclei 34 and the Lande # factor for electrons 3s. For a spinning sphere with its charge and mass uniformly distributed over its surface, the # factor would be unity; hence, the # factor is related to the charge distribution of the particle. For nuclei, fl is called the nuclear magneton (fiN); for electrons, the Bohr magneton. In either case, it is l given in terms of fundamental constants as eh
-
(3)
2mc
where h is Planck's constant divided by 2n, c is the velocity of light and m is the mass of the particle. Combining eqns. (2) and (3), we find that particles with small mass should have large magnetic moments and particles with large mass small moments. This is shown in Table 1, which contains the magnetic properties of TABLE 1 MAGNETIC PROPERTIES OF SELECTED PARTICLES
Particle
Spin I (h)
g
In 'H 2H 7Li 11B 12C
½ ½ 1 ] ~ 0
--3.826 5.585 0.857 2.171
-- 18,326 26,753 4,107 10,398
13C 15N t80 19F 3~p 3SCl Free e -
.~ ½ 0 ½ ½ ] ½
1.405 --0.567
6,728 --2,712
5.257 2.263 0.456 -- 2.002319
y Q (rad/sec.gauss) (10 -24 cm 2)
25,179 10,840 2,184
Resonance freq. at 10,000 gauss (Mc/sec)
0 0 0.00274 0.02 0.0355
29.165 42.577 6.536 16.547 13.660
0 0
10.705 4.315
0 0 -- 0.062 0
40.055 •7.235 4.172 27,994
P l a n c k ' s c o n s t a n t h = 6.6252 × 1 0 - 2 7 erg.sec B o l t z m a n n c o n s t a n t k = 1.38044 × 10-16 erg/deg Bohr m a g n e t o n fl = eh/2mec = 0.92731 × 10 -20 erg/gauss N u c l e a r m a g n e t o n fl = eh/2mpc = 0.50504 × 10 -23 erg/gauss
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
234
j. POTENZA
TABLE 2 V A L U E S O F ,q F O R SOME O R G A N I C R A D I C A L S
Radical
9
Ref.
Vinyl Anthracene cation Coronene cation Allyl Anthracene anion
2.00220 2.00249 2.00249 2.00254 2.00266 2.00437
37 38 38 37 38 38
2.00507
38
2.00512 2.0052
38 39
2.00568
38
1,4-Naphthasemiquinone anion 2,3-Dichloro- 1,4-naphthaserniquinone anion 2-bromo- 1,4-benzoserniquinone anion Tri-t-butyl phenoxyl 2,3,5,6-Tetrachloro- 1,4-benzosemiquinone anion
some fundamental particles and representative nuclei 36. The free electron magnetic moment is some 658 times larger than that of the proton. This factor is not the ratio of the masses because of the different g factors. For electrons, values of g vary from radical to radical depending upon how the spin angular m o m e n t u m interacts with the orbital motion of the electron. This "spin-orbit" coupling causes g to depend upon the chemical environment of the unpaired electron. Typical g values are shown in Table 2 for several organic free radicals. Larger lists may be obtained elsewhere 35' 40. Although deviations from the free-electron value are not large, they have some chemical significance and are important for describing CIDNP. For example, halogen atoms substituted on a radical generally lead to high g values. In general, g values increase as the atomic numbers of the substituents increase. F r o m Table 1, we notice that the magnetic moment of the neutron is not zero. Even though it has no net charge, the neutron does have a charge distribution, hence a magnetic moment. Also, the magnetic moment of the neutron, like that of the electron, is negative, indicating that it behaves magnetically like a negative particle. The magnetic moments of complex nuclei (ZH, 11B, x9F, etc.) are similar in magnitude to those of the neutron and proton because they are composed of these particles. Any nucleus with odd mass number will possess a magnetic moment since not all the nucleons are paired. In addition, some nuclei with even mass numbers will have spin (e.g. ZH) due to unpaired nucleons, while others will have zero magnetic moments. Carbon-12, for example, with all neutrons and protons paired, has no net spin angular momentum. Further, we note that the magnetic moment of the neutron and proton do not quite give that of the deuteron. The magnetic properties of each particle, then, are distinct and characteristic of only that particle. They are determined solely by the 9 value and the spin angular Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
235
POLARIZATION
momentum (equivalently by ~, and I), and cannot be obtained by any simple theory 41. Although we shall not be directly concerned with them, mention should be made here of nuclear quadrupole moments (eQ) (which are also related to the spin of the particle). These are tensor quantities related to the shape of the nucleus (ref. 42). Spherical spinning nuclei have no quadrupole moment, prolate nuclei (shaped like an egg) have a positive quadrupole moment, oblate (doorknob) nuclei a negative quadrupole moment. Hence, if an electron approaches a nucleus with non-vanishing quadrupole moment, the magnitude of the electrical interaction will depend on the direction of approach. Nuclear quadrupole resonance spectroscopy is an area of research in itself~3; however, for our application, quadrupole moments introduce only a complication. We shall not concern ourselves further with them.
2. Spin states in a magnetic field In the absence of other magnetic fields, a single nucleus, such as that shown in Fig. 1, can be oriented in any direction with equal energy. If, however, the nucleus is placed in an external magnetic field H (Fig. 2), there will be preferred
N
/
I t~-" 1
/ 1
Eint
2
Eint
=
-I/dJ
IHI cos 8
,
I
= -I/u [ IH/ c o 5 8'
2
\ Fig. 2. Allowed orientations and energy levels for a particle of spin ~ in a magnetic field. Only one value of 0 and 0' is allowed. orientations. For a classical magnet, all relative orientations are allowed and the energy of interaction between the two magnets is given by E~., = - ~ .
H = - I ~ l IHI cos 0
(4)
where 0 is the angle between the magnetic moments. Thus, the orientation with highest energy corresponds to north poles repelling, the orientation with lowest energy to north and south poles attracting. But nuclear and electron spins are quantized and, for these particles, there will be preferred orientations in the magnetic field. The energy of interaction is again given by eqn. (4), and we must look more closely at eqn. (2). For a given nucleus, g, and ft, are constant, while I, the spin angular momentum, is restricted. In general, only the magnitude of the ddvan. MoL Relaxation Processes,
4 (1972)
229-354
236
J. POTENZA
magnetic moment and one component (say along the external field direction, z) can be measured. The magnitude of the magnetic moment is given by I~1 = y[I(I + 1)]{h
(5)
and its component in the field direction by Pz = I, I - 1 , . .
", - I
(6)
in units of 7h. A particle of spin ½, therefore, has only two allowed energy levels (/~= = + ½7h, -½?h) characterized by the spin quantum number ms = +__½ and the z component may be aligned with or against the field, as shown in Fig. 3 for a proton. The magnetic moment itself will precess about the field direction defined by the laboratory magnet and the z component will remain constant.
\
,__/
(1)
\
,
/
(2)
Fig. 3. Precession o f p r o t o n magnetic m o m e n t in a n external field. T h e z c o m p o n e n t of/~H is c o n s t a n t for a given orientation. Since ~'n is positive, the state characterised by m~ = -}-½ lies lowest.
Since the states are discrete, transitions between them may be observed by shining light (dipole radiation) on the system. If the frequency of the light corresponds to the frequency of precession, light will be absorbed and spins will change their orientation. For nuclei, this is nuclear magnetic resonance (NMR); for electrons, electron paramagnetic resonance (EPR). These techniques are similar except that different instrumentation is required for each since the magnetic moment, the separation between the states and the frequency of radiation required for resonance are much larger for the electron than for any nucleus (Table I). At this point, we note that the resonance frequency is a function of the external field, viz. A E , . t = hv,os = ½ o ~ n - ( - ½ ) g ~ H
= g~H
(7)
for a particle of spin ½. As the external field is increased, the transition frequency increases linearly as shown in Fig. 4. Using the information in Table 1, we may now calculate the resonance frequency of any spin ½ particle at any field. Consider Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
237
POLARIZATION ngz =-~/2
energy~
I
A
E=hu=g~nH
m Z =+I//2
6
.u
Fig. 4. Energy levels for a positive spin ~ particle in a magnetic field.
1H at 10,000 gauss. From eqn. (7), ~'H - -
ON//NIHI h
Inserting appropriate values, we obtain v(10,000 gauss) = 5.585(5.0504 × 10 -24 erg/gauss) × 6.6252 × 10 - 2 7 erg.sec
104
gauss
= 42.575 × 106 c/sec = 42.575 MHz which is the value entered in Table 1.
3. Boltzmann thermal equilibrium population distribution Consider an assemblage of spins in the magnetic field, as, for example, in a 1 ml sample of water which contains some 7 x 1022 protons (Fig. 5). If we assume that the individual protons interact only with the external magnet and not
\
N
/
/\/'I \I\
grin
I n+
Fig. 5. A s s e m b l a g e o f non-interacting spins in a m a g n e t i c field. T h e energy levels s h o w n are highly degenerate.
with each other, there will be only two energy levels for each spin. Because of the large number of spins in the sample, each level will be highly degenerate. We may now ask how many spins are aligned with the field, how many against. Offhand, we might expect all the spins to be in the I+ ) state since that corresponds to lower energy. Indeed, this would be true at zero temperature or for an infinitely Advan. Mol. Relaxation Processes, 4 (1972) 229-354
238
J. POTENZA
strong external field. For other cases, the thermal motions in the liquid will populate the upper level with a consequent increase in spin entropy. When the spins are in thermal equilibrium with their environment, the populations of the individual levels will be governed by a Boltzmann distribution, such that the ratio of spins in the upper state to that in the lower is given by N_ N+
- exp ( - hv/kT)
(8)
where k is Boltzmann's constant and T is the absolute temperature. For protons in a field of 10,000 gauss at 27 °C, N_ _ exp - [(6.625_x 10 -27 ~ c ) ( 4 2 . 5 7 7 × 106_c/sec)7 [_ 1,3805 )< 10-16 erg/OK)(300 OK) j
N+
= exp [ - 6 . 8 1 × 10 -6] ~ 1/(1.00000681) Similar values will be obtained for other nuclei at this temperature. The result shows that at ordinary temperatures, ½ of the spins are aligned with the field, ½ against the field to six significant figures. Nonetheless, it is the difference in the seventh figure that allows NMR signals to be observed. It is not surprising that relatively sensitive apparatus is required to observe NMR signals. A similar calculation for the free electron shows that more spins are in the lower state, as compared with nuclei, because of the large magnetic moment of the electron. Other things being equal, we expect an EPR signal to be much easier to detect than an NMP, signal, if the size of the signal depends only on the relative populations of the spin states. For a spin ½ positive particle, the strength of the NMR signal is proportional to N+ - N _ . The individual populations, N+ and N_, can be calculated from eqn. (8), if the total number of spins, tiT, in a sample is known, since N + + N _ = nT
(9)
For nuclei with spin > ½, the situation is slightly more complicated and the NMR signal is proportional to 44 ~-E mzNm
/tnz
z
(10)
where 1 is the spin of the particle and mz is the quantum number characteristic of the state (for protons rnz = +½). The NMR signal strength also depends on the temperature and it is instructive to examine the ratio (N_/N+) at infinite and zero temperature. As T ~ 0 °K, N_ - - -~ exp [ - h v / 0 ] = 0 N+ Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
239
POLARIZATION
regardless of the strength of the external field which characterizes v. Thus, at 0 °K, all the spins are in the lower state. This is not surprising since at absolute zero there is no thermal energy to reorient the spins. As T ~ aD, N_
exp [ - h v / o o ]
= 1
N+ and exactly ½ of the spins are in each spin state. These results are indicated graphically in Fig. 6. We see that the room temperature population distribution is quite close to the high temperature limit, and that as the temperature changes, so does the expected strength of the NMR or EPR signal. Hence the need for constant temperature in magnetic resonance experiments. I ->
I -->
T---~-O
T -.-=.o o
Fig. 6. Schematic p o p u l a t i o n distribution for p r o t o n s in a magnetic field at zero a n d infinite temperature. T h e r o o m t e m p e r a t u r e distribution is close to the high temperature limit.
4. Saturation
A magnetic resonance signal is generally obtained by shining light (an oscillating electromagnetic field) at the resonance frequency on an assemblage of spins and varying the magnetic field slightly to pass through the value of H which satisfies eqn. (7). An absorption of radiation in and around the calculated resonance frequency is observed. The absorption is not an infinitely narrow line for several reasons 36. These include: (1) Dipole-dipole broadening which occurs primarily in solids and viscous liquids. We have previously assumed that each nucleus feels the effect only of the external field; however, other nuclear magnets are in the vicinity and are in constant motion. A given nucleus will therefore experience a time-dependent fluctuating magnetic field in addition to that from the permanent magnet. The result is a slightly different field for each nucleus and a broadened line. (2) Inhomogeneity of the applied magnetic field, which causes nuclei in different parts of the sample to experience different fields. (3) Spin-lattice relaxation, which will be discussed below. Essentially relaxation reduces the time a given nucleus spends in one state. This contributes to line broadening via the uncertainty principle AE. At ~ h. If At is long, AE will be small and the line will be narrow. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
240
J. POTENZA
(4) Quadrupole effects which afford an additional path for relaxation and affect At. To understand why absorption occurs, we consider the effect of light at the resonance frequency impinging on a collection of spins initially at thermal equilibrium. Three types of transitions are possible: absorption, stimulated emission and spontaneous emission. These are depicted in Fig. 7. In Fig. 7(a), a photon whose frequency corresponds to the energy difference between the I + ) and I - ) nuclear states is absorbed by a spin in the lower state. This raises the spin to the upper state and the photon is annihilated. In Fig. 7(b), an equivalent photon causes a downward transition. Since energy is given off in the process, two photons result, one from the energy loss and one corresponding to the original photon.
a)
~
¢
+ •
hv
•
• •
•
o,m
•
•
_>
•
+>
•
t->
•
•
e
¢
•
•
•
•
->
+>
•
->
I i
I+>
o e
•
c]
~_
•
•
t o o
I+>
~
D
-
I -'~ -
I
-
I
->
¢
+ I+>
°
° ° ' l
I
~
l
w
-
+>
Fig. 7. Schematic representation of (a) absorption and (b) stimulated emission, and (c) spontaneous emission.
With spontaneous emission, a spin in the upper state reverts to the lower state and the energy is emitted as a photon. Spontaneous absorption does not exist. For a given intensity of radiation (number of photons), the number of spins going from the I + ) state to the [ - ) s t a t e (n+_) via absorption is proportional to the number of spins in the lower state multiplied by the probability for the transition
(P+-): n+_
= N+P+_
(11)
Similarly, the probability for stimulated emission is given by n_+
= N_P_+
(12)
For any time-dependent perturbation, U ( t ) , in this case the oscillating magnetic field, applied to this system of discrete energy levels, the transition probability at the resonance frequency is given by 2re Pu = ~- I(ilU(t)lj)l 2
(13)
where (il and IJ ) are the wave functions of the discrete states. The matrix element Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
241
POLARIZATION
(il U ( t ) l j ) m u s t be non-vanishing for transitions to occur. In effect, the perturbation U(t) must mix the states. From the Hermitian property of the matrix element, it can be shown that KiiU(t)lJ>l 2 = [l 2
(14)
whence P i j = eji, or, in our case, P+_ = P_ +. It can also be shown that, for all external fields obtainable in practice, spontaneous emission is negligible .5. Ignoring spontaneous emission, and using the fact that P + _ = P_ ÷, the rate of population change for the [ + > level is given by dN+ _ ( N _ - N + ) P dt
(15)
Recalling that N+ + N _ = rtT, the total number of spins, and defining the population difference N+ - N _ = no, it follows that N+ - (nT+nD) 2
and
N _ - (nT--n°) 2
(16)
Now, since dN+/dt = ldno/dt, we may rewrite eqn. (15) and solve for no, which governs the size of the resonance signal. Thus, dnD
--2nDP
(17)
no = riD(0) exp [ - 2 P t ]
(18)
-
dt
-
whence
Here, no(O) is the population difference at zero time (the thermal equilibrium value calculated above). Equation (18) predicts that, at zero time, the NMR signal reflects the thermal equilibrium population difference between the states, but that as time goes on, the difference is reduced to zero and the resonance signal disappears; viz. as t ~ oo no ~ no(O) exp [ - 2 P o o l
= 0
This is known as saturation, and if complete, the number of spins in the lower state equals that in the upper state, the same effect that would be obtained at infinite temperature. One usually tries to avoid saturation when obtaining quantitative spectra, since if even partial saturation occurs, the resonance signal will not reflect the true thermal equilibrium population distribution. Saturation is usually avoided by keeping the density of radiation small. For DNP, we shall use intense radiation and purposely try to saturate electron spin levels. 5. Relaxation transitions Suppose that, having saturated the resonance signal of a sample via RFAdvan. Mol. Relaxation Processes, 4 (1972) 229-354
242
J. POTENZA
induced transitions, we removed the source of light. Ignoring spontaneous emission, we have no mechanism by which spins in the upper state can return to the lower state. This is unacceptable, since, when saturated, the spin system is not in thermal equilibrium with its surroundings. In addition, we could follow experimentally the return to equilibrium by watching the NMR signal grow to its original value. The spin system returns to thermal equilibrium via relaxation transitions 46. These are radiationless transitions by which the fluid, acting as a thermal bath, absorbs the energy released by the spin transitions (Fig. 8). For relaxation transi-
I I
energy
+
llh i •
•
•
•
molecular motion
absorbed
•
+
I+>
•
•
•
*
by fluid
•-I+>
Fig. 8. Schematic representation of a downward relaxation transition. tions to occur, there must be molecular motions in the liquid at the resonance frequency and the spin system must be coupled to other degrees of freedom. It is this process of relaxation that originally produces the excess of spins in the lower state, and so the downward transition probability for relaxation (w_ +)nmst be greater than the upward transition probability (w+_). We may now write an equation for the rate of population change of the lower spin state as dN+ _ dt
N+ w+_ + N _ w_+
(19)
At equilibrium, dN+/dt = 0 and we find that N_(eq)
-
N+(eq)
w+ _
- exp [ - h v / k T ]
(20)
w_+
The relaxation transition probabilities are in the ratio of the equilibrium populations of the states. Again using eqn. (16), the rate equation describing the change in the population difference due to relaxation transitions can be written as dnD _ nT(W- + -- W+_)-- nO(W- + + W+_) dt
(21)
This can be rewritten as
dnD dt
-
no--riD 7"1
(22)
where W_+ --W+_) /'/0 ~
nT
(w_++w+_)
and
--1 = ( w + _ + w _ + )
TI
Advan. Mol. Relaxation Processes, 4 ( 1 9 7 2 ) 2 2 9 - 3 5 4
DYNAMIC
NUCLEAR
243
POLARIZATION
The solution to eqn. (22) is nD = no + C exp [ - t/T1]
(23)
Now, it is easily seen that n o is the equilibrium population distribution (let t ~ Qo) and that T~, which has units of time*, is characteristic of the approach to equilibrium. It may be regarded as the half-life of the nucleus in the upper spin state. Notice that T 1 is the reciprocal of the total relaxation rate. This will be true in general. For our completely saturated spin system at t = 0, the system is unpolarized; that is, half of the spins are in each level and no = N+ - N _ = 0. In this case, no = no(1 --exp [--t/Tl])
(24)
from which we see that the population difference should increase exponentially to its equilibrium value. By measuring the size of the NMR signal as a function of time after turning off the stimulating radiation, we may measure 7'1, the spin-lattice relaxation time. TABLE 3 PROTON SPIN--LATTICE RELAXATIONTIMES
Compound
T1
Re].
(sec) 11 ~ benzene in CS~ Benzene T o l u e n e (ring) T o l u e n e (CH3) H20 Ethanol H2SO4 Glycerine
60 l 9.3 16 9 3.6 2.2 0.7 0.023
47 47 47 47 48 46 46 46
Spin-lattice relaxation times for several protons in different compounds are shown in Table 3. In general, values for organic compounds are in the range milliseconds to seconds. They decrease with increasing viscosity (compare ethanol, H2SO4, glycerine), and this has been interpreted theoretically. Further, values of T1 depend upon the magnetic field at which the measurement is made, generally increasing with increasing field. This increase results from the field dependence of the relaxation transition probabilities which will be discussed below. Other factors, including temperature, soNent and paramagnetic impurities, also strongly affect the magnitude of T1. The addition of paramagnetic impurities, including O2 * T h a t Tt h a s units o f time is seen f r o m its definition as the reciprocal o f a relaxation rate. If w is given by transitions/sec then the units o f T~ are seconds.
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
244
J. POTENZA
from the air, reduces/'i markedly. Values of 7"1 of the order of 10 -4 sec are not unusual when paramagnetic impurities are present. The measurement and interpretation of T1 in terms of molecular motions in liquids is itself an area of research (ref. 49). We can now obtain a more complete description of the spin system by considering simultaneously the effects of radiation and relaxation. From eqns. (17) and (22), we obtain the rate equation drip _ _ 2 n o p + (no - riD) dt T~
(25)
In a steady state, dno_ dt
0
and
nb
_
no
(26)
1 + 2PT~
Thus, if 2PT1 << I, nD is the equilibrium value, and the NMR signal will reflect this distribution. Alternatively, if P, which is proportional to the square of the resonance radiation amplitude, becomes large, no < no and saturation occurs. For samples with large values of T1, indicating inefficient thermal relaxation, saturation is easier to obtain for a given intensity of radiation than for samples with small 7'i. Overall, since the availability of molecular motions required to induce relaxation transitions varies as the chemical composition of the system changes, we expect T~ and the ease of saturation to be a function of the system chosen. B. The double resonance experiment
We consider the simplest case of a nucleus of spin ½ and an electron of spin ½, each on different molecules, placed in an external magnetic field. In practice, this may consist of a solution of a stable free radical in a proton-containing solvent. When the spins are far apart, each will feel only the influence of the external field. In this case, the spins are uncoupled, and it is possible to observe separately an EPR transition and an NMR transition (Fig. 9(a)). The spin Hamiltonian for this 3
1
I*>
N i ** >
1
2
3
\
4 -4-I->/
(a)
S
~.
q
4
i -.>
(b)
Fig. 9. Energy level d i a g r a m s h o w i n g possible transitions for a system o f two (a) u n c o u p l e d a n d (b) coupled spins. T h e large arrows correspond to electrons, the small arrows to nuclei.
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
POLARIZATION
245
uncoupled system is given by (27)
oY" = - hYl Ho I ~ - hVs Ho Sz
where I~ refers to the nuclear spin quantum number and S~ to the electron spin quantum number. The four energy levels in Fig. 9 are obtained using eqn. (27) and the appropriate values for S, and I~ (+½). The - ½ state lies lowest for the electron since it is a negatively charged particle. The conditions for which this energy level diagram applies have been discussed by Abragam 5o. Owing to Brownian motion, the spins will diffuse into proximity of each other and therefore the nucleus will be affected by the electron and vice versa. The spins are said to be coupled and the possible states are shown schematically in a simplified way in Fig. 9(b). State 1, with both electron and nucleus aligned against the field, is obviously highest in energy, followed by states 2, 3 and 4. Transitions 1-3 and 2-4 labeled p in Fig. 9(b) correspond to the EPR transition since only the electron spin changes. Similarly, q refers to the NMR signal, while r and s are double spin transitions. The symbols p, q, r and s are transition probabilities. Hence, transitions between states 1 and 2 in Fig. 9(b) occur with probability q, etc. The size of the ~MR signal will be proportional to (N2 + N 4 ) - ( N l + N 3 ) . If now we saturate the EPR signal with light of appropriate frequency and intensity, we may enquire as to its effect on the NMR signal, which we shall observe. For complete saturation, N1 = N 3 and N2 = N4, and the question arises as to whether N~ > N2 ; that is, are the spin states on the left-hand side of Fig. 9(b) more highly populated than those on the right or is the reverse true? This will depend on the magnitude of the relaxation transition probabilities q, r and s. Ignoring q for the moment, we may examine the limiting cases qualitatively. If r >> s, we may ignore s, obtaining the spin energy level diagram shown in Fig. 10. Some of the spins entering state 1 will return to 3 via stimulated emission and relaxation, while some will go to state 4 via relaxation transitions. The net effect of this is to populate states 2 and 4 at the expense of 1 and 3. Thus, with r >> s, 1 2
I-->
-
I-÷>
-
-
-
4
I-*>
Fig. 10. Spin energy level d i a g r a m for a two-spin system a s s u m i n g r ~, s.
Advan. MoL Relaxation Processes, 4 (1972) 229-354
246
J.
POTENZA
N~ << N2 and N 3 << iV,. The observed NMR signal will now be larger than the equilibrium value, resulting in a positive enhancement. Alternatively, if s >> r, N1 >> N2 and emission will occur across the q gap, corresponding to a negative enhancement of the NMR signal. Examples of positive and negative enhancements are shown in Fig. 11.
/40:745
Galvinoxyl
Enhonced signal
--~,.
BDPA +
C6F6
CeF6
Enhanced signal
Fig. 11. Examples of negative and positive 19F enhancements obtained at 74 gauss using C6Fe with the stable free radicals galvinoxyl and bisdiphenylene phenyl allyl.
Following Solomon 51, we may now determine a quantitative expression for the enhancement factor by considering the rate of population change for the individual energy states. From Fig. 9(b), it follows that dN+ _
constant
-
pN_ _ + rN_ + + qN+ + - (p + q + r)N+ _ +
-
pN_+
-
pN + _ + sN + + + qN _ + - (p + q + s)N_ _ +
constant
pN+ + + rN+ _ + qN_ _ - (p + q + r)N_ + +
constant
dt
dN++
+sN__
+qN+_
-(p+q+s)N++
+constant
dt dN__ dt
dN_+ -
(28)
dt
The constants may be obtained by considering the system at thermal equilibrium where dN+ _/dt = 0, etc., and inserting the appropriate values for the populations. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
247
POLARIZATION
Experimentally, we can observe the net z component of the nuclear magnetic moment (i~, proportional to the NMR signal strength) or the net z component of the electron moment (Sz, proportional to the EPR signal strength). These are given by (N+ + + N_ + ) - ( n + _ + N _ _ ) = kt z
(29)
(N_+ + N _ _ ) - ( N + _ + N + + ) = kS z
(30)
We can now calculate the rate of change of both nuclear magnetization (dlz/dt) and electron magnetization (dSJdt) by combining eqns. (28)-(30). Thus d(N + + + N _ + N + _ dt -
-
N
_ _) = k di_~ = k[ dt
-
(2q + r + s)t z - (r
-
s)$z + C] (31)
At thermal equilibrium, diz/dt = 0 and we evaluate the constant as C = (2q + r + s)l o + ( r - s)So
(32)
where I o and So are given by eqns. (29) and (30) respectively. Inserting the constant and rearranging, we obtain dlTz _
dt
(2q + r + s)(i z - I o ) - ( r - s ) ( S . - So)
(33)
If the EPR signal is saturated completely, the electron magnetization ~ is reduced to zero, and, in a steady state, the nuclear magnetization is constant, i.e. diJdt = O. Under these conditions, eqn. (33) reduces to 0 = - (2q + r + s)(l~ - Io) + ( r - s)So
(34)
Solving for Tz, we have
t2 = io+
(r-s)So (2q+r +s)
(35)
The enhancement factor G corresponds to the increase in nuclear magnetization over the thermal equilibrium value and is given by
G - 1~-I° (r-s)So Io (2q + r + s)Io
(36)
That G indeed represents the enhancement can be seen most readily by considering the system initially. Then, i z = I 0 and G = 0. Overall, eqn. (36) comprises two factors. The first, [(r-s)/(2q+r+s)] is essentially the ratio of polarizing relaxation transitions to the sum of all possible relaxation transition probabilities. The second factor, So/Io, is the equilibrium ratio of electron to nuclear polarization, which is equal to ~s/~i, the ratio of the magnetogyric ratios of the two spins. Later, by considering the possible magnitudes of the various relaxation transitions, we shall Advan. Mol. Relaxation Processes, 4 (1972) 2 2 9 - 3 5 4
248
J. POTENZA
show that for electronically induced DNP, if ~,~ > 0, the maximum positive signal enhancement is given by I~s/~tl, the maximum negative enhancement by -½1~s/hl. Table 4 lists values of these ratios for several spin systems. We see that maximum enhancements of the order of 0-3 should be obtained for systems of coupled nuclei, while for an electron coupled with a nucleus, enhancements of several hundred to several thousand are expected, depending upon the nucleus in question. TABLE 4 SCALAR AND DIPOLAR LIMITS FOR SELECTED SPIN SYSTEMS
System
Saturate
Maximum negative enhancement a (½es/7l)
laC/1H 19F/1H 19F/1H alP/1H alp# H ~H/exaC/e19F/e3tP / e -
1H 1H 19F IH aap Free Free Free Free
+1.99 +0.53 -~0.47 +1.23 +0.203 -- 329 -- 1305 --350 -- 813
eeee-
Maximum positive enhancement
+658 +2610 + 700 + 1625
" Nuclear enhancements are positive because the sign o f 7 is the same for both nuclei.
The exact limits of the enhancement for this intermolecular case will depend on the magnitude of the relaxation transition probabilities q, r and s in accord with eqn. (36). These in turn will depend on the type of coupling between the spins. Two types, dipolar and scalar, are possible. Dipolar coupling is classical in nature, and is approximately the same as the interaction between two bar magnets (Fig. 12) If the magnets are in relative motion, an oscillating magnetic field due to one magnet will be established at the second. The electron and nucleus may be con-
Fig. 12. Dipolar interaction between two bar magnets. I f the magnets oscillate, so will their energy of interaction.
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR
POLARIZATION
249
sidered similarly, except that now if the molecular motion between magnets is at the resonance frequency, relaxation transitions will be induced. Mathematically, the dipole-dipole interaction is given by the following term in the Hamiltonian.
J f a'
= [_ F#'r~Is"l~s 3 (l~," r,s)(~s"
(37)
where/u, and/~s are the magnetic moments of the nucleus and electron respectively and rts is the distance between them. In practice, ~ should be summed over all magnetic particles in the system. By writing Jd~, in component form 52 and by expressing Pt and Ps in terms of raising and lowering operators ss, it is possible to show that transitions p, q, r and s are allowed. We shall return to dipolar transitions later, after examining scalar coupling. Scalar coupling is quantum mechanical in origin, and for a system in rapid motion, is governed by a term in the Hamiltonian, viz.
~t°; = A i s I " S
(38)
1" S in eqn. (38) represents the overlap between the electron and nucleus, while A~s, the hyperfine coupling constant, is related to the probability of finding an unpaired electron at the nucleus in question. In fact, A~s is given by 34 4zr A's = --3 gs fls g, fit p(O)
(39)
where p(0) is the square of the electron wave function (the electron density) evaluated at the nucleus. For Ats to be non-vanishing, there must be some unpaired s-electron density at the nucleus, since the probability of finding p, d, and higher electrons there is identically zero. In practice, many orbitals may become slightly unpaired during a molecular collision and it is more proper to think of p(0) as the net unpaired spin density at the nucleus. Again, as the molecules move with respect to each other at the resonance frequency, the spin density, hence the electric field, at the nucleus fluctuates periodically with time, inducing relaxation transitions. We shall now show that scalar coupling can only induce transitions of the type } + - ) ~ - I - + ) ; that is, transitions parallel t o t in Fig. 9(b). In general the transition probability, w, between any two states, is given to first order by 5t w=t~ 1
fl
< m j l ~ ( t, ) l,m , > e -ita.fl ' dt t 2
(40)
where ~ ' ( t ) is the perturbing Hamiltonian, mi and mj are two eigenstates (say I + - > and 1+ +>), and ~oij is the angular resonance frequency between the states
colj = 27~v,j = ( E i - Ej)/h
(41) Advan. Mol. Relaxation Processes, 4 (1972) 229-354
250
s. POTENZA
To show that the probability is non-zero, we need only show that the matrix element ( m j l ~ ' l m ~ > does not vanish for the perturbing Hamiltonian A ( t ) l • S. To do this, we express I • S in terms of components, viz. (42)
I. S = I~Sx+IySy+lzSz
and make use of the raising and lowering operators I+ and I_ defined by 52 I+ = I ~ + i I ,
S+ = S ~ + i S y
I_ = I~-iIy
S_ = Sx-iSy
(43)
By Solving eqn. (43) for I~, Iy, S~ and Sy we obtain Ix = ½[I+ + I - ]
Sx = ½ [ S + + S _ ]
(44)
1 [i+_i_]
S,
1 [S+-S_]
The raising operator has the property of connecting an eigenstate characterized by mz, the z component of the spin, to one characterized by mz + ~. In particular, I+ Irnz> = (1(1 + 1 ) - m~(m~ + 1))~lm~ + 1 >
(45)
I-ling> = ( I U + 1 ) - mz(m=- 1))~lmz - 1> For the spin ½ system being considered, I = ½ and m~ = _+½. Therefore, we have
I÷l+ -)
= (½(~)-(-½(½)))~1+ +> = I+ +>
and 1+ I + + > = 0, since the + ½ state cannot be raised further. Similarly for the electron, S + I - + ) = (½(9-(½(-½)))~1+ + ) = l+ + )
etc.
We can now express I • S in terms of the raising and lowering operators: I • S = IxS~+IySy+I~S z
= ¼[I+ + I _ ] [ S + + S _ ] - ¼ [ I + - I _ ] [ S + - S _ ] +I~S~
(46)
= ½(s_I++s+I_)+szt~ Recalling that I~1+ - >
= -½J+->
LI++>
= +½1++>
S,I+-)
=½1+-)
etc.
we can evaluate all terms in (rn~lS • l l m j ) . As an example, to determine whether scalar coupling can induce transitions l+ + ) r a I - - ) , we must evaluate .4doan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
251
POLARIZATION
( + + IS" I I - - ) . Using eqn. (46) this is shown to be ( + + 1[½(S- I+ + S + I - ) + Szlz]l- - ) = ½(+ + i S _ I + I - - ) + ½ ( + + I S + I _ I - - ) + ( +
+lS=I~l--)
=0 The first term is zero because S - I - - ) = 0. The second term vanishes similarly, while for the third we obtain ¼ ( + + 1 - - ) which is zero because of the orthogonality of the spin wave-functions. Similarly, all transitions except I + - ) ~ I - + ) are forbidden via contact relaxation. Inclusion of scalar coupling leads to the following expression for the enhancement. G = 7s
(r + c-- s)
(47)
Yt (2q+r+s+c) Here, r refers to the dipolar transition probability between the I + - ) and I - + ) states, while c refers to the scalar transition probability between the same states. Equation (47) is equivalent to eqn. (36) except that the [ + - ) ~ - i - + ) transition probability has been divided into scalar and dipolar components. We can easily determine a maximum value for the enhancement by assuming that c, the scalar relaxation component, is much larger than any dipolar component q, r or s. In the limit as c ~ ~ , G becomes G -~ ~_s c-~o
(48)
7I
Hence, the maximum possible positive enhancement may be read from Table 4. The limit for pure dipolar coupling (c ~ 0) is more difficult to treat, for here we need to know relative values for q, r and s. For a pure dipole-dipole interaction, these have been determined by Solomon 51 as ze
1
1 +ohz¢ r
2 % 8h " ( F - )
s
1
(49)
1 + ( c o , - co
2z~ 2 1 --h2 ( } F z l ) 1 + (t~t + COs)2.r~2
where CO~ = 27tv~is the resonance frequency of the nucleus, COsthat for the electron. (F02), (IFll 2) and (IF2[ 2) are average (expectation) values for various parts of the dipole-dipole perturbing Hamiltonian and will not concern us further. %, the correlation time, is an important parameter in magnetic resonance. Unfortunately, it is difficult to give it a precise physical definition. It may be regarded Advan. Mol. Relaxation Processes, 4 (1972) 229-354
252
J. POTENZA
as that length of time shorter than which the motion of the two spins is negligible. For dipolar coupling, % is generally found s< s5 to be approximately 10 - ~ sec. Several points are worth noting regarding eqn. (49). First, as the external magnetic field is increased, both COs and cot increase (Fig. 4), such that q, r and s tend to zero at high fields. This is plausible physically, since at high fields molecular motions of extremely high frequency are necessary to induce transitions and these become less available. In addition, since the electron resonance frequency is much larger than any nuclear frequency, r and s will decrease more rapidly with increasing applied field than will q. As Ho ~ m, all the relaxation transition probabilities approach 0, but since r and s decay faster than q, the enhancement approaches zero. Maximum values of q, r and s are obtained near zero field where cotr 2 ~2 << 1 and Wsr~2 2 <~ 1. In this region, which is generally called extreme motional narrowing, eqn. (49) reduces to sl 222 3h ~,YsZc q 2066 222
,-
-
h ~,7s% 10b 6
S --
(50)
5b 6
where b is the distance between spins. While it is not possible to calculate q, r and s directly without knowledge of % and b, relative values o f q, r and s can be obtained directly from eqn. (50). Thus, in the zero-field limit, q: r : s = 3: 2 : 1 2
(51)
Using this result, we can determine the maximum value for the enhancement assuming pure dipolar coupling. F r o m eqn. (47), with c = 0 Gdipolar
__
TS (2-- 12) -~t ( 6 + 2 + 1 2 )
1 YS 2 7t
The negative sign corresponds to an emission signal, while the magnitude is half as large as that expected for pure scalar coupling. Maximum possible zero-field dipolar enhancements are shown in Table 4. As the external field increases, q, r and s decrease as indicated above. For small applied fields ( < 100 gauss), it is possible to obtain relative values for q, r and s from dipolar enhancement curves aS, assuming that the spin-spin interaction is modulated by diffusion and that no scalar coupling is present. For hydrogen nuclei at 74 gauss, the values 3.0, 1.6 and 9.6 have been used 56 for q, r and s. Using these values in conjunction with eqn. (47) and a measured enhancement G, it is possible to calculate the scalar rate c relative to the total dipolar relaxation rate ( 2 q + r + s ) . At higher fields, relative Adman. )Viol. Relaxation Processes, 4 ( 1 9 7 2 ) 2 2 9 - 3 5 4
DYNAMIC NUCLEAR POLARIZATION
253
values for q, r and s have not yet been obtained. Nonetheless, by measuring the sign of the enhancement at high field, it is possible to determine whether dipolar or scalar coupling predominates. The exact form of the scalar transition probability will depend upon the model chosen for the spin-spin interaction. For intermolecular radical-solvent encounters, two models have been used: sticking and diffusion 57. The sticking model assumes that c = 0 except when a free radical and solvent molecule are stuck together. The sticking time, zs, is a random variable described by a correlation function. This model leads to a scalar transition probability, viz. c(~o) -
A2~s
(52)
1 ~- O~2T2
where z~ is the scalar correlation time and A is the hyperfine coupling constant. At zero field, eqn. (52) reduces to
c(0) = a2~s The diffusion model leads to a more complicated expression for c which reduces to c(0) - ns ~A2zs d 222
(53)
at zero field. Here, ns is the number of spins/ml and 2 is a parameter related to the intermolecular pGtential function by
Ad Aii(t ) = - - - exp [ - A(rij d)] -
-
(54)
/'U
where r,3 is the instantaneous distance between the electron and nuclear spins and d is the distance of closest approach. A~j is a function of time because as the molecules containing the electron and nuclear spins move with respect to each other, the overlap between them changes. Both theories give c(0) proportional to AZz~. By studying the field dependence of scalar coupling relative to dipolar coupling, it should be possible to deduce values for A, the intermolecular hyperfine coupling constant, and %, the sticking time for the scalar interaction. The former may be related to the degree to which an odd electron delocalizes over solvent nuclei during a molecular collision. Hence, it is a useful parameter for examining weak complex formation. z~ is also useful for this purpose, in that it gives the time during which the spins, hence presumably the molecules, are associated. Additional DNP theory will be presented before experimental results are offered. Here, we merely note that: (1) Because of cross-relaxation transitions involving two spins, enhanced NMR spectra may be observed if one spin system is saturated electronically. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
254
J. POTENZA
(2) The enhancement may be positive or negative depending upon whether scalar or dipolar coupling dominates the interaction. (3) The enhancement is expected to decrease with increasing magnetic field in a manner consistent with the frequency spectrum of molecular motions. (4) By studying enhancement spectra, information concerning the time of contact between spins (Q and the amount of unpaired electron density at the nucleus observed (A) may be obtained.
C. SYSTEMS WITH SHORT-LIVED INTERMEDIATES - CIDNP
1. Basic observations - chemical pumping
The first mention of CIDNP occurred in 1967. In pioneering experiments by Bargon and Fischer 2~' 25 and independently by Ward and Lawler 26' 27, the appearance of emission signals in the NMR of products obtained from rapid radical reactions was reported. A typical example is the thermal decomposition of benzoyl peroxide in cyclohexanone, which is well known zS' z9 to proceed via radical intermediates. O
O
II
I[
c00¢
O A
[I
2 c0.
-CO~
2 "H
>2¢r
(55)
If the NMR signal of the product benzene is observed as a function of time, the single NMR signal starts out as emission, becomes larger, then smaller and finally passes through zero to become an absorption signal as the reaction proceeds. Figure 13 shows the results obtained for the above reaction at three proton resonance frequencies 25. ~6._4-M-"-z~--u-*k 7"-v-"-'"
Fig. 13. Amplitude o f 1H benzene NMR signal during the thermal decomposition o f benzoyl peroxide at 40, 56.4 and 100 MHz. Reprinted with permission from ref. 25. Advan. Mol. Relaxation Processes, 4 (•972) 229-354
DYNAMIC NUCLEAR POLARIZATION
255
The nuclear polarization observed has been attributed to DNP as follows. Because of the conservation of spin, exactly half of the radicals formed in eqn. (55) by breaking the peroxide bond must initially have spin up, while the other half have spin down. This is exactly the situation obtained by saturating transition p artificially in Fig. 10. Since the reaction is performed in a magnetic field, when the radicals are formed, the electron spin populations are not their equilibrium values, The electrons will relax to their equilibrium distribution given by the Boltzmann Law. This will occur in a time T~e characteristic of electron relaxation (usually about 10-5-10 -6 sec for organic radicals). But the nuclei on the radical, in this case the protons of the phenyl radical, may be coupled to the electron and scalar and/or dipolar relaxation transitions, similar to those considered above, may be induced, causing DNP. From this point of view, ClDNP arises a s a r e s u l t of double spin relaxation transitions analogous to those occurring with stable systems, while the driving force for the polarization is the tendency for the electrons to reach a thermal equilibrium population distribution in the applied field. Later, we shall see that this mechanism cannot totally account for all observations without severe restrictions. Nonetheless, it may apply to some systems and it is instructive, following Bargon and Fischer 25, to develop a quantitative interpretation based on this mechanism. Consider a reactant R which decomposes to give two radical intermediates I . , which in turn react in an abstraction reaction to form a product P whose NMR spectrum is monitored. Rff-~ 2 II .+M%
(56) P+M.
For simplicity, we assume that only a single proton is coupled to the unpaired electron of the radical intermediate. The [I.] will depend upon the rate of decomposition of R (rf) and the rate of production of P (rp). With these assumptions, the energy level diagram for the reacting system is that shown in Fig. 14. The energy levels for the radical intermediate are labeled according to the spin quantum r,-
~
I+-> '~ ,
S
r--
I~-÷
r'~-
S"
,.
-
o >>
L,
"-3- t-,> reQctont
free rodicOl
intermediQte
product
r'-*
Fig. 14. Spin energy level diagram for a radical intermediate and product molecule assuming a single electron coup|ed to a sJng|c nuc|¢us. Advan. Mol. Relaxation Processes,
4 (1972) 229-354
256
J. POTENZA
number of the electron and that of the nucleus. In the diamagnetic product, only nuclear spin states are relevant. The individual levels of the coupled spin system are populated at rates r + _ , etc., and depopulated at r ~ _ , etc. We have also added a term parallel to p to account for electron relaxation transitions other than those caused by the electron-nucleus coupling. In principle, it is possible to observe the NMR signal of the radical, the EPR signal of the radical and the ~MR signal of the product. These are proportional to ANs = (N~ + N , ) - ( N , + N~) a N , = (N~ + N , ) - (N~ + N,) ANp
(57)
= N+--N_
respectively. We are primarily interested in the size of the product NMR signal ANp. As with the simple two-spin case treated above, we may write equations for the rate of change of the populations N+ and N _ . This is best done using the relaxation transition probabilities shown in Fig. 15. Downward transition probabilities are indicated by p, q, r, s, while the upward ones are smaller by a Boltzmann factor, in accord 34 with eqn. (20). r:
-,.l÷->-- -
r2
~.
~
~-~V'/kr
~
\ "\,\
2 I÷÷~.
22TI
- - I - >
p e -hlls//kT
-
-
4
-
-
I-*>
Int er rnediate
Product
Fig. 15. Spin energy level diagram and relaxation transition probabilities for a radical intermediate and product molecule. The upward transition probabilities are shown smaller than the downward ones by a Boltzmann factor. For the rate of change of N+ and N _ , we have dN+ dt dN_
-
r'z+r'4+qpN_-qpN+ entering + state
exp
[-hv,/kT]
leaving + state
- r'x + r ~ + q P N + e x p [ - h v f f k T ] - q P N _
dt Advan. Mol. Relaxation Processes,
4 (1972) 229-354
(58)
DYNAMIC
NUCLEAR
257
POLARIZATION
Similar equations may be developed for the rate of change of N 1 to N4. These may be combined to give expressions for dANp/dt, dANs/dt and dANg/dt which are similar to eqn. (31). In a steady state, these differentials equal zero and the three equations can be solved to give an expression for the observed enhancement G. ( 1 + p'ZL) +
G
_
ANp-AN°AN ° - NRNP TIP i - (I q - p ~ - a 2 z
aZL ~S TI
2]
(59)
Here, Tip is the spin-lattice relaxation time of the nucleus in the product, Np is the total number of protons, NR is the total number of radicals present, while p', p and a are combinations of relaxation transition probabilities.
p = 2q+r+s p' = 2p+r+s+ws
(60)
O" ~ s - - r
The magnitude of the enhancement can be measured only with difficulty in CIDNP experiments, mainly because of problems associated with estimating the zero NMR signal strength (because a chemical reaction is occurring, the number of product molecules and the NMR signal associated with them changes with time). By adding paramagnetic impurities to the reaction system (Fig. 13), it is possible to reduce TI of the product and observe only absorption of radiation at the NMR frequency. The area under the absorption curve at a time corresponding to that for maximum enhancement may then be used as a measure of the zero signal. In this manner, observed enhancements may be obtained. These may then be compared with values calculated using eqn. (59). To calculate a magnitude for the enhancement from eqn. (59), several quantities, including T~, r, z L, p, etc. are necessary. None of these is easy to come by experimentally. Estimates for p, q, r and s can be obtained from equations similar to (49). Values for the remaining parameters can be obtained from the CIDNP experiments or from independent studies of similar systems. We shall return to this point later when experimental results are discussed. At present, we simply state that eqn. (59) assumes that CIDNP enhancements arise as a result of relaxation transitions within a coupled spin system analogous with the ordinary Overhauser effect. The theory predicts smaller enhancements with increasing field because of the frequency dependence of the relaxation transitions (Fig. 13). The Fischer mechanism assumes the existence of free radicals and well defined stationary states. It has recently been criticized 5a and replaced by theories which explicitly involve radical pairs for the production of CIDNF spectra. As of now, there exist grave doubts that this mechanism applies to any CIDNP system. We consider now the alternative proposals. Advan. Mol. Relaxation Processes, 4 (1972) 2 2 9 - 3 5 4
258
J. P O T E N Z A
2. The multiplet effect
From the first experiments involving CIDNP 26'59, it was apparent that additional processes other than those described above were required for a complete analysis. The most apparent discrepancy between theory and experiment was the interpretation of the multiplet effect. We assume that the reader is familiar with multiplet structure in NMR spectra and proceed to describe the effect by means of an example. As shown by G. L. Closs and co-workers 33' 60, the reaction product 1,1,2triphenylethane can be formed by photodecomposition of either the azo compound (~b)ECHN=N-CH2~b or diphenyldiazomethane. For the azo compound, the following reaction is relevant. ~b2CHN=NCH2t~ byor a•
Vradical pair 1 I_intermediate_]
• q~2CH-CH2~b
(61)
In the case of t~2CN2, we have ~b2CN2+~CH3 --, [~b2CH • • CH2~b] ~ ~2CHCH2~b
(62)
The NMR spectra of th2CHCH2~b obtained during the reactions (61) and (62) are shown in Fig. 16. In the absence of CIDNP, we expect to find the normal N ~ absorption spectrum. What is observed is positive and negative enhancements
(o)
5,6 ] I 13
IIc.3
Fig. 16. aH NMR spectra of 1,1,2-triphenylethane obtained during (a) thermolysis of ~2CHN=NCH2~ and (b) photolysis of diphenyldiazomethane in toluene. The downfield multiplets strikingly display positive and negative enhancement. Reprinted with permission from ref. 33. within a given multiplet. Further, the sum of the enhancements within a given multiplet is near zero, indicating that the net z component of the magnetization is not far removed from its equilibrium value. Sometimes, as in the case of the multiplet on the lower right in Fig. 16, a net polarization is superimposed. Last, we note that in some cases the high-field portion of the spectrum is positively Adcan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
259
POLARIZATION
enhanced, while for other cases the reverse is true. In particular, the product from eqn. (61) shows the former behavior, in contrast to that from eqn. (62). Several attempts have been made to interpret this phenomenon. The first is based on the analysis given above and involves special assumptions concerning the populations of the free radical states 6x. For example, with a radical intermediate containing two non-equivalent protons, the energy level diagram shown in Fig. 17 would apply. The diagram consists of the four possible nuclear spin states, split by a single electron. For simplicity, we assume that these states are 4
'5
Intermediate
Product
Fig. 17. Spin energy level diagram for a reacting doublet radical coupled to two non-equivalent protons. F o r clarity, the allowed relaxation transitions are n o t labeled.
2_1`4_3
3_1`4-2 ~/o ~
I 2-1
I ,4-3
3-1
Ho Ca)
`4-2
,,
(b)
Fig. 18. Idealized A B doublets arising f r o m the product in Fig. 17. (a) T h e n o r m a l NMR spectrum, (b) a possible CIDNP spectrum.
retained in the product and give rise to the two AB doublets shown schematically in Fig. 18(a). An observed ClONe multiplet might appear as that in Fig. 18(b), where the low-field lines are negatively enhanced and the high-field lines positively enhanced. The observation of emission of radiation for the 2 ~ 1 transition corresponds to state 2 more highly populated than state 1 in the product. Enhanced absorption for the 4 ~ 3 transition indicates that N3 > N4. Thus, this pattern is consistent with abnormally high populations in nuclear spin states with I z close to zero. If the pattern were reversed, abnormally high populations would be inferred for nuclear levels with I z furthest from zero. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
260
J. POTENZA
The situation depicted in Fig. 18(b) could be obtained if the rates of population of the individual spin states in the radical intermediate rij were different. Fischer and Bargon found no compelling reason to assume such restrictions. On the other hand, they noted that certain restrictions on the rate of population of the radical states would lead to transient emission signals in the ~PR which should be observed immediately after the radicals are formed and before they reach a thermal equilibrium population distribution. Such transient emission signals have been observed for short-lived radical intermediates produced by pulse radiolysis techniques 37, 62. Recently, the idea of different population rates was given foundation by Kaptein and Oosterhoff 6 a, 64. By considering singlet and triplet states within a radical pair, they showed how differences in population rates could arise and how these could lead to transient EPR spectra as well as multiplet effects in the NMR. An alternative explanation for the multiplet effects involving the formation of radical pairs coupled with singlet-triplet crossover was given by G. L. Closs 65. Before describing this, we mention some basic properties of singlet-triplet encounters. Consider two electron spins, each on different molecules. When the spins are far apart, each can be described in the usual way as a spin ½ particle. However, when the radicals approach each other, two possibilities exist: the total electron spin angular m o m e n t u m can either be one or zero. This corresponds roughly to the molecules colliding with spins parallel or antiparallel. The former is called a triplet state, because it consists of three distinct levels characterized by the component of the spin angular momentum Sz about a chosen axis. That three levels must exist for a system with spin angular momentum can be seen from eqn. (6). For a triplet molecule in a magnetic field, the three states are shown in Fig. 19.
\
.o/
N
/
~
Sz=l
\
s
\
Sz=O
- -
& ( ~
s~=-I
- -
I-->
I÷->÷1-+>)=
N
7"0
= E~
\
I++>
~(1.->+1-+>~1
/
li: / I-->
Fig. 19. Allowed spin orientations a n d energy levels for a triplet molecule in a s t r o n g magnetic field.
The spin wavefunction for the upper state may be designated t+ + ) or T 1 and corresponds to both electrons repelled by the external field. Similarly, the lowest state T_ 1 corresponds to attraction. For the Sz = 0 state (To), the wavefunction can be obtained by applying the appropriate lowering operator to [ + + ) . Since a triplet state has net spin, triplet encounters between molecules cannot by themselves lead to the formation of a chemical bond in which all electrons are paired. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
261
DYNAMIC NUCLEAR POLARIZATION
In addition to the triplet encounter, it is possible for two electrons to approach each other in such a way that there is zero spin angular momentum. This leads to a singlet state S whose spin wavefunction is given by ~ks = (l/v/2) (I + - ) - I - + ) ) . Singlet encounters can lead to bond formation. For organic radical pair intermediates at high field, the To and S states should have approximately the same energy. TI should be much higher in energy than either TO or S, while T_ 1 should be much lower. F o l l o w i n g Closs 65, we consider the reaction of diphenyl carbene with toluene to produce 1,1,2-triphenylethane (eqn. (62)). If diphenyl carbene is produced as a triplet, the initial encounter between q~2C: and OCH3 is singlettriplet. This leads to the formation of a radical pair initially in the triplet state which may convert to a singlet and then to product. The situation for the two electrons is shown schematically in Fig. 20. /'I ~
~
Rp(rl)
v~
\ ro rf
~
RP(To)
------S~
\
RP(S)
ws
rf
~
RP (Z~)
triplet
/
crossing or
recombinotion
singlet
product
]Fig. 20. Electron spin energy levels corresponding to the reaction of ~2C: with ~CH3. Reprinted with permission from ref, 65.
Diphenyl carbene in the triplet state is characterized by the wavefunctions T1, To and T_I. Calculation of the electron relaxation rate showed that the populations of these levels are probably in thermal equilibrium before hydrogen abstraction occurs to form the triplet radical pair intermediate. If the rate of formation of radical pairs rf is assumed independent of the electron spin states, the triplet radical pair energy levels RP (Tins) will initially have the same equilibrium distribution as the precursor. These states are also connected by relaxation transitions which are indicated by unlabeled arrows. The downward transition probbilities will be larger than the upward probabilities in accord with the requirements of thermal equilibrium. Singlet radical pairs RP (S) can be obtained from the triplet pairs via two mechanisms: intersystem crossing, or by separation of the triplet components by Advan. Mol. Relaxation Processes, 4 (1972) 229-354
262
J. P O T E N Z A
diffusion and recombination with the appropriate singlet wavefunction. The net probabilities for crossover are given as r l , ro and r_ 1 respectively, and are not equal. Finally, the singlet radical pair produces the product at a rate % . To understand the origin of the rnultiplet effect, we examine the singletriplet crossover in more detail. The simplest case is that of a radical pair containing one proton on each component. Sixteen energy levels result from the two electrons and the two protons. To a good approximation, these are determined by the Zeeman spin Hamiltonian Jt~ = - (/Is, + Psi)" Ho - (/t,, + p,=). H 0
(63)
They are shown in Fig. 21 and labeled according to the z component of the nucleus (rnt.) and that of the electron (ms.). The states are also labeled 1-16 for convenience. In this rather complicated case, the complete Hamiltonian should also take into account scalar and dipolar components which induce the relaxation transitions. Here, we shall consider only scalar contributions (dipolar may be treated similarly) and inquire as to the possibility of obtaining NMR signal enhancement via transitions such as 6 --* 15 and 7 ~ 14, etc., which correspond to r ~ , r o and r_ 1 in Fig. 20. ~_~z
'
o-,1~ -
o
-'1'
o
sz
o -,
4
I LL~ ~,~,
,,,,
~ "-" "-~
_ "-,'-'~" .-'~..,.~6
13/~'/".y7 /
//// ///¢ / / / ,
///." //// #/ / /
'~ f
-~
--
o
1-6
#'--12
iT
Fig. 21. Spin energy level diagram for triplet and singlet radical pair intermediates containing two equivalent protons. Triplet and singlet states are connected by relaxation transitions wo and wo' which do not vanish. Reprinted with permission from ref. 65.
The complete scalar Hamiltonian for this four-spin system is given by Jt°~
= AlxS1
" I1+A12S~
"/'2+A21 82 " /1 + A 2 2 S 2 " / 2 +JeeSt
" S2 + J n n l l " 12
(64)
The first four terms correspond to electron-nucleus coupling, the fifth to electronelectron scalar exchange and the sixth, which we shall neglect because of its small size, the nuclear spin-spin coupling. Equation (64) takes into account all possible unique overlaps between the four spins. It can be s h o w n 66 that if J~e = 0, or if Adcan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
POLARIZATION
263
[J.I >> IAijl, singlet-triplet transitions will not occur. Indeed, Je~ = 0 corresponds to two non-interacting electrons or two doublet states, while IJool>>l,41/ implies that the electrons are coupled strongly to each other and not to the nuclei. On the other hand, if {J~,l m IA ij[, the singlet and triplet states are connected by transitions such as w~ and wo in Fig. 21. This can be verified hy the somewhat tedious evaluation of matrix elements of the form (6]Jt~dl5). This gives expressions such as +¼(All+A22-A12--A21 ) which do not vanish. If the electrons and the nuclei were identical, they would vanish and no transitions would be observed. t Further.• it has been shown 6~ that Wo~>.> Wo, for the diphenyl carbene reaction, leading to the preferred relaxation transitions w0 which connect triplet states of zero nuclear spin to singlet states of the same kind. Now when the singlet radical pair forms a product, the nuclear spin states with rex, = 0 will be overpopulated, leading to the multiplet effect. This development is different from the previous treatment of ONP in several ways. First, the driving force for the enhancement comes from the requirement of spin pairing to form products and not the generation of an equal number of radicals in upper and lower doublet states. Thus, for the multiplet effect to be observed, we would expect radical lifetime requirements to be somewhat different from those based on the attainment of equilibrium in the electron spin system. Here, it would seem that the radical pair need only live long enough for the relaxation transitions connecting triplet and singlet states to establish themselves. Closs used lifetimes z of the order of 10 -8 sec. Secondly, with the multiplet effect, no net z component of spin is obtained. Thus, the assemblage of spins showing only a multiplet effect is in thermal equilibrium with the liquid as a whole, and the process of singlet-triplet interconversion corresponds to a transverse effect in which the x and y components of the singlet and triplet pairs interchange. It has been suggested that this phenomenon, which corresponds to an ordering of spins in the x, y plane or entropy polarization, be termed the transverse Overhauser effect. An ordinary, or longitudinal, Overhauser effect, can also be superimposed on the transverse effect (Fig. 16). The present treatment allows for this in that when product formation occurs with electron spins originally in thermal equilibrium, a net fraction of molecules must undergo upward transitions for all spins to pair. This gives rise to a net change in nuclear z components of spin and an energy polarization. Note that this interpretation is directly the opposite of the previous interpretation which assumed that nuclear polarization occurred before the electron spins reached thermal equilibrium. Last, with regard to x, y polarization, we note that constraints as to the possible magnitude for the polarization need not be the same as those for longitudinal polarization. Thus for protons it would be possible to observe enhancements in excess of ?s/?n = 658. Indeed, proton polarizations greater than 700 have been reported 6 o for multiplets and the theoretical maximum obtainable enhancement remains unknown. Advan. MoL Relaxation Processes, 4 ( 1 9 7 2 ) 2 2 9 - 3 5 4
264
J. POTENZA
The theory developed by Kaptein and Oosterhoff is similar to that given by Closs in that both require singlet-triplet mixing and scalal electron exchange for the multiplet effect to be observed. The major difference involves the manner in which the singlet-triplet mixing is considered. Closs considered the mixing in terms of transition probabilities between well-defined states while Kaptein and Oosterhoff developed the theory in terms of the time evolution of coupled spin states. A review of the latter theory in its simplest form is instructive. The simple theory applies to multiplet effects as observed in EPR spectra immediately after radicals are produced by the breaking of chemical bonds. Consider the dissociation of H-X, where X has no nuclear spin. Although dissociation is continuous, electrons in the H-X bond unpair gradually to produce two doublet radicals. The process may be approximated by a two-step sequence involving a radical pair intermediate (eqn. (65)). The radical pair may be either singlet or triplet; its formation is assumed to take place suddenly. H-X -~ t H ' " X] -~ H " + X -
(65)
The energy level diagram consists of eight states, three triplet and one singlet electronic state, each split by the single proton. As above, we assume that mixing is appreciable only between the singlet (S) and triplet To states, since states with ms, = +_1 differ considerably from the singlet state in energy. The Hamiltonian is given by eqn. (66). = ~ ' ~ . . . . . + Jf~x~ha,~o+ ~ s ~ = o~(S1 + $ 2 ) - d,~(½+ 2S1" S2) + A I . ($1 + S=)
(66)
The first term gives the electron Zeeman splitting, the second corresponds to scalar electron exchange and the third to scalar hyperfine coupling. Angular frequency units are used. Again, it is assumed that Je~ ~ A for significant mixing. For a given H - X molecule, the proton can have only one spin quantum number at any given time. If the radical is initially in a singlet state and the proton has e (or + ) spin, the state of the radical pair would be Se, while for the triplet, the corresponding state would be Toe. These states may evolve in time, one converting to the other. The wavefunction describing this time evolution is given as linear combination of the singlet and triplet wavefunctions. 4~(t) = [Cs(t)S + Cr(t)To]e
(67)
Here ICs(t)l 2 gives the probability at time t that the nuclear spin is e, the electronic state singlet, while ICr(t)l 2 gives the corresponding probability for the triplet electronic state. A similar equation can be written for ~ ( - ) spin. Equations for q~(t) and ~ba(t) in terms of deo and Aij can be obtained from the above Hamiltonian and the time-dependent Schr~Sdinger equation. )f'qS,, a - iO~b~,a 3t Advan. Mol. Relaxation Processes, 4 (1972) 229-354
(68)
DYNAMIC
NUCLEAR
265
POLARIZATION
Substitution o f ¢ , , p into eqn. (68) gives the following differential equations:
idCs(t)
JeeCs(t) + A CT(t)
~t
iOCr(t) _ A dt
4
(69)
C s ( l ) -- gee C T ( t )
These may be solved simultaneously for Cs(t) and Cr(t) in terms of J¢o and A. If the radical pair is initially in a singlet state, Cs(O) = 1, Cr(O) = 0 and
Here, D = (Jee2+A2/16) ~. The important point is that ~t and ,6 wavefunctions change with time regardless of the initial state of the system and that the nuclear spin states influence the electronic spin states as suggested by Bargon and Fischer. This leads to a fluctuating spin density at the H nucleus which may be integrated over the radical pair lifetime to yield electron polarization and transient EPR signals. For the multiplet effect, we are interested in the reverse process ofeqn. (65), that of forming product from a radical pair. As with the Closs treatment, the simplest case involves two protons and two electrons. A typical reaction sequence would be A (p...... o,)
kl
ka
> [RH~ • • RH2] > RHt " + R H 2 • I P* 1/Tt I k2 •
•
(polarized product)
(71)
P
(unpolarized product)
Again, radical pair formation and destruction is assumed to take place suddenly. The precursor A yields radical pair with rate kl ; the radical pair can then either diffuse to form two free radicals (k3) or combine to form polarized recombination and/or disproportionation products (k2). Polarized products become unpolarized with rate 1/T 1 , where T~ is the nuclear relaxation time. An approximate scalar spirt Hamiltonian is
= ~oe(S~t+S~)-Jee(½+2S~" S2)+A, IZ~S~ +A2I~ S~z
(72)
Here, nucleus one is coupled only to electron one, nucleus two to electron two. Further, z components of S and I are used because only these will mix To with So. The state of the radical pair prior to bond formation can be described as above: ¢,(t) = [C~(t)S+Cir(t)To]X,
(73) Advan, Mol. Relaxation Processes, 4 (1972) 229-354
266
s. ~POTENZA
where X~ are the nuclear spin wavefunctions I + + ), J- - >, etc., for two nuclei. From the time-dependent Schr6dinger equation, it was shown 64 that for a radical pair initially in the singlet state
C~s(t) = cos (Di t ) - iJe~ sin (D, t) Di
(74)
and
C~r(t) =
iM, sin (D, t) Di
where D, = (Jee2+M~2) ~ and M~ are hyperfine mixing coefficients dependent upon the nuclear spin states X~. For example, if X = l+ + ), M = ¼(A~-A2), while if X = } + - ) , M = ¼(AI+A2). Since diamagnetic products form only from singlet encounters, the rate of product formation will be proportional to iCs,(t)12 and will be different for the various nuclear states. Hence polarized spectra will result, A quantitative expression for the maximum observed enhancement can be obtained by calculating the population rates wj of the nuclear levels for the polarized product P*. For an originally singlet radical pair, these are given by the average of Cj(t) over the lifetime of the radical pair z.
w i = 1-- 2M~'c2 1 +D~z z
(75)
Use of the steady state approximation for the reactions occurring in eqn. (71) gave the following expression for the maximum enhancement G~j.
I0
~w,
\ k 2 + k 3 NgNflNHolN[Pm]]
Here, the k's are the rate constants given in eqn. (71), l is the total number of nuclear states in the product, [Am] is the concentration of the precursor A at the time of maximum enhancement and [Pm] is the corresponding concentration of product. Using eqn. (76), multiplet enhancements may be calculated if the following parameters are known: [Am], [Pm], kl, k2, k3, TI, A1, A2, Je~ and z. Equations (75) and (76) show that polarized multiplet spectra will arise from the above reaction scheme since M~ and D~ depend upon the nuclear spin states. For example, if A 1 and A2 have the same sign, 1+ +> and [ - - > nuclear states will be populated more quickly than J + - > and I - + > levels. If the nuclear spin-spin coupling constant is positive and the two protons are nonequivalent, one should observe two E/A doublets as shown in Fig. 18. Both this theory and that given by Closs predict a reverse multiplet effect for radical pairs generated in triplet states, and the mechanisms are subject to test. A third explanation for the multiplet effect was given by Fischer 6v and Advan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
267
POLAR1ZA'IrlON
applied to combination, disproportionation and radical transfer reactions. Equation (71) applies except that radicals R" liberated from the solvent cage can react suddenly with other molecules in a transfer reaction of the type R-+X-R' ~ RX+R'.
(77)
A major difference between this and previous theories involves the time scale for polarization production. Previous theories assumed that polarization was produced during the life of the radical pair which was approximately 10-s sec for the Closs mechanism and 1 0 - 9 - 1 0 - 1 0 sec for the Kaptein mechanism. Fischer assumed a smaller time scale, that corresponding to the correlation time z for molecular motions in liquids (10-11-10 -12 sec). The precursor is assumed to form a radical pair continuously with consequent decreasing Je¢. In a time t ~ z, the radical pair will either react to form products or separate to give two free radicals. Destruction of the radical pair is assumed to occur suddenly and may be induced by collisions with solvent or other molecules. Nuclear polarization occurs when the radical pair forms and may be transfered to all products. Using the above ideas and that of singlet-triplet mixing, equations were developed which gave the probability of product formation by recombination, disproportionation or radical transfer. The major new point subject to direct experimental verification was that if transfer products show A/E, disproportionation and recombination reactions should show E/A and vice versa. A unified theory capable of yielding both longitudinal and transverse Overhauser effects within a given multiplet was advanced by Closs and Trifunac 5s. The treatment is based on electron y factor changes within a radical pair and involves electron spin-orbit coupling explicitly. To show how isotropic 9 shifts in radical pairs can lead to net polarization, we consider the simplest case of one proton coupled to the electrons in a radical pair, Precursor
kl
~- [HR~ .- R2] I ~2 ~
k3
> HRI"+Rz"
(78)
HRt-R2+RI+REH
The radical pair can dissociate to give two doublet radicals or polarized products can form via combination or disproportionation. For this three-spin system, the scalar Hamiltonian is given by ~-- ~ ' ~ ..... -4- ~z~eexchange -'1-J~Sl-~~SL
(79)
The first three terms are those in eqn. (66); the fourth term describes the interaction of the electron spin with its orbital motion. If the two electrons have different degrees of spin-orbit coupling, their y values will differ from that of the free elecAdvan. MoL Relaxation Processes, 4 (1972) 229-354
268
J. POTENZA
tron and from each other. For organic products, these differences are expected to be small but significant (cf. Table 2). With the inclusion of spin-orbit coupling, the scalar Hamiltonian becomes
= flno(g~ Sl +g2 Sz)-Joo(½+2S~. S 2 ) + A I . S 1
(80)
Again, this is equivalent to eqn. (66) except that the electrons are non-equivalent and only electron 1 is assumed to be coupled strongly to the nuclear spin (At • S~ vs. A I . (St +$2)). Use of the time-dependent Schr~Sdinger equation for a triplet precursor led to the following expressions for Cs(t) and Cro(t). (t) = - i
Ag + l a
si,
( o ± t)
(81)
D± iJee . sin (O+-t)
C~o(t ) = cos (O+-t) - ~ where
The rate of product formation is proportional to IC~ (t)12 = (½flHo Ag +¼A) 2 sina (D +-t) D-+2
(82)
Therefore, products with nuclear spin state I + ) will form with a rate governed by IC~-(t)12 while products with nuclear spin i - ) will form with rate proportional to ICs(t)l 2. These rates will not be equal unless gl = g2As above, the total rate of product formation will be the average of the singlet coefficients taken over the radical pair lifetime. For a triplet precursor, the product rate is given by w_+ = k 2(½flHo Ag +__¼A)2z 2 1 +4D+2z z
(83)
where k is the rate constant for product formation from the radical pair singlet state. For a radical pair formed as a singlet, w ! is given by I w+ = k
1-
2(½flHoAg +_¼A)2z2-] ~+4D+2 -]
(84)
Triplet and singlet precursors should lead to opposite polarizations. The important point is that differences in electron g values can lead to net polarization, the magnitude and sign of which depends upon the relative magnitude and signs of Ag and A. For systems with more than one nuclear spin, the above arguments may be
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
POLARIZATION
269
amplified 6a to give:
k 2M2z 2
(85)
wj = 1 + 4(M~ + J~e)zz Here, wj gives the rate of population of nuclear spin state j as a function of the radical lifetime v, the scalar electron exchange coupling constant Jee, and a tripletsinglet mixing coefficient Mj. Mj is given by n
My = ½flHo AO + ¼ Z eij A i
(86)
i=1
where eij = __+1. The enhancement factor Gjk for NMR transitions between states j and k then becomes
wk - wj
6jk
(87)
(Wk+ Wj+2Wo)IOk
Here, 1jR ° is the thermal equilibrium population difference for nuclear statesj and k while we describes all relaxation transition probabilities independent of the nuclear spin states, lfJee, Ai, z, we and A# are known, eqn. (87) can be used to calculate enhanced spectra. Comparisons between theory and experiment are quite good and will be presented later. The current status of cioNv theory, then, is this: with the Fischer mechanism, net or longitudinal enhancements arise from Overhauser considerations because of cross relaxations within a coupled spin manifold. Transverse polarization is then accounted for by different population rates for nuclear spin levels. The magnitude of the polarization is limited by the Overhauser mechanism. Further, polarization is assumed to arise when radicals are formed and electrons relax to their thermal equilibrium population distribution in the applied feld. This places limits on free radical lifetimes. On the other hand, the Closs-Kaptein theory accounts for both transverse and longitudinal polarization in terms of singlet-triplet crossover within radical pairs. Transverse polarization arises from scalar nuclear-electron hyperfine interactions while net polarization is explained in terms of # differences between the radical pair components. No limit is placed on the possible magnitude of polarization by this mechanism. Although free radical lifetime considerations are unimportant here since polarization occurs within radical pairs, the lifetime of the radical pair is important. Times varying from 10-11 to 10 -8 sec have been used to compare theory with experiment. The question as to which mechanism applies to a given reaction has not yet been answered completely. However, at the time of writing, the Closs-Kaptein theory appears to have won widespread acceptance. Advan. MoL Relaxation Processes, 4 (1972) 229-354
270
J. POTENZA
3. Field dependence of CIDNP spectra - "zero-field polarization"
The third interesting facet of CIDNP concerns the field dependence of the enhancement. For the decomposition of benzoyl peroxide at several high field strengths 25, the magnitude of the enhancement increased with decreasing field (Fig. 13). Similar observations were reported by Kaptein 59, who studied the thermal decomposition of several alkyl peroxides at 1H resonance frequencies of 15, 60 and 100 MHz. There, multiplet enhancements increased with decreasing field. Both theories above are capable of explaining these observations qualitatively. With the Fischer mechanism, enhancements should decrease with increasing field because of the field dependence of the relaxation transition probabilities (eqn. (49)). With the Kaptein-Closs mechanism, nuclear polarization is also field-dependent since the rates of population of nuclear states depend on Ho (eqns. (76) and (87)). Definitive tests of the latter theory should be forthcoming ss.
f5 20 ~5 30 35 do 4'5 ~0 time (see) Fig. 22. The 1H NMR spectrum of the e-triplet (6 = 4.4-4.8 p.p.m.) of 1-chloro-l-phenyl propane obtained from the reaction of ethyl lithium with e,c~-dichlorotoluene. Spectrum (a) was obtained after mixing reactants in the spectrometer probe. For spectrum (b), reagents were mixed outside the spectrometer and placed in the probe 12 sec after mixing. Reprinted with permission from ref. 69.
Recently, Ward et al. 69 reported nuclear polarization for reactions occurring in the absence of an external magnetic field. An example of such zero-field polarization is shown in Fig. 22 for the reaction of a,~-dichlorotoluene with ethyl lithium (eqn. (88)). C1
\
CH 3CH2Li + C12HC4~--* Fradical pair 1 I_intermediateJ
--* H C C H 2 C H 3
/
(88)
q~ Spectrum (a) shows a positively enhanced nuclear triplet from the a-proton of 1-chloro- 1-phenylpropane. The ratio of peaks in the multiplet is very nearly 1 : 2 : 1, the ratio expected for pure longitudinal polarization. On the other hand, spectrum (b), obtained by placing the sample in the spectrometer 12 sec after mixing the Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
271
reactants shows net negative enhancement and a superimposed multiplet effect. Further, calorimetrfc measurement showed that the reaction was more than 95 complete in 5-6 sec, such that nuclear polarization took place in the absence of an external field and was measured before the nuclei had relaxed completely. Apparently the NMR spectrometer was used only to detect the enhancement. A second example of the zero-field effect was reported 69 for the reaction of benzoyl peroxide in 2-iodopropane and o-dichlorobenzene. Enhancement of the 1H NMR spectrum of 2-iodopropane was observed even though it undergoes no net change during the reaction. The following reaction scheme was advanced to account for polarization observed in C H a C H I C H 3 . ~ C ( O ) O O ( O ) C ~ -~ 2 ~ * - + 2 CO2 ~b*. + i - P r I
~ ~b*I+i-Pr*.
i-Pr*" + i-PrI
~ i-Pr*I + i-Pr*.
~b*.+i-Pr*.
~ Coupling and disproportionation products
(89)
Here, the asterisk indicates species with polarized proton spin levels. (In view of the theory above, reactions (89) should probably be written with radical pair intermediates.)
(b)- ~ p.pm. Fig. 23. Proton NMRspectra of 2-iodopropane (1.48 M) in o-dichlorobenzene containing 0.61 M benzoyl peroxide. Spectrum (a) was taken at 140 °C during the decomposition ofbenzoyl peroxide. Spectrum (b) was taken approximately 5 sec after quenching the reaction which was conducted at 140 °C outside the spectrometer. Reprinted with permission from ref. 69. Observed spectra are shown in Fig. 23 for this reaction both in the presence and absence of a magnetic field. Qualitatively, for the reaction in the field, the doublet expected for the methyl groups of isopropyl iodide shows an E / A multiplet with a positive enhancement superimposed, while the septet for the remaining proton shows a similar multiplet effect and a net negative enhancement. In the absence of the field, the doublet remains approximately the same, while the septet shows almost no multiplet effect. Advan. Mol. Retaxation Processes, 4 (1972) 229-354
272
J. POTENZA
Two points require consideration. First, how may isopropyl iodide become polarized and secondly, how can any polarization arise at zero field? The first point was considered by Gerhart and Ostermann ~°, who regarded the transition state of a transfer reaction as an array of three radicals, viz. R . + X - R ' -~ [R-X'R"] ~ R - X + R ' .
(90)
I f [R'X-R'.] is approximated as a radical pair [R-R'-] split by the spin of X., eight electronic energy levels are obtained (Fig. 24). The six states on the left for [R.X.R'.] correspond to the triplet radical pair state split by X., while the two on the right come from S of the radical pair. It was assumed that only symmetric ms z * 3/2
T1 s
..... S
a
//~
....
~"
/ / / ~
s"
_ ~
-
a'
*112
"~";~%" / ' - -
- - . r
o
-lt2
~-
-3•2
~-.
(
)
[R.V.R ']
t _ _
[R.
v
)
X. R:]
Fig. 24. Electronic spin states for [R • • R] and [R • - X • R']. Reprinted with permission from ref. 70. electronic states with ms= -- +_½ are populated. Following Closs 65, crossover to states arising from S was assumed to occur. Now, if mixing occurs most readily for nuclear states with mr. near zero, E/A multiplets will be observed. The electronic transitions occurring in Fig. 24 can be visualized in a simplified manner, viz. RI"X~R'I" --* RI"X~R'$
(91)
Before crossover, the electron of X is equally bonded to R" and R'. ; after crossover, bonding occurs only between R. and X.. This mechanism, which could account for polarized i-PrI, was criticized 58 on chemical grounds since it requires three uncoupled electrons and transition state lifetimes of about 10-1 o sec. Most likely, polarized i-PrI arises from non-reactive encounters in radical pairs of the type IX..i-Pr] and is transferred to the product in an abstraction step before it has time to decay. N o explanation has been offered for the zero-field experiments. However, we note that at very low fields, the theories presented above will not hold. As the field is decreased, states T1 and T_ 1 of the triplet electronic manifold will have to be considered sS. Experiments similar to those of Ward et al. 69 have been performed by AbragamTa, 72, but with solids. A crystal of LiF at 2 °K was allowed to equilibrate in a weak magnetic field Ho (0-40 gauss). The crystal was then removed from the Advan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
POLARIZATION
273
magnet and placed in a stronger field (4840 gauss). The resonance signal of 7Li was found to depend only on the strength of the initial weak field and did not approach zero as Ho ~ 0. Scrutiny of Abragam's experiments may provide some insight concerning the zero-field experiments mentioned above. However, for a liquid in rapid motion, it is difficult to see how polarization or net magnetization can arise at zero field. The interesting results obtained so far with CIDNP point towards a wealth of chemical information stored within polarized spectra. The interpretation of these spectra should contribute heavily to the development of free-radical chemistry and mechanistic interpretations in organic chemistry. In the next section, we summarize the experimental procedures and instrumentation required to obtain enhanced NMR spectra. IlI. INSTRUMENTATION AND EXPERIMENTAL ASPECTS OF DNP
A. Electronically induced DNP 1. Extrapolated enhancements
We consider first the quantitative measurement of NMR signal enhancements. From eqn. (36), the enhanced NMR signal amplitude G is given by G - i ~ - I o _ Vs (r-s+c) Io Vt ( 2 q + r + s + c )
(36a)
Two difficulties are encounteted if one tries to apply this equation to experimental observations. First, the derivation of eqn. (36) tacitly assumed that S~ = 0; i.e. that the electron spin levels of the coupled spin system (Fig. 9(b)) were completely saturated. In practice, this would require an infinite intensity of radiation at the radical EPR frequency, which is impossible to obtain. For any finite intensity, the magnitude of G would be less than that given by eqn. (36). Second, the relaxation transitions p, q, r, s and c were assumed to be the only relaxation transitions occurring in the fluid, leading to the factor ( r - s + c)/(2q + r + s + c) in eqn. (36). This factor gives the ratio of polarizing transition probabilities (those which simultaneously change an electron and nuclear spin) to the total relaxation rate. If other relaxation processes not involving the electron spin occurred (e.g. nuclear or electron relaxation via spin-spin coupling), the total relaxation rate would be larger than that expected from eqn. (36). These considerations lead to two additional terms in the expression for the enhancement, the saturation factor and the leakage factor 73 The electron saturation factor S~(P) is given by: Se(P) - (So - Sz)
(92)
So Advan. Mol, Relaxation Processes, 4 (1972) 229-354
274
J. POTENZA
and the leakage factor by
f=
(2q+r+s+c) (2q+r+s+c+w)
(93)
where w is the total probability for relaxation transitions other than those of interest for the coupled spin system. Inclusion of these factors gives the following expression for the enhancement. G - Ysy,(2q+ +s +r(sr+- c) c)fSe(p)
(94)
For complete saturation, Sz = 0 (definition) and the saturation factor is unity as expected, while for zero intensity of radiation, S~ = So and Se(P) = O. That is, no enhancement is observed without saturating the EPR signal. Experimentally, one generally assumes that Se(P) is related to the power P applied to saturate the EPR signal in such a way that a plot of ]/G vs. 1/P should give a straight line whose value extrapolated to infinite power gives the enhancement for complete saturation. Typical plots 74 of 1/G vs. 1/P for hydrogen and fluorine nuclei are shown in Fig. 25. Scatter of the points for these nuclei give errors of typically __.10 700. We note, however, that this relatively simple procedure has previously 0 . 0 7
,
f
r
J
,
,
-
f
,
o H y d r o g e n (TTBP in C<;H6) . j , 0.0(5 . Fluor'in¢ ( T T B P ooo °04
0.03 0.02 0.01 i
0
J
J
0.04
i
008 p-1
t
i
0.12
I
•
0.16
r
0.20
Fig. 25. Plot of I/G vs. 1/P for 1H nuclei in C6H6 and 19F nuclei in C6F 6. The abscissa is calibrated in reciprocal watts. The sample consisted of 50 vol. ~ C6H6, 50 ~ooC6F6 and O. 1 M tri-tert.-butyl phenoxyl. Reprinted with permission from ref. 74.
been criticized ~3 and should not apply in all cases. Corrections, which are beyond the scope of this review, are particularly important for quantitative work at high external magnetic fields and will depend on the type of ~MR detection circuit employed. For our purposes, we shall neglect these corrections and quote enhancements as reported in the literature. The leakage f a c t o r f m a y be rewritten as f = 1-
W
(2q+r+s+c+w)
- 1
W
wt
(95)
where wt is the total relaxation rate. Since the total relaxation rate is the inverse Advan. MoL Relaxation Processes, 4 (1972) 229-354
275
DYNAMIC NUCLEAR POLARIZATION
of the spin-lattice relaxation time 7"1 in the radical solution, while w is the inverse of T~ for the same solution without free radicals, f r e d u c e s to f = 1
TI
(96)
T,B
T~B, the bulk relaxation time, pertains to the diamagnetic solution. Thus, the effect of additional relaxation may be accounted for by measuring 7'1 for the paramagnetic solution of interest and for a similar solution without free radicals. This is the easiest way to correct for leakage. A second method sometimes encountered in the literature ~7' 7s assumes that q, r, s and c are proportional to the free-radical concentration [R] such that at infinite radical concentration/'1 = 0. Hence, a plot of 1/G vs. 1/[R] should give a straight line whose extrapolated value corresponds to f = 1. This method requires the preparation of many samples at different radical concentrations and generally is not employed for that reason. In sum, by measuring an observed enhancement as a function of saturating power and by measuring two relaxation times, an ultimate or extrapolated enhancement, U~, corresponding to eqn. (36), may be obtained. It is this value which must be used whenever quantitative comparisons between different systems are offered.
2. Sample preparation For the study of systems containing stable free radicals, it is imperative that molecular oxygen be removed from the samples. Oxygen is paramagnetic; therefore, it will give rise to additional relaxation mechanisms and will affect 7"1 of the sample and TIB of the bulk fluid used to correct for leakage. If the concentration of oxygen is unknown and varies from sample to sample, erroneous values for the extrapolated enhancement will be obtained. Further, because it is paramagnetic, oxygen will shorten the electron relaxation time in the radical of interest, thereby making its EPR spectrum more difficult to saturate. Finally, 02 may react with and destroy the radical. For instance, the lifetime of semiquinone radicals is known to increase with the removal of oxygen 17. A simple vacuum apparatus, such as that shown in Fig. 26, generally suffices
VOcuu pumpm
~~
Dewar
Trop
II ~- StOpcOck ~--Dewor -
~Sam
pie
Fig. 26. Vacuum line for sealing samples. Advan. Mol. Relaxation Processes, 4 (•972) 229-354
276
J. VOT~NZA
to remove oxygen. The sample is frozen in liquid nitrogen, after which it is evacuated. A vacuum of the order of 10 pm Hg is usually sufficient and this can be supplied with an ordinary oil-filled vacuum pump. After pumping, the stopcock is closed and the sample is allowed to melt. This freeze-pump-thaw procedure is repeated five times and the sample is sealed while frozen. An alternative method for obtaining oxygen-free samples consists of bubbling dry nitrogen through the sample tube, followed by sealing. The sample size is governed mainly by the ease of detecting the unenhanced NMR signal. Since the strength of the NMR signal is proportional to ( N + - N _ ) , which in turn is related to the Boltzmann factor, low field measurements will require larger samples than high field measurements. For hydrogen nuclei, which are the easiest to detect, 6 ml samples have been used for fields in the range 50-300 gauss, while at earth's field, pint-sized samples are required. At these low fields, the sensitivities of nuclei other than ~H and 19F are such that unenhanced signals cannot be seen. As an example, at 74 gauss, the a ~p zero signal of neat triethylphosphate, which contains approximately 6 M phosphorus, lies buried in the noise; enhanced signals, however, are plainly visible. If quantitative measurements are desired for a~p, 7Li ' etc., at low fields, some way must be found to obtain quantitative zero signals. This could be accomplished by increasing the sample volume with the disadvantage of severely limiting the number of samples which can be examined because of cost. Generally, for low-field studies, a computer of average transients (CAT) is used to detect zero signals. This is a device which divides a given signal into a large number of parts (generally 256 or larger). The signal is repeatedly scanned and the total intensity at each point remembered. For random noise, this total increases as the square root of the number of scans, while the signal increases linearly. Typically, one may increase the signal-to-noise ratio by about a factor of 10 using this method before instrumental instability leads to erroneous results. This allows 31p and 7Li to be examined at 50-100 gauss. To study 13C in natural abundance conveniently, a minimum field of about 500-800 gauss will probably be required. Limitations on sample size also arise from the type of double resonance spectrometer used. For high resolution, because of the stringent requirements for field homogeneity, small samples give better resolution. High-resolution DNP spectrometers operating at 3300, 8500 and 12,500 gauss have been employed 73 with sample volumes ranging from 0.1 to 1 ml. 3. Radicals used
The most important factors governing the choice of radical are stability, solubility in the solvent of interest, and ease of saturation of the EPR signal. Generally, dilute solutions (0.001-0.05 M) are employed and solubility is not a great problem except when it is desired to compare the effects of the same radical Advan. 54ol. Relaxation Processes, 4 (1972) 229-354
TABLE 5 SELECTION OF STABLE RADICALS USED FOR D N P EXPERIMENTS
Name
Abbreviation
1. 2,4,6-Tritertiary butyl phenoxyl
TTBP
2. Galvinoxyl
GALV
Formula
~
6
NO 2
3. Diphenylpicryl hydrazyl
DPPH NO 2
4. Tetrachloroserniquinone
CI
CI
CI
CI
TCSQ
5, Bisdiphenylene-phenyl allyl
BDPA
6, Peroxylamine disulfonate
PODS
7. 2,4,6-Triphenylphenoxyl
TPPO
q)
4~
~\~/® 8. Triphenylverdazyl
xPv
9. Triphenylpyrylyl
TPPY
N
N
I
I
CH
10. Wurster's blue perchlorate
WBPC
C~I3 /N--~
CH 3
11. Naphthalene negative ion
NNI
12. Ditertiarybutylnitroxide
DTBN
~
N
I
O° O.
13. 2,3-Dichloronaphthaquinone
DCNQ O"
/'t::=z N ~CH3
CIO 4-
278
J. POTENZA
in a wide variety of solvents. On the other hand, radical stability is often a criterion for deciding which samples may be examined. In favorable cases, radical solutions will last for months, especially if they are kept frozen when not in use; more generally, lifetimes of the order of days are obtained. Many stable radicals have been used for DNP studies, some of which are shown in Table 5. Space does not permit a description of the advantages and disadvantages of each. Rather, the following discussion is intended to acquaint the reader with the considerations involved in choosing an appropriate radical. A large number of stable radicals were described by Buchachenko 76, and recently by Forrester et al. 77. (a) Commercial availability. Of the radicals shown, only DPPH, GALV and PODS can be obtained commercially as the radical. However, radicals derived from commercially available quinone or phenol precursors may be generated quite easily via simple, one-step syntheses. For instance, TTBP is readily generated in a variety of hydro- or fluorocarbons by oxidation of 2,4,6-tri-tert.-butyl phenol with excess PbO2. o
while TCSQ may be obtained either from tetrachloro-p-quinone by reduction in base with glucose or by air oxidation of the corresponding hydroquinone. For the reduction
0 C,~C,
,oco o
O° C,~C,
NaOMe C,
I] 0
C,
C,
1 o-
(98)
"el
Other quinone and phenolic radicals may be prepared similarly. The major disadvantage with these radicals is that the reactions do not go to completion, and it is therefore difficult to reproduce a given radical concentration. This increases the difficulty of a concentration extrapolation in that the radical concentration must be measured independently by EPR techniques. (b) Nitrogen-eontainin 9 radicals. WBPC, D P P H and TPV* all contain nitrogen, and all have relatively broad EPR spectra (Fig. 27). For this reason, they are almost impossible to saturate completely. This is a general feature of nitrogencontaining radicals and can only be corrected for conveniently at low applied field. For high-field work, these radicals should be avoided unless care is taken to ensure an EPR line narrow enough to be saturated completely. (c) Semiquinone radicals. Except for TCSQ and DCNQ, the majority of semiquinone radicals are not of great value for double resonance work 74. p-Benzo* Many verdazyl derivatives were reviewed by Kuhn and Trischmann7s.
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
GALV
NUCLEAR
279
POLARIZATION
TCSO TPV
TTBP
@DPPH TPP~, BDPA@ Fig. 27. EPR spectra o f selected free radicals used for DNP studies. T h e EPR spectra were taken at 3400 gauss with a p p r o x i m a t e l y 0.01 M solutions. Reprinted with permission f r o m ref. 74.
semiquinone, for example, yields stable solutions in many cases, but the EPR spectrum contains 5 lines (one electron coupled to four equivalent protons) and is difficult to saturate. As a final observation, we note that semiquinone radicals are produced as the anion, such that if they are generated in relatively non-polar solvents, they should exist as ion pairs. This adds an additional complication for the interpretation of enhancement data. A procedure for obtaining stable solid semiquinone radicals for DNP work was described by Richards and White z. (d) Perchloro radicals. O f these, TCSQ has been the most widely used. Because the chlorine nuclei possess a quadrupole moment, no hyperfine coupling of C1 with the radical is observed. Instead, the EPR signal (Fig. 27) is a sharp single line which is extremely easy to saturate. Because they should have similar desirable properties, perchlorohydrocarbon radicals, as they become available, should be widely used in DNP. A general synthesis for highly chlorinated compounds 79 and radical derivatives a° has been reported by Ballester et al. As more of these radicals become available, they will likely be used for DNP because of their favorable EPR parameters. R
(e) Nitroxide radicals'. Radicals of the type
R'
\N j
, although they have
O" not been widely used in the past for DNI-, will probably be used more in the future for several reasons. First, the unpaired electron is highly localized on the N - O group, in contrast to many of the radicals above where it is highly delocalized. Second, the groups R and R' can be varied to give almost any organic functional group without destroying the radical. Third, at least one of these radicals (diAdvan. Mol. Relaxation Processes, 4 (1972) 229-354
280
J. POTENZA
tert.-butyl nitroxide) is a liquid at room temperature which should permit a wide range of radical concentrations to be studied easily. Lastly, several of these radicals are water soluble, which will foster the development of DNP in aqueous solutions, perhaps those containing biologically important macromolecules. The only apparent disadvantage of nitroxide radicals is a relatively broad EPR line, but the advantages mentioned above may compensate for this. Since their discovery s~' s2, a large number of nitroxide radicals has been prepared and their properties examined (refs. 83-85). Some are available commercially 86. ( f ) Hydrocarbon anions. Radical anions, such as NNI, may conveniently be prepared by reaction of the hydrocarbon with Na metal. Procedures for preparing radical cations of hydrocarbons have also been described 87. Both anions and cations have been studied extensively by EPR 35. For DNP, these radicals have the disadvantage of being relatively unstable. Further, an excess of sodium metal must sometimes be maintained in the sample and this causes NMR signals to be difficult to detect. In addition, the effects of counterions must be considered. On the positive side, hydrocarbon radicals are for the most part planar and the unpaired electron is easily accessible to solvent molecules. Nonetheless, because of the disadvantages, it is unlikely that these species will find widespread applicability for DNP. At present, the radicals most favorable for DNP include TTBP, GALV, DPPH, TCSQ, TPPY and BDPA. The synthesis of BDPA has been described by Koelsch 88, and a large number of pyrrilium salts were examined by Dimroth 89. For TPPY, the radical may be obtained from the fluoroborate salt by reduction with zinc. TTBP and TCSQ, although their concentration cannot be easily reproduced, are easily saturated. GALV gives a broader Et'R line which can still be saturated. D P P H is convenient to weigh, but difficult to saturate, while the major difficulty with BDPA is its lack of availability. Most of the results to be presented will refer to these six radicals. 4. Instrumentation (a) The NMR spectrometer. Before considering DNP spectrometers, we should examine the phenomenon of resonance further. As shown in Fig. 3, nuclear magnetic moments precess in an applied magnetic field with an angular frequency proportional to the field strength. ~o = 2~rvr~ - gN fin Ho h
(99)
However, the z component of the magnetic moment is constant in time and may be measured, while the x and y components of ~ change with time as p rotates (Fig. 28(a)). For a large number of spins in the magnetic field, the total z component adds and leads to a permanent magnetization in the z direction. On the
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
\
.
/
281
\
/ Mx=My=O /
-,.~x z
.uy M z -i~ 0
/
s
\
\
/
(a)
(b)
Fig. 28. (a) The motion of a single nuclear magnet in an applied field. The z component of/~ is constant in time while ttx and/~r change; and (b) the motion of a collection of magnetic nuclei in an applied field. All the nuclei precess about the field direction. When plotted from a common point, the assemblage uniformly covers the surface of a cone. The macroscopic x and y components of the magnetization (M= -- ~k~x, My = 5~/~r) vanish, while the z components add to give the resultant magnetic moment shown. other hand, since the assemblage of nuclei is precessing randomly, the x a n d y c o m p o n e n t s will add vectorally to zero. T h a t is, there is n o net x or y c o m p o n e n t of the magnetic m o m e n t for a large n u m b e r of spins (Fig. 28(b)). The resonance experiment consists of i m p i n g i n g radiation on this assemblage of precessing spins in the x, y p l a n e a n d observing the effect produced o n the macroscopic c o m p o n e n t s of the magnetization. Consider r a d i a t i o n at a frequency v i m p i n g i n g o n the collection of spins shown in Fig. 28; this could be provided by the experimental a r r a n g e m e n t shown in Fig. 29. The a.c. oscillator sends a n alternating signal t h r o u g h the coil at a frequency which depends on the characteristics of the transmitter. The oscillator generates a magnetic field directed along the l a b o r a t o r y x axis. F r o m the geometric a r r a n g e m e n t of the coils, the signal amplitude increases a n d decreases in the x direction with the frequency v. However, this linear oscillating magnetic field (called H ' as c o m p a r e d with H o , the p e r m a n e n t magnetic field), is equivalent to two fields, one rotating clockwise in the x - y plane, one rotating counterclockwise
\
N
/
z
-N'
Oscillator Oscillator output
Sample NO
Fig. 29. A simple NMRprobe consisting of a coil of wire wound around a sample vial. The oscillator connected to the coil provides an alternating current of frequency ~ which causes a secondary field H ' to be directed along x. This field increases and decreases in the x direction with the frequency of the oscillator. ,4dvan. Mol. Relaxation Processes, 4 (1972) 229-354
s. POTENZA
282
((:1)
(b)
(c)
Fig. 30. (a) T h e H ' field m a y be regarded as the s u m o f two fields rotating in the x, y plane with a n a n g u l a r frequency co c o r r e s p o n d i n g to that o f the oscillator. O n e o f the rotating fields (H1) precesses in the s a m e direction as the magnetic m o m e n t s . (b) T h e rotating fields in the laboratory f r a m e o f reference at a later time. (c) T h e HI field interacts with the nuclear magnetic m o m e n t s a n d exerts a torque T = ft × H1 on t h e m which tends to change their orientation.
in the same plane. This is shown in Fig. 30(a). The vector sum of the two rotating fields gives the linear field generated by the coil arrangement. In effect, then, one has a magnetic field H~ perpendicular to the static field H 0 and precessing in the same direction as the spin magnetic moments of the nuclei. The second field is precessing in the opposite direction and will be ignored. Classically, the effect of the rotating field is to exert a torque (T -- M x H1) on the magnetic moment which tends to reorient the spins (Fig. 3 0 ( C ) ) 36. I f the oscillator frequency is not at the resonance frequency, this component of torque will vary in time and will exert little net effect on the total nuclear moment (actually it will cause it to wobble). When the applied frequency corresponds to that given by eqn. (99), the applied and nuclear frequencies will be the same and the component of torque will always be such as to reorient the nuclear spin. This will result in a decrease in the z component of magnetization and a change in the x and y components as they attempt to follow or stay in phase with the H~ field. The net Oscillator
output
z
resonance Mx , My-4:0
Mz~O Amplitude
IL
(a)
(b)
Fig. 31. (a) A t resonance, # a n d H1 are precessing at the s a m e frequency. T h e torque is c o n s t a n t a n d spins are reoriented. (b) T h e energy required to reorient the spins c o m e s f r o m the H1 field. T h e oscillator o u t p u t is reduced a n d absorption o f energy is observed.
.4dvan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
283
POLARIZATION
result is a decrease in the z component and an increase in the x and y components of the magnetization. Pictorially, the individual magnetic moments may be considered to bunch up at resonance as shown in Fig. 31 (a). Quantum-mechanically, the constant torque exerted on the nuclear moments corresponds to spin flips of the individual nuclei. The energy required to flip the spins comes from the alternating H 1 field provided by the oscillator (Fig. 31). At resonance, the output of the oscillator is reduced because the nuclei absorb energy; this change in amplitude may be amplified and the result displayed on a recorder or oscilloscope. The usual method for observing resonance consists of varying the magnetic field Ho by means of sweep coils wound about the magnet pole caps while the oscillator frequency is kept constant. As the field increases, the frequency of nuclear precession given by eqn. (99) changes. When the resonance frequency is reached, the oscillator and precession frequencies are the same and a net absorption occurs. A block diagram for this simplified NMR spectrometer 9° is shown in Fig. 32. The sweep coils which vary the H o field strength are connected to the x axis of an oscilloscope such that
~mpLe .
fo,o,,,o,or } ] ome ''''or rectifier
Oscilloscope
~Sweep coiI Sweep generotor ~ _
Ho
Fig. 32. A simplified NMR spectrometer. The sweep generator slowly increases and decreases the Ho field and hence gives a measure o f the external field strength. The signal from the oscillator is rectified, amplified and displayed vertically on the oscilloscope.
the x direction is a measure of the field strength. Output from the oscillator is rectified, amplified and fed to the y channel of the oscilloscope which then gives a measure of the NMR signal strength. In actual practice, more complicated arrangements of coils and detection equipment are used. In particular, many high resolution NMR spectrometers employ both a transmitter coil for stimulating the NMR signal and a receiver coil at right angles to the transmitter coil to detect the NMR signal. This procedure has the advantage of isolating the NMR signal from background noise in the transmitter. The reader is referred to standard texts 9°- 92 for a thorough discussion of spectrometer design and characteristics. In principle, EPR may be observed in a like manner with the exception that at a given field, a much higher oscillator frequency is required for the electron. Usually, however, EPR spectrometers are designed to display the derivative of the Advan. Mol. Relaxation Processes, 4 (1972) 229-354
284
J. POTENZA
absorption curve aS' 93. Resonance frequencies for the various nuclei and for the different electrons at any given field may be calculated from eqn. (7). For fields less than 1000 gauss, NMR and EPR frequencies fall in different regions of the radio spectrum. For fields between 1000 and 25,000 gauss, which includes most commercial NMR and EPR spectrometers, the NMR signal is in the radio region, while the EPR signal corresponds to microwave radiation. The basic problem in designing double resonance spectrometers is to permit detection of the NMR signal while simultaneously stimulating an ~PR signal. (b) DNP spectrometers For a DNP spectrometer, the question of introducing radiation at the appropriate EPR frequency to an ordinary NMR spectrometer is the one we consider first. In principle, this can be accomplished by inserting an additional set of coils at the EPR frequency in the double resonance probe. A schematic arrangement of a DNP spectrometer might then look 9° like that shown in Fig. 33. The permanent magnet (usually a large electromagnet) supplies the H o field while the sweep EPR c o i l s ~ , , , ,\
Power meter \\
~,r
--JJ Sweep coil
//
jNMR coil
TransmiterEPR ~ at frequency /
..L. /
Sweep col I
_//.~ ]'-,~
z
Fig. 33. A simplified DNP spectrometer. The diagram is similar to Fig. 32 except that a set of EPR coils has been introduced perpendicular to both sweep coils and the NMR coils. The EPR coils are powered by a radio transmitter or microwave generator and the amount of power is measured with a meter M.
generator slowly increases H o to pass through resonance. The NMR transmitter and coil provide an oscillating H1 field in the x direction which induces nuclear transitions in the solvent. Similarly, the EPR transmitter, which is at a much higher frequency, provides an oscillating field in the y direction which induces EPR transitions if the solution is paramagnetic. Since the EPR and NMR coils are at right angles, the two H1 fields should interact minimally. Consider now what is occurring in the solution. When a free radical collides with a solvent molecule containing a magnetic nucleus, an energy level diagram such as that given in Fig. 10 applies. The two spins are coupled via the relaxation transitions, and an attempt to saturate the EPR signal will result in a change in the NMR signal amplitude. The Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
POLARIZATION
285
exact design of a DNP spectrometer will depend on several factors, including: (1) whether high or low NMR resolution is required, and (2) whether qualitative or quantitative enhancement data are required. A wide variety of DNP spectrometers has been employed for various purposes and an excellent review of DNP, including high-field DNP spectrometer design, has appeared recently 73. We shall detail the experimental requirement for a low-field low resolution spectrometer, then mention some considerations in going to high field and high resolution.
Magnet and probe ~
I
Coaxial lead to EPR coils ,
Power supply for Frequency counter
1
\
\
/ l o c k - i n amplifier ' Sweep generator
Power supply .....
transmitter
~
'~
,,,afar
Mogoe,
" Oscillator,"
Lock-in a m p l i f i e r
Fig. 34. A low-field DNP spectrometer.
A schematic of a DNP spectrometer designed to operate at 74 gauss is shown in Fig. 34. In this apparatus, the EaR transmitter, contained in the left-hand rack, is designed to operate at 210.7 MHz. The circuit design is standard and may be found in a UHF--VHVmanual. The top portion of the rack contains the oscillator and several amplification stages, while lower parts contain power supplies and regulators to control the power output. Unfortunately, simple transmitters and usual probes will operate conveniently at only one EPR frequency. This determines the magnetic field strength at which resonance will occur and so the entire spectrometer will operate at only one field (here, 74 gauss) with this transmitter. Since the magnetic field required for resonance with organic free radicals (g = 2.00) is fixed by the EPR transmitter, the NMR frequency for any nucleus is determined. Thus, protons will resonate at 319.7 kHz, 19F nuclei at 300.8 kHz, 3tp nuclei at 129.4 kHz, etc. Attached to the cage shielding the magnet is a wattmeter which is connected to the RF transmitter and then to the EPR coil. This serves to measure the power used to saturate the EPR signal. At low field, in apparatus similar to that shown, considerable amounts of power (50-200 watt) should he used if quantitative measurements are desired. This level of power corresponds approximately to 1 watt of power per milliliter of sample volume. The reason for this large power Advan. Mol. Relaxation Processes, 4 (1972) 229-354
286
J. P O T E N Z A
requirement may be seen by considering Fig. 25. There, the reciprocal of the signal enhancement decreases as the power P is increased. If high powers are available, the extrapolation to infinite power is short and therefore more reliable. Secondly, if the plot of 1/G vs. 1/P is not precisely linear, as is sometimes observed, the high power values will lead to a more accurate extrapolated enhancement. Lastly, high powers give large enhancements, and if an experiment is designed only to detect a given nuclear species, high powers will be desirable. The transmitter shown will generate 70 watt maximum which provides an Hie field of 1 gauss peak and this is usually sufficient to obtain extrapolated proton enhancements reproducible to about _+ 10 ~o- For high-field work, less power (about 1-5 watt) is generally required to obtain comparable saturation, because more efficient probes may be constructed. Often, however, plots of G - 1 vs. P - 1 are not linear at high field, and elaborate correction procedures 73, 94, 95 are required to obtain quantitative extrapolated enhancement data. The N~R transmitter is shown on a stand protruding from the front of the shielded electromagnet. In this spectrometer, the transmitter is actually a marginal oscillator, and the NMR coil forms part of the oscillator circuit. Essentially, an oscillator is an amplifier in which part of the amplified output signal is fed back to the circuit as input. This maintains continuous oscillation. For a marginal oscillator, an additional automatic gain control feedback is adjusted so that oscillation is just barely maintained. As a result, the level of oscillation is very sensitive to the small changes which result from resonance. The marginal oscillator shown can be adjusted by means of tuning capacitors to oscillate anywhere in the range 80 kHz-2 MHz and is thus satisfactory for observing a large variety of nuclei over a wide range of field strengths. For example, by inserting appropriate capacitors, the resonance frequency may be changed from 319.7 kHz (for all) to 3C0.8 kHz (for 19F). Lower frequencies can be obtained by further increases in capacitance until the oscillator no longer oscillates. The point at which this occurs will depend upon the number of turns of wire in the NMR coil. Typically, 100 turns are used. By changing the appropriate capacitors and the numbers of turns on the coil, frequencies down to 80 kHz and up to several MHz can be obtained. The exact NMR frequency (to seven figures) may be continuously monitored with a standard frequency counter such as that shown in the center rack. This permits calculation of the field strength when resonance is observed and serves as a useful check on the oscillator. A 150 V d.c. power supply, directly below the frequency counter, provides the operating voltage for the oscillator. The modulated output of the oscillator is displayed on the oscilloscope next to the frequency counter. Before and after resonance only incoherent noise coming from the power supply is observed. During resonance, a sine wave pattern at the modulation frequency (to be discussed below) is displayed, and, if the feedback is appropriately adjusted, the maximum height of the wave gives the amplitude of the NMR signal. This type of detection is unAdvan. Mol, Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR
287
POLARIZATION
satisfactory for several reasons: the signal-to-noise ratio is poor and no permanent record of the NMR trace is obtained. To increase the signal-to-noise ratio, a phase-sensitive detector, shown on the bottom of the rightmost rack, is used. These commercially available devices reject noise from a large portion of the spectrum and amplify the remaining signal and noise. The output of the phase-sensitive detector has a large signal-tonoise ratio and this signal is fed directly to an x - y recorder, shown on the right, to obtain a permanent trace of the NMR signal. At the top of the right hand rack is the magnet power supply and the sweep generator. The power supply is current regulated and supplies a constant current through the coils of the large electromagnet. This produces the steady field Ho which increases with the current from the power supply. The sweep generator is connected directly with the magnet power supply in such a way as to increase and decrease periodically the current flowing through the magnet coils. By adjusting the sweep generator, the magnetic field strength may be made to vary over almost any desired range. For most applications, variations of about 1000 c/sec are usual, but larger sweeps (m the range 40 kc) are used for some applications. At 74 gauss, protons resonate at 319.7 kc and so 1000 c/sec corresponds to (74)(1000)/319,700 = 0.2 gauss. The sweep generator also controls the rate at which resonance is passed. Perhaps the most critical part of any magnetic resonance spectrometer is the probe into which the sample is inserted. A schematic of a probe used at 74 gauss for DYe studies is shown in Fig. 35. The probe is inserted between the poles of the magnet such that the Ho field is coaxial with the induced field of the large coils. This particular probe consists basically of three coils. The innermost white coil is used to stimulate and detect the NMR signal. Each notch in the coil contains the requisite number of turns (say 10) and the induced field H ' is directed along the coil axis (up and down in Fig. 35). With this arrangement, H' is perpendicular to the H o field. The EPR "coil" consists of two half turns of thick wire (one on either side of the sample) which are connected to each other in such a way that their induced fields are in the same direction. With this geometry, a minimum amount of EPR power is introduced directly into the NMR circuit. MoOulotion coils
\\\
NM R
coils
Tuning c a p o c i t o r ~.__~ f o r E PR CooxiQI lead D~tO oscilletor
Cooxiel leod to EPR t Pclnsrnitter
TuF3ing cQ pQci~or f o r EPR
Fig. 35. A low-field DNP probe. .4dvan. MoL Relaxation Processes, 4 (1972) 229-354
288
J. POTENZA
Extending from the NMR coil is a coaxial cable which is connected directly to the marginal oscillator. The coaxial cable extending beneath the NMR coil connects the EPR coil to the radio transmitter. It is interrupted three times by adjustable capacitors which are varied to minimize reflected power and tune the circuit. Consider what happens to radiation at the EPR frequency. It emerges from the transmitter, passes through the coaxial cable and into the EaR coils. Only if all the power transmitted through the cable is used to generate the EPR H ' field will a plot of 1/G vs. lIP be linear and accurate extrapolated enhancements obtained. If any power is reflected back from the coils to the transmitter, the probe circuit is not tuned and will be extremely temperature-sensitive. By suitably adjusting the capacitors shown, the reflected power can be reduced to zero. The large set of coils perpendicular to both the EPR and NMR coils have their induced field in the Ho direction. They are not sweep coils; rather, they are modulation coils which are used primarily to increase the signal-to-noise ratio of the NMR signal. The frequency fed through the coils is usually low and can be varied. For the spectrometer shown, 53 Hz is used. To understand the usefulness of modulation, consider only the N~R system near resonance. The field of the permanent magnet is slowly being increased by the sweep generator and the precession frequency of the individual nuclear magnetic moments is approaching that of the H1 field. Without the modulation coils, we would expect one pass through resonance with a decrease in oscillator energy as shown in Fig. 31. However, the modulation coils provide an additional small amplitude sweep field of 53 Hz with the result that durin9 resonance the Ho field is being varied at a rate of 53 c/sec. The output of the marginal oscillator, therefore, does not decrease regularly; rather, the steady decrease has superimposed on it an oscillation corresponding to 53 Hz (Fig. 36). The advantage of modulation is that now an audio-frequency amplifier, such as that found in a phase-sensitive detector, can be used to amplify the 53 Hz signal which is proportional to the NMR signal strength as defined above. This arrangement provides a convenient means for utilizing narrow band amplification combined with synchronous or lock-in detectors. x= c_S_
31g k.¢
Before resono.nce
During resonQnce
After resonance
Fig, 36. Oscillator output with modulation (schematic). The high frequency corresponds to
the NMRfrequency at resonance. The low, superimposed frequency is the modulation frequency. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
POLARIZATION
289
In sum, any DNP spectrometer will consist of the components considered above. Except for the probe and perhaps the NMR oscillator, all items are commercially available. Modifications of the probe shown in Fig. 35 are not useful for fields above about 500 gauss because as the EPR and NMR frequencies increase, the size of the corresponding coils should be decreased accordingly. Such coils become increasingly difficult to make in miniature at high fields, and the sample sizes which can be treated decrease drastically. ONP probes which have been used successfully at 3500 gauss and higher have been described in detail elsewhere 7s. Basically, the NMR coil still consists of a wire wound about the sample, but now the EPR "coil" is a resonant cavity (like an organ pipe), the length of which can be adjusted so that radiation at the EPR frequency resonates within the cavity. At high field, one may decide to employ high resolution NMR to examine chemically distinct resonance signals. A high resolution DNP spectrometer in principle does not differ from an ordinary high resolution NMR spectrometer, except that a microwave cavity must be used in conjunction with the modulation and NMR coils. Several high resolution t)NP spectrometers operating at about 3300 (refs. 3, 96, 97), 8500 (ref. 98) and 12,500 (refs. 99, 100) gauss have been described and reviewed in the literature. Low resolution spectrometers operating at about 15 (ref. 101), 175 (ref. 102) and 1070 (ref. 18) gauss have also been described. In practice, to obtain high resolution and quantitative data, a great deal of experimental ingenuity is required. We note that the resolution to be expected using any DNP spectrometer is less than that obtainable with commercially available high resolution equipment using diamagnetic samples because DNP samples of necessity contain paramagnetic additives which increase the NMR linewidth. At high field, linewidths of several Hz may be expected. The importance of high resolution DNP will be considered below when experimental results are described. B. CIDNP The experimental aspects of C1DNP are quite different from these governing electronically induced DNP. These differences arise in the main because ODNV inherently implies a chemical reaction producing radical intermediates, generally in a low steady state concentration ( ~ l0 -4 M). In addition, since the NMR signal of a diamagnetic reaction product is observed, the size of both enhanced and unenhanced NMR signals is a function of time. This makes quantitative enhancement data difficult to obtain. Further, because of the chemical reaction, it is diffÉcult to correct for leakage. Nonetheless, some idea of the magnitude of the enhancement may be obtained by one of several techniques 25'6° to be discussed below. The sign of the enhancement (emission (E) or absorption (A)) is usually evident by comparison with ordinary spectra. If ODNP is employed only to test for the presence of radical intermediates, the observation of an enhanced signal (E or A), or of a multiplet effect, is usually sufficient. On the other hand, to Advan. Mol. Relaxation Processes, 4 (1972) 229-354
290
J. POTENZA
obtain all the information relevant to the reaction mechanism contained in CIDNP spectra, quantitative measurements may be required. Finally we note that CIDNP differs from electronically induced DNP in that only a high-resolution NMR spectrometer is necessary for detection. The following paragraphs examine the above statements in greater detail. 1. Quantitative CIDNP enhancements
In the original C|DNP experiment 24, 2~, benzoyl peroxide was decomposed at 105 °C in cyclohexanone according to eqn. (55). As shown in Fig. 13, an emission signal was observed which grew to a maximum and then decayed through zero to give the absorption signal of the product when the reaction subsided. The zero signal at the time of maximum enhancement was estimated by decomposing benzoyl peroxide in the presence of FeC13 . Since Fe + 3 is paramagnetic, polarized benzene molecules were relaxed rapidly and only normal absorption signals occurred. The height of the absorption signal at a time corresponding to the maximum enhancement was then taken as a measure of the unenhanced signal strength. Enhancements so obtained will be accurate provided the added paramagnetic impurity does not affect the reaction sequence or broaden the NMR line of the product significantly. This will have to be determined for each experiment. A second approach leading to quantitative enhancements involves estimation of the steady state concentration of polarized product 6°. As an example, we consider the photodecomposition of diphenyldiazomethane in the presence of toluene (eqn. (62)). The product 1,1,2-triphenylethane showed a large multiplet effect (Fig. 16(b)). The magnitude of the multiplet enhancement was estimated by calculating the steady state [~b2CHCH2~b]* from [~b2CHCH2~b]* = n k T 1
( oo)
where n is the yield of triphenylethane, k is the zeroth-order rate constant for the decomposition of diphenyldiazomethane and 7"1 is the spin-lattice relaxation time of $2CHCH2~b. Each of n, k and T1 was measured independently and [~b2CHCH2¢]* was found to be 3.5 x 10 -4 M. The intensity of a separate standard solution of ~b2CHCH2~b was measured and compared with the CIDNP spectrum to obtain the enhancement, which in this case was 760+ 100 for one set of lines. Again, quantitative measurement of the CIDNP enhancement is not straightforward and depends on parameters obtained from other systems. Relatively large errors may be introduced if any of these parameters is inaccurate. For example, T1 is quite sensitive to the nature of the solution in which it is measured ~03 and care should be taken to ensure that 7'1 is measured for a solution closely approximating the reaction mixture. If possible, the yield of product should be obtained from the reaction mixture itself. Advan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
291
2. High-field positive enhancements The observation of enhanced signals during chemical reactions proves beyond a doubt the existence of free radicals or of radical pairs somewhere during the reaction sequence. Emission signals are easily detected and can arise from no other source. However, the observation of a small positive enhancement (ca. 2 or 3) at high external field leaves some ambiguity since this could arise from heating effects if the reaction occurs at elevated temperatures, from the transient formation of product, or from line narrowing. For protons, positive enhancements observed to date have either been extremely large or have had associated with them a multiplet effect which left no doubt as to their nature. When no multiplet effect is observed and the enhancement is too small to indicate the presence of radicals, the system should be rerun at a lower field, which should increase the size of the enhancement.
3. Radical lifetime considerations The range of radical lifetimes that can be detected by C1DNP depends on whether nuclear polarization is produced 25'27 when the radical is formed, when it is destroyed 6s, or by a radical pair mechanism. I f the former case prevails, the following considerations apply. We consider the simplest case of one electron and one nucleus each of spin ½ (Fig. 14). Because of spin conservation, when the radical forms, the ] + ) and I - ) electronic levels of the coupled spin system are equally populated if it is assumed that the electronic populations are independent of the nuclear spin states. Thus NI = N3 and N2 = iV,. The populations N1, N 3 and N2, N4 will tend toward their thermal equilibrium values with a time constant characteristic of pure electronic relaxation, T1,. I f the relaxation times for cross relaxation (1/r and 1Is) are much larger than TI~ (that is, if the relaxation rates r, s << p), no appreciable polarization will occur. Since electronic relaxation times for organic radicals are of the order of 10 .6 sec, the relaxation times for r and s transitions should be of this magnitude. Second, the rate of formation of product, kd, should be greater than the nuclear relaxation rate for the radical, q. I f ka << q, nuclear polarization will have decayed before the product is formed and observed. According to this condition. one would estimate 59 favorable radical lifetimes to lie between 1 0 - , and 10- a sec. For longer-lived radicals, the polarization would decay in the radical before observation. However, such long-lived radicals, if present in large enough concentration, should be detectable by EPR or electronically induced DNP. Finally, the steady-state concentration of radicals should be small ( ~ 1 0 - 3 - 1 0 - 4 M); otherwise, the radicals will shorten the relaxation time of the product and cause NMR detection to be difficult. I f polarization is produced via singlet-triplet crossover within radical pairs, Advan. Mol. Relaxation Processes, 4 (1972) 229-354
292
J. POTENZA
different considerations apply. For appreciable CIDNP tO be observed 65, 6 8, several conditions should be met. First, to observe net enhancement at high field, A# for the radical pair should be non-zero. This occurs, for example, when one component of the radical pair contains a heavy atom. Second, to observe multiplet spectra, the scalar electron-electron exchange coupling constant Jee should, at some point during the diffusion process, be of the same order of magnitude as the electron-nucleus coupling constant A~j, as discussed above. Finally, the rate of electronic relaxation must be small enough to permit appreciable polarization (eqn. (87)), and this polarization must be detected before it decays via spin-lattice relaxation in the product. For the systems studied by Closs 65, the ratio of polarizing transition probabilities (Wo in Fig. 21) to all transition probabilities was found to be ~0.01 and this gave large polarizations. At present there is no general consensus regarding the lower lifetime limit for the detection of radical pairs. Closs and Trifunac 1°4 have used • ~ 10-9 sec to reproduce observed spectra, Kaptein has used z > 10-10 sec, while Fischer 67 has used 10 -1~ sec. It seems safe to conclude that ~ ~ 10 - l ° sec can be detected. 4. Reaction conditions
Here, the usual conditions of kinetics apply. Concentrations of radical precursors and the temperature of the reaction mixture should be such as to provide a steady-state concentration of radicals which is neither too large or too small. For photochemical applications, the light intensity should be such as to satisfy this condition; a focused 500 watt super high pressure Hg lamp has been used successfully in many reactions 6°. In addition, the duration of the reaction should be approximately 5 min so that enhanced spectra can be recorded conveniently with commercial NMR equipment. For very fast reactions, it is possible to record NMR signals displayed on oscilloscopes photographically or with tape recorders. The latter technique has been applied 24. To conclude, we mention that, while observation of enhanced NMR signals definitely indicates the presence of unpaired electrons in the reaction vessel, the absence of such signals, because of what has been said above, does not preclude their existence.
IV. EXPERIMENTALRESULTSAND CHEMICALAPPLICATIONS-- DNP In general, the magnitude of extrapolated enhancements in solutions containing free radicals will depend upon a variety of factors, including (1) the external field strength; (2) the ratio of scalar to dipolar coupling; Advan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
(3) (4) (5) (6) (7) (8)
the the the the the the
293
temperature of the system; viscosity of the solution; free radical used; chemical environment of the receptor nucleus; type of receptor nucleus examined (e.g. 1H, 19F, sac, asp, etc.), and nature of any additional solvent.
These factors fall into two major categories: physical (1)-(4) and chemical (5)-(8). Many of these factors are also important, though in a different way, for the interpretation of high resolution NMR spectra. From a chemical standpoint, one aim of DNP measurements is to utilize observed enhancements which arise from relatively weak spin-spin interactions as a probe for the much larger electronic interactions which accompany molecular collisions in solution. Before presenting experimental results from a chemical point of view, we should examine some of the physical factors mentioned above. A. Physical factors affecting enhancement 1. Spectral density curves - dipolar vs. scalar coupling
We have already seen that the scalar transition probability c is a function of the external field strength. Depending upon the model chosen for the scalar interaction, one obtains more or less complicated expressions for c. The sticking model mentioned above gives 1°5 c(co)-
A2z~ 1 + O)2T2
(52)
while a scalar interaction modulated by molecular diffusion in the liquid gives 57 c(~o) - ns ~AEd 2 [1 +(sin/~-cos/~) exp (-/~)]
(101)
2~,2D# where # = (t~zs) ~ and o~ is the angular frequency corresponding to transition c. The other parameters involved are given by eqn. (53) except for D, the average diffusion constant of the radical and receptor nucleus. D is defined in terms of the radical-solvent distance of closest approach d and the scalar correlation time zs b y 57
z~ --
d2 D
(102)
In the zero-field limit, as ~o ~ 0, eqn. (101) reduces to eqn. (53). Different authors (ref. 106) use slightly different definitions of z. In a similar manner, expressions for the dipolar relaxation transition probAdvan. MoL Relaxation Processes, 4 (1972) 229-354
294
J. P O T E N Z A
abilities q, r and s as a function o f the external field strength may be obtained. If the dipolar interaction is modulated by rotation, one obtains 74 for q
q
3h 2 -
2 2
7~7"Zr
-
20
(103)
2 2) b 6(1 +~0nZr
where 0). = 2uv., the angular NMR frequency. Similar expressions may be obtained for r and s. Alternatively, if the dipolar interaction between the two spins is modulated by translational diffusion, q is given by s7 3r:
222
[ne h ~ v . ~ [p2 _ 2 + ((#2 _ 2) sin p + (#2 -t- 4# + 2) COS /~) exp (-- p)] q = iO \ dDp 5 ] (104) where/~ = (~o,ra) ÷ as above and the other terms are defined as previously. Similar expressions hold for r and s with the substitution o f o)e +__o9, and insertion o f the factors 2 and 4 before the right-hand side o f eqn. (104). Overall, then, the exact form of the relaxation transition probabilities will depend upon the model chosen for the spin-spin interaction (rotation, diffusion, (a) C) "rd long
eT,~l ,re(e)
( ~ I"d short
i
xi
i
I
i
ii
V2 =1 ~
i
~ ~ 1 1 1 ~ / i i i i
I
i
103 104 105 106 107 108 109 10101011 1012 ResonGnce frequency • to (b) -330 -300'
UC~H (~) -100.
I
I
I
I
I
10
102
103
10 `4
105
H (gouss)
Fig. 37. (a) Schematic dipolar spectral density plot. The n u m b e r o f molecular m o t i o n s is given as a function o f the resonance frequency o9. Curve 1 corresponds to a long dipolar correlation time, curve 2 to a shorter correlation time. (b) Anticipated extrapolated p r o t o n e n h a n c e m e n t as a function o f the external field. Scalar coupling is assumed to be absent.
Advan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
295
etc.). The choice of model then introduces certain parameters characteristic of the model such as radical-solvent distance of closest approach d, average diffusion constant D, etc. We need not concern ourselves immediately with the exact form of q, r, s and c. Rather, we will concentrate on similarities between the various formulations. All of the transition probabilities given above have several common characteristics. First, they all depend upon the quantity ~or, the frequency of interest multiplied by the correlation time between the two spins. Since the correlation time is a constant characteristic of the system, as the external field increases, co, and hence o)z, also increases. As cot ~ o% each of the transition probabilities given above approaches zero. Thus, a plot of transition probability vs. either external field strength, co, or cot would be large at low field and small at high field, as shown in Fig. 37. The correlation time for the interaction may be determined from such a plot. For the curve at half its maximum height, cot ~ 1 (ref. 45). Now, since (n is known, z may be calculated. From eqn. (102) and knowledge of the diffusion constant, one may obtain a distance of closest approach between the radical and receptor molecules. In general, individual relaxation transition probabilities cannot be measured. Rather, one measures the NMR signal enhancement or nuclear polarization 44' 73 as a function of external field. In the absence of scalar coupling, this is proportional to ( r - s ) / ( 2 q + r + s). But since s is greater than r for pure dipolar coupling, we expect large negative enhancements at low field which decay towards zero at high field (Fig. 37(b)). I f scalar coupling is also present, the situation is slightly more complicated because scalar coupling leads generally to positive enhancements. Further, since scalar and dipolar coupling are different in nature, they may have different correlation times. This is most easily understood by considering the radical solvent collision process. For a given system, the collision between radical and solvent is governed by electronic interactions between the two species and is largely independent of the external magnetic field strength, which acts as a small perturbation on the total energy. The external field, however, strongly influences the relaxation transitions which we monitor via the NMR enhancement. Now, dipolar coupling is long range while scalar coupling occurs at short range. Hence, the ratio of scalar to dipolar coupling will vary with the distance between the two spins. When the spins are far apart, dipolar coupling will predominate, while at closer distances, the ratio of scalar to dipolar coupling will increase as the electron-nucleus overlap increases. This is shown schematically in Fig. 38. Since the scalar and dipolar interactions sample the collision differently, different correlation times might be expected, and the two situations depicted in Fig. 39 arise quite naturally 2 o. More complicated behavior of the spectral density curves has also been reported 1°7 The upper part of the figure shows a dipolar spectral density such as r - s characterized by a dipolar correlation time za. Also shown are two scalar spectral densities, one for t~ < To and one for zs > zd. In terms of observables, the case z~ < Zd Advan. Mol. Relaxation Processes, 4 (1972) 229-354
296
J. POTENZA
T
I n t e h s i t y of interaction DipoLar ScaIQr
Fig. 38. Schematic comparison of scalar and dipolar coupling for bimolecular collision. For large electron-nucleus separations r~j, dipolar coupling dominates. As r~j decreases, scalar coupling becomes increasingly important.
0J "o •-
j
tt) J
c
•,oo!
I
rs>~a
L/I
j
10~ 104 109 106 107 10a 109 10~o10~110TM 101~ EPR frequency, Hz
Fig. 39. (a) Schematic scalar and dipolar spectral densities. (b) NMR enhancement curves expected from combinations of the spectral densities in (a).
would lead to a large negative NMR enhancement at low field and positive enhancements at high field (Fig. 39(b)). At zero field, the enhancement would not be the full dipolar value because of the presence of scalar coupling. With z~ > zd, the reverse would be true and we expect large positive enhancements at low field and negative enhancements at high field. By appropriately dissecting the observed enhancement spectrum, the ratio of ~ to zd may be obtained, while a single measurement at low field determines the presence of scalar coupling. 2. Effect o f viscosity I f the free radical and the solvent molecule undergoing collision are assumed to be spherical with radii r 1 and r2 respectively, the average diffusion coefficient mentioned above can be related to the viscosity of the solution t / b y the StokesAdvan. Mol. Relaxation Processes, 4 (1972) 229-354
297
DYNAMIC NUCLEAR POLARIZATION
Einstein equation. For a pure solvent, the diffusion coefficient is given by 42
O -
kT
005)
6zc~Ir
where k is Boltzmann's constant, Tis the absolute temperature and r/is the viscosity. For two species in solution DAy = (Dr +D2)/2, or DAv -- 12rtq Now, if we define a translational diffusion correlation time by za obtain 3, 10s -
121rd2 ( rl r22 1 k T \r t +r2/
=-
d2/DAv, we
(107)
whence the correlation time is directly proportional to the viscosity. Equation (107) implies that translational diffusion modulates the spin-spin interaction, that the colliding species are spherical and that chemical effects other than those contributing to viscosity are negligible. From eqn. (107), we expect an increase in viscosity to lead to longer correlation times. But since in the diffusion expressions for the relaxation rates the expression (¢oza)~ occurs as a unit, an increase in Zd has the same effect as an increase in ~o or an increase in external field strength. For pure dipolar coupling, then, we expect the extrapolated enhancement to approach zero with increasing viscosity.
3. Effect of temperature variation The effect of temperature variation upon enhancement may be treated most conveniently by considering the temperature dependence of viscosity. The typical dependence of q upon T is given by 42 =
exp
[AE/RT]
(108)
where v/o is a constant characteristic of the liquid, R is the universal gas constant, and AE is an energy barrier that must be overcome before the elementary flow process can occur. Thus, the exponential term in eqn. (108) is a Boltzmann factor related to the fraction of molecules with energy greater than that of the barrier. As the temperature increases, the viscosity of the liquid and the correlation time decrease. In fact, by combining eqns. (107) and (I08), we obtain ~°s ~a =
[_ k T
\rl +r2/
r/o exp (AE/RT)
(109)
Advan. MoL Relaxation Processes, 4 (1972)229-354
298
J. POTENZA
and, if we set the term in square brackets equal to %IT, we have TO
Zd = - T e x p ( A E / R T )
(11o)
Since a decrease in za is equivalent to lowering the magnetic field strength, an increase in T will give an increase in enhancement for pure dipolar coupling modulated by diffusion. The presence of scalar coupling and/or rotational contributions to the relaxation rate will lead to more complicated behavior.
4. Physical parameters obtainable from DNP measurements In principle, by utilizing the equations developed above in conjunction with DNP measurements, it is possible to determine values for electron nucleus correlation times z, radical-solvent distance of closest approach d, energies of activation AE, and average diffusion constants D. Further, DNP can yield information regarding the type of molecular motions in the liquid (rotational, translational, etc.). When scalar coupling is present, the intermolecular hyperfine coupling constant A and the scalar correlation time z~ may also be determined. The scalar correlation time may be related to the length of time molecules "stick" together in solution, while, in some cases, A may be governed by the intensity of the electronic interaction during collision. The manner in which these parameters are obtained is not straightforward since generally a given solution has more than one type of coupling or motion. As a result, one generally assumes a value for one parameter and calculates the remaining variables with respect to the one assumed. By iteration, a consistent set of parameters may be obtained. Overall, DNP measurements have the potential of yielding a rather detailed microscopic description of the liquid state.
B. Experimental results for protons In this and following sections, no attempt will be made to survey completely all experimental results. Rather, those results will be presented which serve to illustrate general trends and amplify points presented above.
1. Low-fieM measurements At low fields ( < 200 gauss), proton NMR enhancements generally extrapolate close to the dipolar limit. That is, regardless of the free radical or receptor molecule used, protons in organic solutions containing free radicals generally show no scalar coupling 3' 109. No value of lU® n[ smaller than 330 has ever been reported for intermolecular collisions. Typical results at 74 gauss for a variety of free radicals are shown in Table 6 for mixed hydrocarbon-fluorocarbon solutions TM. Several
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCELAR
299
POLARIZATION
TABLE 6 D Y N A M I C P O L A R I Z A T I O N IN HEXAFLUOROBENZENE S O L U T I O N S
Reprinted with permission f r o m ref. 74. Radical
Additional solvent
Relaxation time (sec) TH
Tv
Maximum observed Extrapolated enhancement enhancement Uoov
Contact component cv
Gn
Gv
Uoon
--22
-- 14
--310 a --200
2.6
PODS
D M S O (80 %)
GALV
None Benzene (50 9/oo) Acetone (90 %)
1.1 i.8
0.7 1.0 1.0
--225 --210
-- 165 --155 --120
--325 --315
-- 200 --200 --145
2.6 2.6 3.9
None Benzene (50 %) A c e t o n e (50 9/oo)
0.5 0.3
0.5 0.2
--295 --285
--115 --170 --120
--310 --315
--150 --190 --135
3.8 2.8 4.2
TPPO
Benzene (90 %)
6.7
5.3
--155
--16
--310
--32
7.3
PAC a
Benzene (50 ~ ) , CC1. (40 %)
2.6
1.7
--53
--7
--310
--40
7.0
None Benzene (50 %) A c e t o n e (50 ~ )
0.6 0.7
0.8 0.7 0.6
--55 --80
--0.3 --2.3 --9
--310 --310
--2 --13 --35
8.4 7.9 7.2
None Benzene (50 %/00)
4.7
<0.3 3.4
--210
--300
+20 +40
9.2 10.0
TTBP
DPPH
BDPA
+16 +30
PBSQ b
A c e t o n e (80 ~ )
--20
--5.5
--310
--75
5.9
"I-FSQ c
A c e t o n e (90 ~ ) E t h a n o l (90 ~o)
--4 --24
+0.5 --13
--310 --310
+35 --150
9.7 3.3
TCSQ
Acetone (90 ~ )
3.4
2.7
--210
+165
--280
+195
18.5
TPV
Benzene (50 ~ ) A c e t o n e (90 %)
1.0
0.3
--75 -- 105
+75 +95
--310 --310
+300 +270
28.0 24.7
TPPY
Benzene (90 9/00) A c e t o n e (90 %)
7.8 5.1
3.5 1.9
--140 --170
+170 +260
--270 --270
+210 +300
19.7 28.0
WBPC
A c e t o n e (90 ~ )
2.3
1.4
--130
+135
--300
+240
22.1
NNI
T e t r a h y d r o f u r a n (99 ~ )
--5
+I0
--225
+450
56
a P A C = picryl a m i n o carbazyl; b PBSQ = p-benzo-semiquinone; T F S Q = tetrafluoro semiquinone. n Figures in italics were obtained u s i n g the ratio m e t h o d TM.
points are worth mentioning with regard to proton enhancements. First, although the maximum observed 1H enhancements Gn cover a relatively large range, extrapolated enhancements U~a are all near the dipolar limit. The values for TCSQ and TPPY fall somewhat above this limit, but not outside the experimental error. Advan. MoL Relaxation Processes, 4 (1972) 229-354
300
J. POTENZA
Thus, the presence of scalar coupling is questionable. Second, we note that the radicals used in this study cover a wide range of chemical types. For example, GALV and TTBP both contain bulky t-butyl groups with little or no electron density as determined by EPR. Hence, for these radicals, the unpaired electron should be unable to effectively delocalize over the proton-containing solvent and little or no scalar coupling is expected. On the other hand, radicals such as TCSQ are not sterically well shielded and the unpaired electron, which is located primarily in the molecular 7t system, should be able to interact strongly with solvent electrons. In addition, we note that the chemical environment of the proton also has little or no effect upon the ultimate enhancement; e.g. the protons of acetone, benzene, etc., behave equivalently at low field 3. Because low-field 1H enhancements are purely dipolar in character, they are largely uninteresting except in their relation to highfield measurements, to which we now direct our attention.
2. High- and multifieM measurements Proton DNP measurements x09 for a variety of substituted methanes at 3300 and 12,500 gauss are shown in Table 7. As expected, all enhancements are negative and U~oHat both fields changes markedly as the receptor molecule is changed. The results shown were interpreted in terms of dipolar coupling only. A model for the electron-nucleus spin-spin interaction based on translational diffusion was assumed and a comparison of extrapolated enhancements with those expected on the basis of the model chosen gave values for the diffusional correlation time Za the radical-solvent distance of closest approach d, and the mean diffusion coefficient D. Notice that the values for zd increase with increasing viscosity as expected from eqn. (107). In addition, the values for D increase with decreasing viscosity as expected intuitively and from eqn. (106), although the agreement here is not exact. TABLE 7 PROTON DNP RESULTS AT 3300 AND 12,500 GAUSS USING T T B P R e p r i n t e d with p e r m i s s i o n from ref. 109.
Solvent
Uooa(3300) Uoon(12,500)
zd d (sec×lO u ) (/t)
D × 106 ~7a A# (cm2.sec -1) ( P x I O 2) (p.p.m.)
CHa*OH CHaOH* CHaI CH2Iz CH2Br2 CH2CI2 CHBra CHCl3 CHFCIz
--200d:30 --235±35 --2564-20 --102±8 --141+8 --2314-17 -- 674-5 --213d:10 --265±10
84-2 5il 3+1.5 244-2.5 15±2 54-0.6 364-1.5 6±1.5 2.4~0.5
15 19 28 5 9 12 9 11 18
-- 654-20 -- 905:40 --1214-30 -- 3 7 i 1 5 -- 5 4 ± 1 5 --1034-15 -- 214-4 -- 854-5 --134±20
a T a k e n from Handbook of Chemistry and Physics.
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
3.3 3.0 3.0 3.3 3.6 2.4 5.5 2.6 2.1
0.597 0.597 0.500 2.822 1.030 0.430 1.975 0.580 0.412
0 0 219.0 187.0 139.5 1.9 136.0 9.4 39.6
DYNAMIC
NUCLEAR
POLARIZATION
301
Two results from Table 7 are quite interesting. First, the diffusion coefficient for the methyl protons on methanol is smaller than that for the O H protons. To interpret this, it was suggested that chemical exchange contributes significantly to the diffusion of the O H proton. The second result of interest concerns the last column in Table 7 which gives solvent g shifts for the TTBP radical in parts per million. The values of Ag entered in the Table measure the extent to which the electron resonance of the free radical is shifted to higher g values. Since Ag values were corrected for nuclear resonance and bulk susceptibility effects 1°9, Ag indicates that some of the unpaired electron interacts with the solvent. However, even though the unpaired electron is perturbed, no scalar coupling for protons is observed. Since there would appear to be no lack of translational molecular motions to modulate the coupling, it would seem that the lack of contact coupling here arises because very little of the unpaired electron is actually present at the H nucleus. For most proton systems studied, translational motions describe the relaxation quite well. However, Kruger et al. 99 found that for solutions of toluene in p-chloroBDPA, a rotational contribution was required at low temperatures. This they determined by measuring Uoo. at five widely separated field strengths (15, 175, 1070, 3410 and 13,200 gauss) and several temperatures between 73 °C and - 120 °C. Their experimental results are shown in Fig. 40. At 15 gauss, proton enhancements all lie within experimental error of the dipolar limit. As the field is
"-, L "'i,""
'
:
'7,~/r<-1o T,/r<-2r,/r<~l
10 8
i
,
:
IC#
44MHz
i }
493MHZ
i"2 1(~° :
~\
\
] I 10"
I°
] ', S -~ 10 '2
3GHz ~SGHZ 37GHz CaS
Fig. 40. Extrapolated proton enhancements for toluene as a function of frequency and temperature. The radical used was bisdiphenylene-p-chlorophenyl allyl. Reprinted with permission from ref. 99. increased, U~n becomes more and more sensitive to temperature. At all fields, the enhancement decreases with decreasing temperature as expected. Analysis of the data showed that enhancement spectra between - 4 0 and 73 °C could be interpreted by translational diffusion alone. At temperatures below - 4 0 °C, rotation became important, and the curves could be fitted by assuming that the relative importance of rotation to translation was 0.3. This gave the ratios of rotational to translational correlation times Zr/Zt shown in Fig. 40. With decreasing temperAdvan. Mol. Relaxation Processes, 4 (1972) 229-354
J. POTENZA
302
ature T,/rt increases. It was further shown that both rotational and translational motions followed an activation law T t , r ~--- "t"0 e x p
[AE/RT]
(111)
By measuring the relaxation times T1 and 7"2 at various temperatures, the energies of translational and rotational activation were evaluated, Thus AEt = 3.1 kcal/ mole and AEr = 7.8 kcal/mole for toluene. In chemical terms, toluene does not solvate the free radical at high temperatures. As the temperature is lowered, complexes form, probably because of collisions between the n systems of the radical and solvent. On the average, the coordination number of toluene with the radical was 0.6, indicating extremely weak solvation. This may be contrasted with aqueous solutions where the coordination number is much larger and solvation effects much stronger.
3. Exceptions to the rule--scalar coupling for protons Proton scalar coupling has been observed in several cases. The first case reported was for MnC12 in aqueous solutions ~°. Here, Mn + ÷ was used to supply unpaired electrons and the proton NMR spectrum of water was recorded. At 10 gauss, large positive enhancements were observed (Fig. 41) for various concentrations of MnCI2. Very high RF power was required to saturate the Mn ÷ ÷ hyperfine multiplets because of the short relaxation time of Mn + +. Short relaxation times are characteristic of transition metal ions. 10.C
& X o [3
0.001M MnCI~aqueous Solution 0.0025M = ,, ,, o 0.005 M . . . .°x~ x 0.01M t3
GH 1C
9/°
o
/~ O/° 1"~.1 1,o Electron resonance s a t u r a t i n g
/4x & Ho-lOGQUSS Ternp~ 25"C 10 field Hle ~n GQU$S
Fig. 41. Proton resonance enhancement in aqueous MnCIz solutions as a function of RF saturating power. Reprinted with permission from ref. 10. Positive 1H enhancements were also observed in organic solutions by Dwek et al. 110 for the t-butyl groups of tri-t-butyl phenol in TTBP. Many solvents similar to tri-t-butyl phenol were used, but these did not.give positive enhancements (Table 8). As a result, it was concluded that both TTBP and its precursor were
Advan. MoL RelaxationProcesses, 4 (1972) 229-354
DYNAMIC
TABLE
NUCLEAR
303
POLARIZATION
8
PROTON DNP MEASUREMENTS WITH T T B P Reprinted
AT 3 3 0 0 GAUSS
w i t h p e r m i s s i o n f r o m ref. 110.
Compound
Mono-t-butyl
Si#n o f enhancement
benzene
1,3,5-Trimethyl benzene Hexamethyl
CHa
Aromatic
Other
--
--
--
--
--
--
OMe
--
--
OMe
--
--
OMe
--
--
OMe
--
--
benzene
1- M e t h o x y - 2 , 4 , 6 - t r i m e t h y l 1-Methoxy-4-t-butyl
benzene
benzene
1-Methoxy-2,6-t-butyl
benzene
1-Methoxy-3,5-t-butyl
benzene
Di-t-butyl benzene 1,3,5-Triphenyl benzene Tri-2-butoxylethyl
phosphate
Tri-t-butyl phosphate 1-Methoxy-2,4,6-t-butyl
benzene
Tri-t-butyl phenol
--
CH2
--
--
--
--
q-
--
OMe
required to give the positive enhancement, and that this arose as a result of proton exchange between TTBP and tri-t-butyl phenol, viz. ROH+RO. = RO.+ROH
(112)
In the radical, all protons are subjected to strong scalar coupling. When proton exchange occurs to form the diamagnetic phenol whose NMR spectrum is being recorded, the positive polarization will remain and will start to decay to the expected negative value for intermolecular coupling. That the ring protons exhibit no scalar coupling is attributed to the lack of a suitable modulating mechanism (motion). For the t-butyl protons, modulation by rotation of the t-butyl groups was postulated. However, this interpretation was questioned by Hausser and Stehlik 73. For the aqueous MnC12 solutions considered above, a similar interpretation is possible. While in the solvation sphere of Mn + +, the protons of water are subjected to strong scalar coupling. If they exchange rapidly with the solution, a net positive enhancement can be observed. The examples above serve to illustrate the type of information obtainable from 1H DNP measurements. In addition to protons, X 9 F and 3 1 p nuclei have been studied in some detail, and these have the added characteristic of showing scalar coupling. We turn now to 1 9 F . Advan. Mol. Relaxation Processes,
4 (1972) 229-354
304
s. POTENZA
C. Experimental results f o r fluorine nuclei 1. Low-field measurements
In contrast to hydrogen, the dynamic polarization of 19 F nuclei is extremely sensitive to the detailed chemical environment of the resonating nucleus. Observed enhancements are governed both by the type of free radical and fluorocarbon present. The effect of varying the free radical 74 is vividly demonstrated in Table 6 which lists DNP results at 74 gauss for C 6 F 6 with a variety of free radicals. Extrapolated 19 F enhancements vary from - 2 0 0 , which is far removed from the dipolar limit ( - 3 5 0 for fluorine) to +450, which is approximately 65 ~ of the scalar limit. Fluorine contact components, cv, derived from the observed enhancements using eqn. (47) with q/3.0 = r/1.7 = s/10.1, vary from c F = 2.6 for PODS and G A L V to 56 for naphthalene negative ion. Hence, for systems with large negative enhancements, dipolar coupling dominates the spin-spin interaction, while for systems with large positive enhancements, the reverse is true. For example, with WBPC, we may calculate the ratio of scalar to dipolar coupling as: c
22.1 -
2q+r+s
1.24
17.8
It is interesting to note that sterically well shielded radicals such as TTBP and GALV, which contain bulky t-butyl groups, lead to more negative enhancements than relatively planar radicals such as TCSQ and TPPY. It may be, then, that 19F scalar coupling is related to the availability of the odd electron at the radical edge. A second example of the sensitivity of 19 F NMR enhancements to radical type is given in Table 9 which shows values 74 of U~ovfor CFaCCI 3. Again, some fluorine scalar coupling is observed in all cases. Further, comparison with the C 6 F 6 TABLE 9 DYNAMIC POLARIZATIONIN 1, I, I-TRIFLUORO-2,2)2-TRICHLOROETHANE Reprinted with permission from ref. 74.
Radical
Additional solvent
Relaxation Maximumobserved Extrapolated time (sec) enhancement enhancement TH
GALV TTBP DPPH TCSQ WPBC
Acetone None Acetone Acetone Acetone
(50 ~) (50 ~o) (90~) (75 ~)
TF
1.4 1.1 0.3 0.6 0.6 2.5 2.8 5.1 3.6
GH
--245
GF
--210 --220 --89 --68 --265 --115 --70 +9
Advan. MoL Relaxation Processes, 4 (1972) 229-354
U~H
U~F
--320 --270 --280 --310
--240
--325
--160
--310
+40
Contact
relaxation component cF
1.1 1.0 1.7 3.6 10.0
DYNAMIC
NUCLEAR
305
POLARIZATION
results shows that for any given radical, CFaCC13, which contains aliphatic fluorine, shows less scalar coupling than C6F6. Fluorine scalar rates for a larger selection of aromatic and aliphatic fluorocarbons 56 are shown in Table l0 and in Figs. 42 and 43. For Table 10, the free radical DPPH was used exclusively. Relatively small values of cF for aliphatic fluorocarbons are again reported, and it is interesting to note that the largest scalar rate for aliphatics comes from 1,2,4-trifluorobromobutene which has one F adjacent to a double bond. Figure 42, which shows cF for a variety of fluorobenzenes, is interesting in several respects. First, with DPPH, CF increases with T A B L E 10 EXTRAPOLATED
~gF ENHANCEMENTS
DPPH
WITH
AT
74 GAUSS
R e p r i n t e d with permission f r o m ref. 56.
Fluorocarbon
Additional solvent
Uoo
c~
1,1,1-Trifluoro-2,2,2-trichloroethane 1,2-Dichloro- 1,2-difluoroethane
50 % acetone None 50 ~ acetone 50 % acetone 50 ~ acetone None 5 ~ a c e t o n e - 9 0 % CCI, None 5 % a c e t o n e - 9 0 % CC14 5 % acetone-90 % CCI, None 50 ~ acetone 50 % acetone 50 % acetone 50 % acetone 50 % acetone 50 % acetone
-- 235 -- 170 -- 180 --230 --205 -- 185 --205 -- t90 --240 --200 -- 170 -- 15 --40 --55 --25 --35 -- 50
1.8 3.1 2.8 1.8 2.3 2.7 2.3 2.6 1.6 2.4 3.0 7.5 6.6 6.2 7.1 6.8 6.4
!,2-Difluoro-l,l,2,2-tetrachloroethane 1,1,2,2-Tetrafluoro- 1,2-dibromoethane 0q~,0t-Trifluorotoluene Perfluoro-n-hexane 1-Fluoro-n-octane Perfluorocyclohexane Perfluorodecalin 1,2,4-Trifluorobromobutene Hexafluorobenzene
1,2-Dibromotetrafluorobenzene 1,2-Diiodotetrafluorobenzene Chloropentafluorobenzene Bromopentafluorobenzene Iodopentafluorobenzene
*20 • DPPH a Golvinoxyl
•
0
-50
~ "U u
(J
~5
n
E
-~oo
~
-200
~
4
o 3 o
2
ee D o O D o D
~,
81 0
1
2
3
4
5
6
-350
Number of fluorines on benzene ring
Fig. 42. Fluorine contact coupling in substituted fluorobenzenes with G A L V a n d D P P H . Reprinted with permission f r o m ref. 56.
Advan. MoL Relaxation Processes, 4 (1972) 229-354
306
J. POT~NZh
4.4
4.2
,~ •"
/ l > " ~ " - - m NOz i,,¢,-- . . . . . . -a I
4.0
3.6
./
.2 u 3,2 2.8 P-6
/
x
g '. . . . ORTHO META
' PARA
Substituent p o s i t i o n r e l a t i v e to fluoPine
Fig, 43. Fluorine contact coupling in substituted fluorobenzenes with DPPH. Reprinted with permission from ref. 56.
the number of fluorines on the ring, in contrast to GALV. Secondly, values for these aromatic fluorines are all larger than the aliphatic values in Table 9. Lastly, DNP measurements for several disubstituted benzenes (Fig. 43), show that fluorine meta to any substituent shows a higher scalar rate than when it is ortho or para. Apparently, DNP measurements are sensitive to ~-orbital effects. In sum, these low-field results indicate a sensitivity of fluorine DNP to chemical environment at least as great as that of the chemical shift.
2. Possible interpretations for scalar coupling Physically, variations in cv could arise from changes in either A or zs (eqn. (52)). An increase in A upon change of radical would indicate greater unpaired electron density at the fluorine nucleus (eqn. (39)), while an increase in zs would indicate either greater microviscosity or a tendency for the colliding species to stick together. Values for A and Ts may be obtained from multifield measurements, and these will be presented later. Chemically, two mechanisms for scalar coupling are plausible: exchange polarization 111, after the manner of coupling on free radicals, and complex formation. Exchange polarization may be understood as follows. Consider a radical such as benzene negative ion which has an unpaired electron in arc orbital formed from the atomic 2p= orbitals of carbon. Since the n orbital contains a node in the plane of the ring, we expect no spin density at hydrogen. However, EPR results for this and other hydrocarbon radicals 3~ show beyond doubt that the protons of aromatic free radicals contain some spin density which originates via exchange polarization of the C - H sigma bond. For example, the EPR spectrum 112 of C6Iq 6 - consists of 7 equally spaced lines because of hyperfine coupling of the electron with six equivalent protons. Adman. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
307
POLARIZATION
In Fig. 44(a), one of the C - H bonds of C6H6- with two paired electrons is shown, along with a C2pz orbital which has some spin density. The question is" does this electronic configuration give a valid description of C r H 6 - ? The answer is no, because the odd electron will tend to unpair the electrons in the C - H bond. A more realistic description of the bonding is shown in Fig. 44(b). There, the electrons in the C - H bond are correlated with the odd electron. This slight unpairing of electrons in the C - H bond gives rise to spin density at H of the opposite sign from that of the unpaired electron if it is assumed that the partial triplet formed is lower in energy than the corresponding singlet; in this case the hyperfine coupling constant would be negative. For protons on aromatic radicals, one electron in a 2p orbital at C produces 35, 113 a hyperfine splitting A of approximately 25 gauss. Smaller values of spin density give proportionally smaller splittings. 1 e - ~ 25 G
(a)
(b)
1e-~ 100 G
66
1 e-tu 700 O
(c)
Fig. 44. Intrarnolecular exchange polarization. (a) T h e n a n d a orbitals o f C r H r - are regarded as distinct. (b) A zt-cr interaction unpairs slightly the electrons o f the C - H b o n d leading to spin density at H. (c) F o r C r H s F - , two polarizations are possible, each o f different sign, a n d a net spin density is observed.
For fluorine, the situation is more complicated in that fluorine may participate in the n system, Two types of polarization, shown schematically in Fig. 44(c), are possible. The first is equivalent to that with protons except that 1 e at C gives114 a splitting of approximately 100 gauss. At fluorine, one electron in a 2p orbital gives 114 a splitting of approximately 700 gauss. Further, the sign of the spin density will be opposite to that for polarization at carbon and one should observe a hyperfine splitting A which depends upon the n e t spin density at F. This in turn should depend on the fraction of the odd electron located at C and at F. For intermolecular coupling, similar arguments apply except that the unpaired electron and the magnetic nucleus are on different compounds. Figure 45 shows one possibility for fluorobenzene colliding with p-benzosemiquinone. During the collision, the odd electron may slightly unpair the electrons at fluorine, or it may interact with the vacant n orbitals of fluorobenzene if one is available. Advan. MoL Relaxation Processes, 4 (1972) 229-354
308
J. POTENZA
Fig. 45. Interrnolecular exchange polarization. The unpaired n electron of benzoserniquinone delocalizes into vacant z~orbitals on fluorobenzene. By a n-a polarization of the C-F bond, spin density arises at F. In either case, some spin density can result at the F nucleus by the above mechanism, but here the degree of polarization depends upon the relative orientation and time of contact of the colliding species. Complex formation, the second mechanism, occurs when the electrons of both molecules become delocalized or redistributed upon association. Complexes have been found responsible for solvent effects in EPR spectra lj5' 116. There, the solvent perturbs the unpaired electron causing a change of electron density and consequent changes in A. With one, we are looking at the reverse effect, that of the radical on the solvent. Qualitatively, exchange polarization and complex formation can account for low-field 19F enhancements 19. For example, since a-orbitals do not lead to complex formation in general, aliphatics should have lower scalar rates than aromatics if this mechanism is dominant. Further, well-shielded radicals such as TTBP and GALV which contain very little spin density in exposed positions should neither complex well nor lead to large degrees of exchange polarization. They should then give large negative enhancements, as is observed. On the other hand, poorly shielded planar radicals colliding with aromatic fluorocarbons should complex readily, polarize strongly and give large positive enhancements. The absence of scalar coupling for protons in C - H bonds may be understood in terms of the relatively small coupling parameter of hydrogen (25 gauss/electron) as compared with fluorine. These ideas received further support from molecular orbital calculations involving benzosemiquinone and various fluorocarbons 19. Induced spin densities at fluorine for comparable collision attitudes were shown to increase in the order CF 4 < C6HsF < C6H 6 < C10F8 (Fig. 46). The behavior of the fluorobenzenes with D P P H in Fig. 42 may be understood on this basis. Further, plane-plane collisions between aromatics were shown to be much more effective in leading to Advan. MoL Relaxation Processes,
4 (1972) 229-354
309
DYNAMIC NUCLEAR POLARIZATION
Q
0
2"2~5A~-1.70
~
3.75
O.
0.85
Q05
~'I"~F0.00
105 F
0.60 Q 0.15 Q30 O.I
OO5
0.30
F4.35
5~~.~F
Q95
o~o.L ~""~/~,/ ~Fa05 F 035
F 1.10
0.95 3.80.'"
ODO F
O35
F F
Q10
.Q
F010
005
Fig. 46. Induced spin densities ( × 104) for several fluorocarbons in collision with benzosemiquinone. The radical is located 2.25 A from F with its plane in the plane of the paper.
spin density at F than edge-on collisions. This raises the question of possibly detecting stereospecific collisions in liquids. The results in Fig. 46 also indicate that collisions far removed from F can effectively produce spin density at F; e.g. spin information is transmitted over a relatively long distance. Last, we observe that only a small fraction of the electron (about 0.001) need be transferred to the solvent to produce appreciable polarization. 3. MultifieM measurements M u l t i f i e l d 19F DNP results have been reported by several groups (refs. 20, 55, 105, 106, 108, 109, 117, 118). Except for the results presented below, these have been restricted in nature, either with regard to the number of fields examined or to the chemical compounds used. Below, we shall consider a variegated array of radicals and fluorocarbons at widely separated field strengths. This has the advantage of allowing broad chemical trends in the data to be examined. U l t i m a t e 19F NMR enhancements at four field strengths 118 are shown in Table 11. Sixteen radical-solvent pairs were studied. These included all combinations of the fluorocarbons C F 3 C C 1 3 (TCF); ~,a,~-trifluorotoluene (TFT), hexafluorobenzene (HFB) and octafluoronaphthalene (OFN) with the radicals TTBP, GALV, TCSQ and TPPY. Both radicals and fluorocarbons span a wide Advan. Mol. Relaxation Processes, 4 (1972) 229-354
310
J. P O T E N Z A
T A B L E 11 ULTIMATE 1 9 F NMR ENHANCEMENTS AS A FUNCTION OF MAGNETIC FIELD STRENGTH
Reprinted with permission f r o m ref. 118.
Field TCF strength (gauss) U~H
Uoov
U~on
UooF
U~H
UooF
U~H
U~v
TTBP
74 3050 3650 8900
--310 --250 --260 --82
--235 --55 --40 +5
--310 --190 --165 --81
--240 -- 27 --22 --7
--315 --260 --275 --83
--135 --21 +11 +48
--310 --260 --240 --66
--180 --22 --20 +39
GALV
74 3050 3650 8900
--320 --175 --170 --28
--225 --19 --6 +12
--310 --185 --155 --33
--230 --25 --7 +3.5
--315 --210 --185 --34
--145 +7 +13 +29
--320 --145 --155 --32
+135 +25 +49 +44
TCSQ
74 3050 3650 8900
--325 --145 --140 --66
--240 --26 --7 --23
--315 --140 --140 --45
--150 --13 --7 --3
--280 --110 --97 --38
+195 --20 --11 -- 15
--280 --105 --120 --40
+375 --35 --29 --23
TPPY
74 3050 3650 8900
--310 --175 --170 --37
--80 --12 --6 +6
--310 --175 --150 --76
--30 --7 --2 +3
--270 --165 --160 --63
+300 +31 +22 +60
--300 --185 --185 --45
+445 --31 --17 +21
Radical
TFT
HFB
OFN
range of chemical types. Examination of the results reveal that the enhancements fall into two distinct categories: systems which give large negative low-field enhancements tend to cross the axis and become positive at high field, while systems with positive low-field enhancements become negative at high field. Curiously, TPPY with OFN, the most positive low-field system studied, crosses the axis twice. A single crossing of the axis is consistent with the spectral density curves in Fig. 39, and indicates that systems with large positive low-field enhancements have zs > zaHowever, the simple spectra in Fig. 39 do not predict two crossings, and this could be due to two scalar correlation times or to a more complicated frequency spectrum of molecular motions '°7. Analysis of the results in Table 11 gave the values of A, zs and za shown in Table 12. Dipolar correlation times show no apparent trends, while both zs and A increase with increasing low-field enhancement. Hence, systems with small values for cv show weak hyperfine coupling and short scalar correlation times. In contrast, systems with large values for CF have both strong hyperfine coupling and long scalar correlation times. Overall, this is precisely the behavior expected chemically if increases in A correspond to increases in exchange polarization and increases in zs to sticky collisions and increased complexation. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR P O L A R I Z A T I O N
311
TABLE 12 CORRELATION TIMES a AND RELATIVE SCALAR HYPERF1NE COUPLING ENERGIES FOR FLUORINE NUCLEI IN FREE-RADICAL SOLUTIONS
Reprinted with permission from ref. 118. Radical
TCF
TFT
HFB
OFN
Td
Ts
Arel
Td
Ts
Arel
Td
Ts
Arel
Td
Ts
-~rel
TTBP
1,6 (S)
0.7
2.3
2.4 (S)
0.9
2.4
1.6 (S)
0.8
3.0
1.8 (S)
0.7
2.9
GALV
3.2 (S)
0.9
2.6
2.9 (S)
1.0
2.4
2.6 (t)
1.4
2.9
3.5 (D)
4.0
4.1
TCSQ
2.3 (S)
1.0
1.8
3.3 (1)
2.2
2.7
2.4 (O)
6.0
3.1
2.0 (O)
11.0 3.5
PPY
3.0 (1)
2.5
2.7
2.0 (D)
1,8
3.2
2.1 (D)
5.5
3.9
2.4 (D)
11.5 4.5
a Times are in units 10-11 sec. A l t h o u g h it is n o t i m m e d i a t e l y a p p a r e n t , several a d d i t i o n a l interesting conclusions m a y be d r a w n f r o m the analysis o f the d a t a in Tables 11 a n d 12 when s u p p l e m e n t e d b y results o f L C A O - M O calculations, W e assume that the three generalized r a d i c a l - s o l v e n t collision attitudes shown in Fig. 47 are representative o f the collision process between a r o m a t i c molecules 19. F o r p l a n e - p l a n e a n d at y p e collisions, o v e r l a p o f the 2p electrons c o m p r i s i n g the radical ~ system with the F2p o r b i t a l is o f the ( 2 p - 2 p ) a-type, whereas for n collisions, it is ( 2 p - 2 p ) re. T h e relative effectiveness o f these collisions for the t r a n s m i s s i o n o f spin inform a t i o n to fluorine nuclei m a y be crudely assessed by c o m p a r i n g ( 2 p - 2 p ) a a n d (a) ~
(b)
CONTACT
ff CONTACT
f~ jJ
(c~ PLaNE-PLANECONTACT i I
'/ ~J
Fig. 47. Generalized collision attitudes for fluorobenzene and benzosemiquinone. Reprinted with permission from ref. 19. Advan. MoL Relaxation Processes, 4 (1972) 229-354
312
J. P O T E N Z A
TABLE 13 O V E R L A P I N T E G R A L S S FOR F " ' " O SYSTEM
Reprinted with permission from ref. 19. ru
S,
S,
SdS,
2.00
0.05615
0.00980
5.74
2.25 2,50
0.02839 0.01367
0.00417 0.00173
6.81 7.90
2.75
0.00633
0.00070
9.08
3.00
0.00284
0.00028
10.2
3.25
0.00124
0.00011
11.3
(2p-2p) n overlap integrals for a F atom separated by a distance r o. f r o m an oxygen a t o m (if the collision is with G A L V or TTBP). These integrals are given in Table 13, f r o m which it is apparent that a overlap is much greater than n overlap, the ratio increasing with increasing distance between the nuclei. Somewhat more refined calculations confirmed these results and led to estimates o f intermolecular potentials for the various collision attitudes between benzosemiquinone and several fluorocarbons. A screened c o u l o m b potential of approximate form exp [ - 2 ( r ~ - d ) ] was assumed. Here r u is the distance between F and O nuclei, d is the distance o f closest approach, and 2 describes h o w rapidly the interaction energy increases as the molecules move closer together. Values 19 for 2 are shown in Table 14. F o r both n and plane-plane collisions, 2 is nearly independent o f the fluorocarbon chosen, while for tr collisions this is not true. M o r e important, 2 for plane-plane collisions is considerably smaller than for either rc or a collisions. A small value of ), indicates a gently rising potential and therefore for plane-plane collisions, we expect buildup and decay of spin density
Spin density
¢ T~me
(a)
~
Time
P
(b)
T~me ~
(c)
Time
(d)
Fig. 48. Schematic comparison of collisional pulse shapes for (a) plane-plane, (b) a, (c) ~ collisions. The height of the pulse will depend on the spin density at F, while its width is governed by 2 or r~. Part (d) shows the pulse that best fits ONP data for C 6 F 6 with GALV and TTBP (ref. 106). Advan. Moi. Relaxation Processes, 4 (1972) 229-354
313
DYNAMIC NUCLEAR POLARIZATION TABLE 14 AVERAGE VALUES OF /~ FOR V A R I O U S F L U O R O C A R B O N S A N D C O L L I S I O N T Y P E S
Reprinted with permission from ref. 19.
a Plane-plane
CH4
CF4
C6H~F
~
6.2 9.8
6.4 6.6 3.2
6.6
2.8
3.4
at fluorine over a relatively long period of time. In contrast, for n and a collisions, the interaction time should be smaller. This is shown schematically in Fig. 48. The half width of each pulse is roughly equal to the scalar correlation time. We are now in a position to interpret multifield fluorocarbon DNP results in terms of probable collision pulses 106, 1a8, 119. For systems with predominantly n interactions, we expect short scalar correlation times, while when plane-plane collisions become important, zs should increase. Qualitatively, this is in agreement with the enhancement data, since aromatic radicals and aromatic fluorocarbons give the largest correlation times. A more detailed analysis of these collision pulses (ref. 119) also accounts for the rate of enhancement decline with increasing feld strength. An example of stereospecific collision pulses was given by Mi.iller-Warmuth et al. 106 who studied the DNP field dependence of several fluorocarbons with GALV and TTBP. For aliphatic fluorocarbons, the enhancement spectra could be interpreted in terms of simple pulses such as those in Fig. 48(a)-(c). However, with C6F 6 , the only aromatic fluorocarbon used, a simple pulse shape could not be used. Rather, the complex pulse shown in Fig. 48(d) was used. This pulse probably arises from a combination of n and tr collisions. The above results show that the type of information available from 19F DNP, because of scalar coupling, is quite different from that obtained from ~H spectra. Because they are sensitive to chemical effects, 19F enhancements may be used to probe molecular collisions more from a chemical viewpoint.
D. Experimental results for phosphorus nuclei 1. Low-field results Phosphorus DNP results are not as extensive as those for either 19F o r tH. This is because phosphorus NMR signals are relatively difficult to detect experimentally, and because many free radicals decompose rapidly in the presence of phosphorus-containing compounds. Fortunately, BDPA is stable for weeks with almost any phosphorus-containing compound 12°, and with this radical, many systems Advan. Mol. Relaxation Processes, 4 (1972) 229-354
314
J.
POTENZA
T A B L E 15 3 I p DNP PARAMETERS FOR PENTAVALENT PHOSPHORUS WITH B D P A AT 74 GAUSS R e p r i n t e d with permission f r o m ref. 120.
Solvent
Gloon
G~n
Gloop
G~p
Uoop
ce
--160 --115 --195 -- 285 --280
--270 --70 --2 + 550 +430
--300 --90 --5 + 825 +600
--590 --240 --8 + 895 +670
1.3 4.8 7.9 39.1 25.6
--220 --320 --230 --310
--350 --480 +245 +550
--420 --550 +370 +705
--600 --550 +500 +705
1.2 1.6 19.2 27.2
--165 --210 -- 180 -- 160 --170 -- 330 --275
--310 --190 -- 195 -- 270 --80 -- 445 --60
--350 --280 -- 350 -- 300 --150 -- 580 --90
--650 --415 -- 595 -- 590 --280 -- 580 -- 100
0.8 2.8 1.2 1.2 4.3 1.4 6.5
--155 --330 --155 --155
+40 +30 +30 +95
+60 +40 +45 +130
+125 +40 +90 +260
10.1 8.6 9.4 12.8
Phenylphosphonic halides (C6Hs)aPO/C6H6 (C6Hs)2P(O)C1 C6HsP(O)C12 P( O) CI a/C6H6 P(O)Bra/C6H6
--140 --100 --115 -- 185 --165
Phenylthiophosphonic halides ( C6Hs)aPS/C6 H6 (C6Hs)aPS/CHC13 (C6Hs)PSC12 P(S)CIa/C6H6
--190 --270 -- 145 --220
Alkyl and thioalkyl phosphates (MeO)aPO (EtO)sPO (n-BuO) 3PO (C6HsO)zPO/C6H6 (EtO)2P(O)C1 (EtO) 3PS (EtO)2P(S)C1
--135 --160 -- 105 -- 140 --75 -- 225 --95
Dialkyl and diaryl phosphites (MeO)zP(H)O (EtO)2P(H)O (n-BuO)zP(H)O (C6HsO)2P(H)O
--110 --190 --115 --95
were examined at 74 gauss. Experimental results are listed in Table 15 for pentavalent phosphorus compounds and in Table 16 for trivalent compounds. Similar results for many of these compounds were also obtained 121 with TTBP, although there only the sign of the enhancement could be measured because of rapid radical decomposition. In Tables 15 and 16, Gloou is the largest observed proton enhancement, Go~n is the proton enhancement extrapolated to infinite RF power, while Gloov and Go~p are corresponding values for phosphorus in the same solutions. Values for G~H fall short of the dipolar limit primarily because the EaR line of BDPA was too broad to saturate completely and not because of proton scalar coupling. For this reason, values of the ultimate 3 t p enhancement were obtained by the ratio method mentioned above 74. Values for cp, the 31p contact component, were obtained using q/3.0 = r/1.6 = s/9.6. A cursory glance at Tables 15 and 16 shows that phosphorus enhancements, like those for fluorine, are extremely sensitive to chemical environment. ExtraAdvan. Mol. Relaxation Processes, 4 (1972) 229-354
315
DYNAMIC NUCLEAR POLARIZATION TABLE 16 3tp DNP PARAMETERSFOR TRIVALENTPHOSPHORUSWITH BDPA AT 74 GAUSS Reprinted with permission from ref. 120. GlooH
GooH
Gloop
Goop
UQcI,
cp
Phenylphosphine halides (C6Hs) aP/C6H6 --110 (C6Hs)aP/CS 2 --155 (C6Hs)2PC1 -- 125 CnHsPCI2 --200 PCla/C6H6 -- 190 C6HsPBr2 -- 135 PBr3/C6H6 --200
--150 --255 --200 --320 --205 --250 --250
+290 +555 +480 +665 +870 +460 +870
+415 +800 +670 +1090 + 1070 +600 +1050
+860 +970 + 1040 +1090 + 1610 +745 +1300
36.4 45.4 52.8 59.4 oo 29.3 109
Trialkyl phosphites (MeO)3P (EtO)aP (i-PrO)3P (n-BuO)3P (C6HsO)aP/C6H6
--200 --210 --200 --130 --240
--310 --330 --290 --230 --285
+660 +675 +565 +380 +795
+1000 +950 +775 +605 +1000
+1000 +950 +835 +825 +1050
48.3 43.5 34.7 33.8 54.1
Miscellaneous (EtO)2PCI (C6Hs)2PH
--200 -- 140
--310 -- 155
+540 +460
+790 + 525
+790 + 1060
32.4 55.4
Polyhedral phosphorus Pa/CS2/C6H6 --235 P4S3/CS2/C6H6 --280
--285 --325
+915 + 1180
+970 + 1420
+1050 + 1420
54.1 182
Solvent
p o l a t e d e n h a n c e m e n t s v a r y f r o m - 6 5 0 for t r i m e t h y l p h o s p h a t e to + 1610 for p h o s p h o r u s trichloride. This covers a l m o s t the entire theoretical range o f enh a n c e m e n t expected (Table 4). I n addition, the large observed e n h a n c e m e n t s indicate t h a t DNP m a y be a v a l u a b l e tool for investigating 31p N~R at low concentrations. Chemically, several effects are significant. F o r example, where c o m p a r i s o n s are possible, trivalent p h o s p h o r u s always shows m o r e scalar c o u p l i n g t h a n p e n t a v a l e n t p h o s p h o r u s ( c o m p a r e ( M e O ) 3 P with ( M e O ) 3 P O , PC13 with POC13, etc.). This is a general o b s e r v a t i o n first n o t e d by D w e k a n d R i c h a r d s 122. In a d d i t i o n to the large differences in e n h a n c e m e n t between t ¢~I a n d pV, several smaller substituent effects m a y be noted. Thus, for the p h e n y l p h o s p h o n i c halides, enh a n c e m e n t s increase as 4~ is replaced by CI, indicating t h a t CI t r a n s m i t s spin density to P better t h a n q~. W h e n Br is substituted for CI, the e n h a n c e m e n t decreases ( c o m p a r e P O B r 3 , POCI 3 a n d PBr3, PCI3). W h e n R O is replaced by H, the e n h a n c e m e n t increases ( c o m p a r e ( M e O ) 3 P O with ( M e O ) z P ( O ) H , etc). Finally, the effect o f substituting S for O is n o t clear since ( E t O ) 3 P S shows less scalar coupling t h a t ( E t O ) a P O , the reverse o f ( E t O ) 2 P ( S ) C I a n d (EtO)2P(O)CI. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
316
J. POTENZA
A detailed examination of the data shows that scalar coupling decreases in the order: lone pair > H > C1 > Br > C6Hs > RO. Such large substituent effects undoubtedly arise from the central location of P atoms in phosphorus compounds with consequent possibilities for substitution. In contrast, fluorine and hydrogen are always located at molecular peripheries and are therefore always available for interaction with the free radical. Thus, for phosphorus, we may make an additional distinction between intermolecular coupling mechanisms. Coupling may be either direct or indirect, depending on whether the radical acts directly upon electrons situated at phosphorus or indirectly via long-range conjugation. The fact that enhancements increase with increasing substituent size strongly suggests the presence of direct coupling, while the large positive enhancements obtained with compounds such as C13PO , in which phosphorus is well shielded sterically, suggests spin transmission through delocalized bonding orbitals. As an example of direct coupling, the large positive enhancements of trivalent phosphorus may be regarded as due primarily to radical collisions with the lone pair electrons. Since these contain some s-orbital character, any unpairing of these electrons will result directly in spin density at P and resultant large scalar coupling. Several chemical applications of 31p DNP have been reported. In an attempt to determine the extent of electron delocalization in phosphonitrilic ring compounds of formula (PNCI2)~, x = 3-7, ~ P enhancements were measured with several radicals 22. The degree of aromaticity in these compounds has been of concern for several years 123' 124. The detailed order of enhancements, shown in Fig. 49, was found to be nerarly independent of the radical used, indicating that cp depends primarily on the chemical properties of the (PNCI2)x rings and less on the nature of the radical. Interpretation of the enhancement data led to the -300
• ,.,.200 8 E 0 u
e- ~100 o ¢0
~
0
E
~
BDPA
TTBP GALV DPPH
-100
I
3
i
i
I
}
4
5
6
7
n in (PNCla) n
Fig. 49. Extrapolated alp NMR enhancements for (PNC12)~ compounds with the four free radicals indicated. Reprinted with permission from ref. 22. Advan, MoL Relaxation Processes, 4 (1972)229-354
DYNAMIC
NUCLEAR
317
POLARIZATION
suggestion of delocalized orbitals in the rings. It was suggested that the question of aromaticity in P N ring systems could be resolved further by comparing polarizations for compounds such as PsNs(NMe2)9C1 and PsNs(NMe2)lO. The latter gives negative 31p enhancements, while the former, because of the positive substituent CI, should give a positive enhancement. I f positive enhancements were observed at all phosphorus atoms in the chloride, delocalized orbitals would be present. Unfortunately, monochlorinated phosphonitrilics are difficult to prepare. A second chemical application of 31p DNP involves the detection of stereospecific collision attitudes and hyperfine interactions zl. Ultimate 31p enhancements were measured at 74 gauss for eight phosphorus compounds with three free radicals. Values for U~p and cp are shown in Table 17. Overall, these results substantiate the conclusions presented above. Well shielded pV compounds show highly negative Uoo values independent of the radical chosen, whereas stericaUy exposed pli! compounds give large positive enhancements. And, variations in enhancement due to differences in phosphorus chemical environment far outweigh variations due to radical type. T A B L E 17 31p DNP ENHANCEMENTS AT 74 GAUSS FOR SEVERAL FREE RADICALS
Reprinted with permission from ref. 21. Compound
q~aP
BDPA
TTBP
cp
U~op
100
DPPH
Cp
Uoop
cp
U~op
+1270
70
+1160
27
+700
(MeO)aP
29
+
740
21
+
550
19
+500
(PNCI2)3
14
+
300
12
+
225
10
10
+
110
6.8
-- 75
-----
300 600 700 500
4.0 0.6 1.6 7.5
--300 --680 --560 -- 35
(MeO)2P(O)H
9.5
+
85
(EtO)2P(S)CI (MeO)aPO (EtO)aPS (Me2N)aPO
5.2 2.1 1.8 0.4
-----
200 500 530 750
4.0 1.2 0.4 2.1
+
50
It is interesting to note the radical order for decreasing scalar coupling. With six of the eight compounds tested, scalar coupling decreases with free radical in the order B D P A > TTBP > D P P H . This behavior is different from that for fluorocarbons where in general B D P A > D P P H > TTBP. With (MeaN)3PO, the radical order is D P P H > TTBP > BDPA, while for (MeO)2P(O)H, it is TTBP > B D P A > DPPH. For fluorocarbons, differences in scalar rate with different radicals were related to spin exposure at the radical edge. Here, a different interpretation must apply, and it was suggested that the observed radical order arose partially from stereospecific hyperfine interactions. Adoan. Mol. Relaxation Processes, 4 (1972) 229-354
318
J. POTENZA
This may be understood as follows. In addition to peripheral electron distribution, the radicals differ further in one significant way - the atomic species which has maximum spin density. The O atom of TTBP, the N atoms of D P P H and the allyl C atoms of BDPA are each expected to share some 30-50 9/00of the unpaired electron. Thus, observed scalar rates for, say, TTBP could arise from a combination of peripheral electron exposure and primary collisions with oxygen. Evidence for such collisions comes from (Me2N)3PO which shows an unusually large scalar coupling with DPPH. It was suggested that this indicates a significant amount of transient bonding, perhaps between the radical and solvent lone-pair electrons. The large scalar rate observed for (MeO)2P(O)H with TTBP may similarly be interpreted in terms of transient hydrogen bonding between the TTBP oxygen atom and the solvent proton bonded to phosphorus:
.•
~/OMe & . . . . H--P~oMe
Additional evidence for the microscopic detection of hydrogen bonding came from a study of phosphorus DNP with nitroxide radicals ~25 which have almost all of the unpaired electron at the N - O sites. There, (MeO)2P(O)H gave an exceptionally large positive enhancement. Hydrogen bonding has also been detected by DNP in proton solutions at high field 126. Considering these results, it is interesting to speculate about the possibility of examining motion along a reaction coordinate. That is, for reacting systems, do those collisions which give large scalar coupling ultimately lead to chemical reactions? Many of the ideas presented above could be examined further by calculating correlation times and hyperfine coupling constants from multifield measurements. 2. Hiyh-fieM measurements Few 31p high-field DNP results have been reported, and none has been interpreted in detail in conjunction with low-field results. The available data are listed in Table 18. All measurements were made at room temperature with the free radical TTBP. For the data at 74 gauss, extrapolated enhancements are reported127, while at 12,500 gauss, maximum observed enhancements are given 128. At 3300 gauss, only the sign of the enhancement could be observed 12a, and this precludes accurate calculations of %. Nonetheless, we note that of the eight samples investigated, only two enhancements change sign, and these do so at 12,500 gauss. For the remainder of the systems, and for all pm systems, the sign of the enhancement does not change. This contrasts sharply with aromatic fluorine data, where axial crossings were observed below 3300 gauss, and indicates that scalar correlation times in 31p solutions containing well-shielded radicals do not depend Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
319
TABLE 18 MULTIFIELD 31p ENHANCEMENTS WITH
TTBP
Compound
74 yauss
3300 oauss
12,500 oauss
~aP (EtO)3P (MeO)aP (MeO)2P(O)H (Me2N) 3PO
+ 1160 + 660 + 550 + 110 -- 500 - - 600 -- 700 -- 750 Not studied
+ + + + ------
+20 +30 +50 Not studied 0 0 + 3 0 + 3
(MeOa)PO
(EtO)3PS (EtO)3PO (EtO)2P(O)CI
critically u p o n the n a t u r e of the solvent. Further, the scalar spectrum is seen to extend t o very high frequencies, especially for trivalent phosphorus. It has been suggested x6 that DNP, because of the possibility of observing large NMR e n h a n c e m e n t s , could be used to o b t a i n high-resolution NMR spectra of nuclei with low NMR sensitivity. A n example of a 31p high resolution spectrum is s h o w n in Fig. 50 for trimethyl phosphite with 10-3 M T T B P at 12,500 gauss (ref. 122). The multiplet resolution is good, b u t this is a favorable case since pin comp o u n d s give large e n h a n c e m e n t s at high field. F o r pV c o m p o u n d s , observed enh a n c e m e n t s at 12,500 gauss seem too small with T T B P to be o f m u c h value for e n h a n c i n g spectra. However, other radicals m a y give larger e n h a n c e m e n t s at high field.
Fig. 50. 31p spectrum of P(OMe)3 containing 10- 3 M TTBP. The arrow indicates the unenhanced signal. The enhancement shown is +35. Reprinted with permission from ref. 122. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
320
J. POTENZA
Recently, Dwek et al. 23 applied DNP to enhance the a l p NMR spectra of relatively insoluble phosphorus chalcogenides. Accurate chemical shifts and coupling constants were reported for several compounds, as shown in Table 19. In the case of P4Se3, which has the polyhedral structure
the resolution was good enough to obtain 31p-77Se coupling constants, the first to be reported. Since all results were obtained with non-spinning samples, increased signal-to-noise ratios could be obtained by spinning. Greater sensitivity could also be obtained by using a CAT. Although the enhancement of aXp NMR spectra by D ~ is not likely to find wide applicability over routine high-field methods, applications akin to that above are likely to be forthcoming, especially with dilute samples. TABLE 19 a l p DNP RSULTS FOR PHOSPHORUS CHALCOGENIDES Reprinted with permission f r o m ref. 23.
Compound
Enhancement 3300 y
P4 P406 P4Sa
P4S5 P4S7 P4Slo P4SaI2 P4Sea
P459
12,500 g
~-{~- 600 a -[- 60 P+ P+76 P'+ P'-}-69 P: P ' I . 0 P: P' 1.1 N o t observed N o t observed + ca. + 2 0 + + P+ P+80 P'+ P'+80 P : P ' 1.0 P : P ' 1.0
-F
Chemical shift b (p.p.m. from ext.
Coupling constant
(Hz)
P406)
d- 45.5 zL0.2 +233.6i0.2
+ 55.9j 0.4 -- 14.3=1=0.6 + 75.3±0.2 +217.7±0.2
2j(p...
p,) = 71=[:1
2j(p...p,) = 72+1 1J(P-Se) = 263 ~_ 10 I J ( P ' - S e ) = -r-563:k20 2 j ( p . . . . Se) = - - 5 7 i 1 0 1j(p, p,) = 157:k10
~-
a M a x i m u m value observed. Extrapolation to infinite microwave p o w e r gives + 11004-200. b Uncorrected for susceptibility; estimated correction is i 0 . 2 p.p.m.
In addition, some use with systems of biological importance 129 may develop, particularly if radicals are found which give large enhancements for pV compounds. Here, one can envisage a radical colliding with a phosphorus-containing macroAdvan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
POLARIZATION
321
molecule, and via the magnitude and field dependence of the enhancement, giving information on the chemical environment of phosphorus. In some ways, this is analogous to the well known spin-labeling techniques ~3°-~35 developed by McConnell and co-workers where an unpaired electron is bound to a macromolecule and its environment monitored by EPR. With DNP, additional information concerning the nature of collisions near phosphorus may be obtained and the two techniques could supplement each other.
E. Experimental results for carbon nuclei Because of its small magnetic moment and low natural abundance (1.1 ~), 13C is extremely difficult to detect using NMR techniques. However, 13C NMR spectra can be observed using a CAT and such spectra are finding increasing importance in organic chemistry136' ~37. Precisely because of the small value of/~ for 13C, we expect 13C NMR enhancements to be extremely large (Table 4), and zero signals extremely small. This makes quantitative enhancement measurements difficult to obtain, and, as a result, few DNP experiments have been performed. The first mention of ~3C ONe was by Hausser and Reinbold ~3s. At 3300 gauss, they measured 13C enhancements of 0.5 cm 3 samples of C6H6 and C 6 D 6 with the free radical BDPA. Their results are shown in Fig. 51. Unenhanced spectra
~H o
°
:~ H0
p
e
T ~ ~H0 Fig. 51. N a t u r a l a b u n d a n c e e n h a n c e d l s C NMR signals f r o m (a) benzene, (c) C6D6 ; (b) is a triple resonance experiment. Reprinted with permission f r o m ref. 138.
could not be observed, but by comparison of signal strengths with protons at the same frequency, they concluded that C6H6 was enhanced - 300 times, C6D 6 - 350 times. In addition, by simultaneously saturating the electrons of BDPA and the protons of C 6 H 6 (Fig. 51(b)), they obtained an enhancement of -1200. The Advan. MoL Relaxation Processes, 4 (1972) 229-354
322
J. P O T E N Z A
latter is a triple resonance experiment t a9, 14o which we have not discussed. Basically, it corresponds to a nuclear-nuclear Overhauser effect coupled with the electron-nuclear Overhauser effect. When the protons are saturated, the multiplet structure of carbon collapses as expected for heteronuclear decoupling and the signal is enhanced slightly. Small enhancements of this type have been observed in nuclear decoupling experiments without free radicals 141. Overall, Fig. 51 shows that 13C spectra may be recorded with one sweep at 3300 gauss. With a CAT, it should be possible to detect 13 C zero signals and obtain quantitative enhancements. In 1965, Imbaud 142 reported enhanced 13 C spectra for several hydrocarbons and fluorocarbons. Well resolved spectra were obtained, although enhancement magnitudes were not given because zero signals could not be measured. The most complete experimental treatment of I~C DNP to date has been that of Natusch and Richards 14a. At 3300 gauss, using the free radical TTBP, they measured ~aC enhancements for a variety of compounds, with the results shown in Table 20. TABLE 20 13C
DNP RESULTSAT 3300 GAUSSWITH TTBP
Reprinted with permission from ref. 143. Solvent
Sign of
Notes
enhancement
Very strong Very strong
c6n 6
CGF6 C6D 6 C6HsF
C~Hs-CHs C6Hs-CFs C6H4-(CH s)z C6Htz Fe(CO)s CHCIs CHBrs CH~CI2 CH2Brz CH2I~ CHsl CCI~ CFCIs CFaCCIs CH3OH CHaCN H'CO2"CH3 CHs'CH2"OH (C2Hs)2CO CS2 2,4,6-Tri- t-butylphenol
Enriched sample + + + + + +
N o resonance observed --
SCN resonance very strong --
-+(t-Butyl) Conc. solution in benzene -- (Aromatic)
Advan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
POLARIZATION
323
In general, negative enhancements, indicative of dipolar coupling, were obtained except for all but one of the halo-substituted methanes, which showed positive enhancements. Tri-t-butyl phenol in benzene also gave a positive enhancement, but because of the possibility of chemical exchange, this should be regarded as a special case (see above). The 13C spectrum of tri-t-butyl phenol (Fig. 52) shows clearly a positively enhanced quartet from the t-butyl protons and negative enhancements for the ring protons in accord with the 1H results presented above. That large halogen atoms lead to positive enhancements is in accord with the lowfield phosphorus data presented above. a
a - 13CH3 q u a r t e t b - '3C(CH3)3 s i n g l e t c - A r o m a t i c 13C of s o l v e n t b e n z e n e + phenol
a
Fig. 52. Natural abundance ~aC spectrum of tri-t-butyl phenol in benzene with TTBP. Reprinted with permission from ref. 143.
Some idea of the magnitude of the enhancement at 3300 gauss was obtained by studying a 62.5 ~ ~3C enriched sample of Fe(CO)5. The zero signal was seen easily and an enhancement of - 3 5 was observed. Attempts were made to observe enhanced 13C spectra at 12,500 gauss, but none could be observed with natural abundance samples. Since the enriched Fe(CO)5 sample gave an enhancement of 4 at 12,500 gauss, it was concluded that the frequency spectrum is near zero at that field. In terms of magnitude of the enhancement, then, these preliminary results indicate that 1a C behaves like a~p, which suggests that fields of 3300 gauss or lower may be used to obtain relatively large enhancements and high resolution. The most dramatic example of the possibilities which exist with a3C in natural abundance was given by Gr~tzedick and Miiller-Warmuth 144. They reported observing both enhanced and unenhanced ~3C NMR spectra of benzene with TTBP at 176 gauss. At this low field, all signals were accumulated on a CAT; the enhanced signal required 40 min and the unenhanced signal a week to observe. Relaxation times were measured and the a3C NMR signal was extrapolated to infinite RF power in the usual way. In this manner, the quantitative enhancements shown in Table 21 were obtained. (The values for CHaI were obtained using an enriched sample and BDPA.) Analysis of the data indicates that the scalar relaxation component in both cases is less than 30 ~ . Qualitatively, this agrees with the fluorine data presented above, which showed large negative enhancements for Advan. MoL Relaxation Processes, 4 (1972) 229-354
324
J. POTENZA
TTBP. Significantly, the benzene spectrum was a resolved doublet, as expected, which demonstrates the possibility of obtaining high resolution ~aC spectra at relatively low fields where enhancements are large. TABLE
21
Uoo C AT 176 GAUSS FOR C 6 a 6 IN T T B P AND C H a l I N
BDPA
R e p r i n t e d w i t h p e r m i s s i o n f r o m reE 144.
Temp. 333 294 270 250 232 218
°K
(C6H6/TTBP)
(CHal/BDPA)
--210 --450 --540
--- 20 - - 55 --100 --130 --140
If DNP is to find application as a tool for observing weak NMR signals, it will probably be for 1aC where chemical shifts and coupling constants are large enough and natural sensitivity low enough to warrant the additional effort required to construct and maintain the double resonance spectrometer. Regardless of applications to high resolution NMR spectroscopy, 13C enhancements, because they seem sensitive to chemical environment, are likely to be measured with increasing frequency in the future. With time averaging computers, stable systems and large sample volumes, zero signals can probably be measured conveniently at fields as low as 500 gauss, and this may be close enough to the zero-field limit to permit scalar parameters to be obtained. Values so obtained could be compared with proton, fluorine or phosphorus data taken on the same compound and this would give a better understanding of molecular collisions in liquids.
V. E X P E R I M E N T A L RESULTS - C I D N P
A. Alkyl and aryl radicals Alkyl and aryl radicals generated by the thermal decomposition of peroxides or azo compounds were studied by Kaptein 59 (alkyl) and by Bargon and Fischer (refs. 24, 145) (both). In the simplest case, phenyl, chlorophenyl and o,p-dichlorophenyl radicals were produced 145 by thermally decomposing dibenzoyl-, p-chlorodibenzCyl- and o,p-dichlorodibenzoyl peroxides respectively. Here, the reaction scheme given by eqn. (55) applies and the products showing ODNP were benzene, chlorobenzene and m-dichlorobenzene. Observed enhancements increased in the order Advan. Mol. Relaxation Processes, 4 ( 1 9 7 2 ) 2 2 9 - 3 5 4
DYNAMIC
NUCLEAR
325
POLARIZATION
T A B L E 22 OBSERVED AND CALCULATED ENHANCEMENTS (40 MHz) OF C6HsCI AND C6H 6 Reprinted with permission f r o m ref. 145.
Temp.
C6Hs CI
IIO°C 120 ° C
C6H6
Gobs
Gcalc
Gobs
Gcalc
- - 6.3 - - 16
--6.2
--20
--20
[m-C6H4CI2I < 1C6H5Cll < IC6H61. Experimental enhancements, shown in Table 22, were obtained for C6H5C1 and C 6 H 6 ; m-C6H4CI2 gave a complicated spectrum and could not be compared with benzene and chlorobenzene. Calculated enhancements, also shown in Table 22, were obtained from eqn. (59) assuming pure dipolar coupling. ]?he various parameters required to calculate G from eqn. (59) were approximated either from values taken from the chemical literature on other systems or they were estimated. For example, T1M, the spin-lattice relaxation time of the product, was taken to be that of the pure solvent 146, while the correlation time • for chlorobenzene was estimated from that of benzene 146. Values for p, p' and a, the relaxation transition probabilities, were obtained by using the abovementioned correlation time. On the basis of enhancements calculated using these parameters, it was concluded that the Fischer cross-relaxation model described above adequately described the polarization process and that chlorobenzene gave smaller enhancements than benzene, as a result of different parameters. Presumably the even smaller enhancement for m-dichlorobenzene would arise for the same reason. The results are probably better interpreted in terms of the KapteinCloss theory of CIDNP. The reaction intermediates are regarded as radical pairs during the bond-breaking step and the observed enhancements are accounted for if it is assumed that Ay varies regularly as C1 substitutes for H on the phenyl radical. This is a reasonable assumption since CI has a much larger a5 spin-orbit coupling parameter than H. A similar quantitative treatment based on eqn. (59) was offered for methane produced via decomposition of diacetyl peroxide in dimethylphthalate, viz. O
II
O
JJ
O
fl
CH3COOCCH 3 ~ 2 CHACO" ~ 2 CH3"+2 CO2 C H 3 • q- solvent
(113)
~ CH4 + solvent.
Again, the intermediates are more properly characterized as radical pairs. During the reaction, a transient emission signal at 6 = 0.79 p.p.m, was observed and attributed to dissolved methane. The coupling was assumed to be purely dipolar Advan. Mol. Relaxation Processes, 4
(.1972) 2 2 9 - 3 5 4
326
J. POTENZA
and quantitative agreement was reported. Lists of the parameters used to calculate enhancements may be found in the original literature 1¢5. The results here can also be interpreted with the Kaptein-Closs theory, assuming only scalar coupling terms in the Hamiltonian. Overall, these relatively simple systems demonstrate the possibility of detecting and determining the properties of short-lived radicals and reaction intermediates. Because their NMR spectra are simple, they should probably be studied in more detail to determine exactly what information can be obtained. A thorough experimental treatment of alkyl radicals was given by Kaptein 59. Methyl, ethyl, propyl, isopropyl and t-butyl radicals were studied at 3500, 14,000 and 23,000 gauss in two reactive solvents: thiophenol and hexachloroacetone. Except for t-butyl, all radicals were generated by thermal decomposition of the appropriate diacyl peroxide (RCOO)2. The following reactions apply. O
O
II
I1
(RCO)2 ~ 2 RCO"
(114)
O II RCO.
(115)
-o R-+CO
O
2
O
R" + RCO. --', RCOR
(116)
2 R. -~ R-R
(117)
2 R. ~ Disproportionation products
(118)
In addition to the above products, the radical intermediates may react with the solvent as follows. In thiophenol, we obtain O
O
RCO-+t~SH -o RCOH+qSS.
(119)
R- +~bSH
--* RH +q~S.
(120)
R- +~bS-
--, ~bSR
(121)
R" +thS-
~ Disproportionation products
(122)
In perchloroacetone, the possibilities are 0
0
II
II
R" + CI3CCCC13 --* R-CI+ CCIaCCC12, Advan. Mol. Relaxation Processes, 4 (1972) 229-354
(123)
327
DYNAMIC NUCLEAR POLARIZATION O
G
II
II
R - + CC13CCC12" ---, CCI3CCCI2R
(124)
o R.+CCIaCCC12" ~ Disproportionation products
(125)
Thus a host of products are possible, and for many, enhanced spectra were observed. For example, the results of thermal diacetyl peroxide decomposition are shown in Table 23. Appended to the chemical shift is the letter A, E or N, depending upon whether the signal was observed in enhanced absorption, in emission, or was normal (unenhanced). TABLE 23 CIDNPRESULTSFROMTHERMALDECOMPOSITIONOF DIACETYL PEROXIDE Reprinted with permission from ref. 59. 6 (p.p.m.)
Assignment
Product o f reaction
Methane Acetic acid CH3 Thioanisole CH3
120 119 121
Ethane 1,1,1,3,3-Pentachloroacetone Methyl acetate (acetate CH3) Methyl acetate (OCH3) Methyl chloride
117 125 116 116 123
From thiophenol
0.13 A 1.84 N 2.24 E In perchloroacetone
0.83 E 1,69 1,96
E N
3.54 E 2.94 A
In thiophenol, three products were observed: methane, acetic acid and thioanisole. Methane, which is formed via the abstraction reaction (120) shows a positive enhancement, while the methyl protons of acetic acid formed from reaction (119) show no enhancement. The results with perchloroacetone may be analyzed similarly. Overall, for methyl radicals involved in these reactions, products from radical coupling reactions show negative enhancements while those from abstraction reactions give positive enhancements. The positive enhancement observed for methane here is exactly the opposite of that reported above ~4s for a different solvent. That the acetate protons of both methyl acetate and acetic acid are unenhanced was attributed to a short radical lifetime for the acetate radical 14~ which would cause polarization to decay in the radical before products formed and would be the determining factor if polarization is effected when the radicals form. Advan. MoL Relaxation Processes, 4 (1972) 229-354
328
J. POTENZA
However, if radical pairs are required for polarization, a modified interpretation will be required. The information contained in these spectra is almost unbelievably detailed. In principle, they contain information for the several product species similar to that presented above for non-reacting samples. Results for the decomposition of dipropionyl peroxide, which gives ethyl radicals as intermediates, are shown in Table 24. The major difference between these results and those for methyl radicals is the appearance of emission and absorption within enhanced multiplets. In thiophenol, only emission or enhanced absorption is observed within a given multiplet, while in perchloroacetone, all enhanced multiplets show simultaneous emission and absorption. For the product butane formed in a radical combination reaction, low field multiplet lines are negative, high field lines positive, while for ethyl chloride formed by C1. abstraction from the solvent the reverse is true. This is in accord with the recent theory developed by Fischer67. TABLE 24 CIDNP
RESULTS FOR
THE
THERMAL
DECOMPOSITION O1~ D I P R O P I O N Y L
PEROXIDE
Reprinted with permission from ref. 59.
Assignment
Product of" reaction
From thiophenol 0.75 E 0.93 triplet N 2.09 quartet N 0.95 triplet N 2.12 quartet N 1.12 triplet A 2.68 quartet E 2.45
Ethane Propionic acid CH3 Propionic acid CH2 DiproDionyl peroxide CH3 DiproDionyl peroxide CH2 Thiophenetole CH3 Thiophenetole CH2 Spinning sideband of solvent SH peak
120 119 119
From perchloroacetone 0.90 triplet E/A 1.30 E/A 1.21 triplet N 2.40 quartet N 1.47 triplet A/E 3.52 quartet A/E
Butane CH a Butane CH2 Dipropionyl peroxide CH3 Dipropionyl peroxide CH2 Ethyl chloride CHa Ethyl chloride CH2
117 117
(p.p.m.)
121 121
123 123
Enhancements for thiophenetole are more difficult to treat. It was suggested that the positive enhancement of the methyl protons might indicate modulation of the scalar field by rotation of the methyl group in the ethyl radical. The methylene protons are not free to rotate with respect to the unpaired electron, and for them a dipolar mechanism might be dominant. However, other interpretations Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
329
based entirely on scalar coupling with radical pairs seem possible. For example, different signs could arise because the signs of the hyperfine coupling constants for the CH2 and CH 3 groups in the ethyl radical are opposite. Systems with propyl, isopropyl and t-butyl radical intermediates gave spectra similar to those above and will not be considered in detail here. However, two points should be mentioned. First, in the decomposition of dibutyl peroxide, no 7 proton enhancements could be observed. This indicates that spin information in alkyl chains is rapidly attenuated, encompassing no more than 2 or 3 carbon atoms. The second point concerns the reaction of t-butyl radicals produced by the following reaction scheme.
In thiophenol, isobutane is formed via reaction (120) and the methyl protons give a negatively enhanced doublet. In perchloroacetone, isobutane is also formed, but this time by disproportionation (reaction (118)). Here, the CI-[3 doublet shows emission at low field and absorption at high field. That the abstraction product in thiophenol shows net enhancement is in accord with the theory of Closs if polarization is produced in a radical pair with A# # 0, such as might occur in the initial bond-breaking step or in a non-reactive encounter between ~bS" and t-Bu.. For isobutane produced by disproportionation, A# ~ 0, and only transverse polarization is expected. Results of this type, when interpreted completely, may lead to a detailed description of individual steps in a reaction sequence. Bargon et al.24 also examined the thermal decomposition of diacyl peroxides. O II They decomposed (CH3(CHz),CO)2, n = 1, 6, 7, 8 and 10 in hexachlorobutadiene. During the course of the reaction, transient emission and enhanced absorption lines were observed in the region 6 = 4-5.5 p.p.m. These lines, which were not present after the reaction was over, were attributed to intermediate unsaturated compounds produced by disproportionation reactions. Reaction (118) gives an n-alkane and a 1-alkene, the latter may give the transient signals, then react further to give branched alkane products whose N~R spectra appear at the end of the reaction. CIDNP, then, may be used to detect and determine the nature of transient diamagnetic intermediates in rapid radical reactions. B. Photochemical appfications - tests o f the Kaptein-Closs theory
As indicated above (eqns. (61) and (62)), DNP can also be produced by optical transitions which lead to radical pair intermediates. The first mention of such optically induced DNP was by Cocivera 14s, who studied anthraquinone. A Advan. MoL Relaxation Processes, 4 (1972) 229-354
330
J. POTENZA
0.005 M solution in C 6 F 6 w a s irradiated at 3000-4000/~ using a 3500 watt mercury lamp. Under these conditions a steady triplet state concentration of anthraquinone is obtained which then reverts to the ground state (eqn. (127)). o
o
(127) o
o
Here, no net reaction is occurring; however, DNP may arise by triplet-singlet crossover according to the mechanisms presented above.
R A f,
li
R
b
I
i
I
I
It
d
Fig. 53 (a) 1H NMR spectrum of 0.005 M anthraquinone in C6F6 prior to irradiation (47 scans with CAW);(b) the same spectrum during irradiation (12 scans); (c) slow passage IH NMR spectrum without irradiation (65 scans); (d) slow passage spectrum during irradiation (16 scans), and (e) slow passage spectrum after 30 min irradiation (65 scans). Reprinted with permission from ref. 148.
The results are shown in Fig. 53. Note that all spectra required several passes with a CAT to be observed because of the low concentration of anthraquinone. Two points should be mentioned. First, all signals in the enhanced spectra are negative; however, all proton enhancements do not have the same magnitude. Second, the emission signals are broader than the normal absorption signals. Presumably the broadening arises from a triplet energy transfer process while the enhancements Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
331
arise from different mixing coefficients for the various nuclear states. The important point is that studies of this sort may prove valuable for investigating the excited states of organic molecules. Photochemically induced DNP has also been employed by Cocivera et al. (refs. 149, 150) to examine photochemical mechanisms, including those proceeding via chain reactions (to be discussed below). In one experiment, benzaldehyde was irradiated with 2000-4000 A light; the resulting 60 M H z proton NMR spectra are shown in Fig. 54. With C 6 D 6 as the solvent (spectra (a), (b)), a positive enhancement (A) for the low-field aldehyde proton was observed in addition to some emission in the ring proton region. A negatively enhanced high-field peak not belonging to benzaldehyde was also observed. Similar experiments with CC14 gave spectra (c) and (d). The spectra are similar to those for C6 D 6 except that the highfield region shows additional peaks.
I
c._~
I
,
I
I
I
#'~_
't "-
Fig. 54. (a) 60 MHz 1H spectrum of ~CHO in C6D6 before irradiation (12 scans); (b) the equivalent spectrum during irradiation (2 scans); (c) 1H spectrum of ~CHO in CC14 before irradiation (3 scans); (d) 1H spectrum of ~CHO in CC14 during irradiation (3 scans), 1H spectrum of benzoin in C6D6; (e) before irradiation; (f) during irradiation, and (g) after irradiation (all 2 scans). Reprinted with permission from ref. 149.
On the basis of this evidence, it was suggested that the reactions proceed via a radical pair mechanism and that the high-field peak in spectrum (b) results from the C - H proton of benzoin, ~bC(O)CH(OH)@. This assumption was tested by photolysing benzoin, which gave spectrum (f), equivalent to spectrum (b). Hence radical pair formation is a reversible process. Overall, the CIDNP results support the following mechanism for the photolysis of benzaldehyde. Advan. MoL Relaxation Processes,
4 (1972) 229-354
332
J. POTENZA
4,CH
•
4, H
E I" oII 4, H
?"1
+4,CH
OOH LII
• 4,CC-~ I
(128)
H 'l
O II > 2 4,CH •
polarized
polarized
O OH
I[ I 4,c-c-4 1
> 4 H
H
""
>2~CH'~
polarized
J
The scheme accounts for polarization of both the aldehyde proton of benzaldehyde and the C - H proton of benzoin. Photochemical reactions proceeding via triplet state intermediates were studied by Closs and co-workers. In one series of experiments 6°, the photo-decomposition of 4,2CN2 was studied in several solvents containing benzylic H atoms. Focused light from a 500 watt super high pressure Hg lamp was used for irradiation and reaction times were approximately 8 min. The reactions are hv
4,2CN2 ~
4,2C:
[
(129)
I1 X
1 4,2C: + ArCH2X ~ III
X X
I
I
4,zCHCHAr + A r C H C H A r + 4,2CHCH4,2 IV
V
VI
where (a) Ar = 4,, X = H (III = toluene) (b) Ar = 3,5-(CH3)2C6H3, X = H (1II = mesitylene) (c) Ar = ~b, X = COOCH3 ( I I I = methyl phenylacetate) (d) Ar = 4,, X = CN (III = benzyl cyanide) A typical spectrum is shown in Fig. 16(a). All systems showed multiplet effects and some had net polarization superimposed, reproducing many of the expectaAdvan. Mol. Relaxation Processes, 4 (1972)229-354
333
DYNAMIC NUCLEAR POLARIZATION
tions noted in the theory section. In particular, the products t~2CHCHt ~
and
I COOCH3 q52CHCH~b, obtained with substituents (c) and (d) respectively, both showed AB
I CN quartets (Fig. 18) with lines 2-1 and 3-1 positively enhanced and lines 4-3 and 4-2 negatively enhanced. Lastly, an interesting comparison between photochemically and thermally induced spectra was offered. Polarized spectra of t~2CHCH2C6H 3(CHa)2, q52CHCHtk and qSCHCH(CN)q5 were obtained both by thermolysis
I
COOCH 3 and photolysis of t~2CN 2 in the appropriate solvent. In all cases the spectra
obtained were identical, indicating that the same processes produce polarization. Several additional systems which do not lend themselves to thermal decomposition were also studied photochemically. Thus, 0.1 M benzophenone was photoreduced T M by toluene and ethylbenzene to give the products shown in eqn. (130). OH q52CO+ RCH2q5
• tkEC-CHth + qSCH-CH~b+ (qSCH)2
I
I
l
OH OH VIII
R
VII
(130)
I R
IX
With toluene (R = H), the methylene protons of VII showed A with an enhancement of approximately 250. The steady state concentration of polarized VII was estimated to be 2 × 10-* M, indicating the sensitivity of detection. With ethylbenzene (R = CH3) , the methyne quartet of ~b2C(OH)CH(q~)CH3 showed A/E and the outermost lines were enhanced the least. Analysis of the central lines of the quartet gave G = 1300_ 200 for the magnitude of polarization. This is the largest proton polarization reported to date. Overall, C1DNP seems well suited for the qualitative detection of radical pairs in photochemical reactions. We turn now to a more detailed examination of the spectra in terms of the Kaptein-Closs theory. A thorough test of the Kaptein-Closs model incorporating variations in both g and A was given by Closs et al. 68. To show that variation of Ag within a radical pair can produce net enhancement, radical coupling products derived from the photochemical reactions of substituted benzophenones with substituted toluenes were studied. p - X C 6 H 4 C H 3 + [O = C(C6H4-p-Y)2]
hv •
OH [p-XC6H4CH2" X
"C(C6H,-p-Y)2] XI
~
(131)
p - X C 6 H 4 C H 2C(C6H4-p-Y)2OI-[ Advan. Mol. Relaxation Processes, 4 (1972) 229-354
334
J. POTENZA
where (a) X = H ,
Y=C1
(b) X = H,
Y=H v=H
(d) X = B r ,
Y=H
For these systems, the methylene protons are equivalent and are coupled to component X. The OH proton is rapidly exchanged68; hence all methylene NMR transitions are equivalent and no enhancement should be observed if Ag = gx -#x~ = 0. This is verified by the mixing coefficients M i for this system, which are shown in Table 25. With Ag = 0, oniy hyperfine mixing terms are present. But since g of a radical depends on the spin-orbit coupling parameter, which increases with atomic TABLE 25 MIXING COEFFICIENTS
Ms
FOR SYSTEMS WITH TWO NUCLEAR SPINS
Reprinted with permission from ref. 68.
Nuclear state
Both spins on component 1 M1
One spin on each component Mj
tiff ~xfl flc~ ~
flHoA,q/2--A~/4-- A2/4 flHoAg/2 + A~/4-- A2/4 flHoAg/2-- Ax/4 + A2/4 flHoAg/2 + A~/4 + A2/4
flHoAO]2-- Ax/4 + A2/4 flHoAg/2 + A x/4 + A2/4 flHoAg/2-- A~/4-- A2/4 flHoAg/2 + A~/4--A2/4
number, we expect Ag to increase from reaction (a) to reaction (d). If the hyperfine coupling constants are such that A~ = A2 and both are negative, methylene spectra from reactions (a) and (b) should show absorption while spectra (c) and (d) should give emission. The observations (Fig. 55) are in excellent agreement with the predictions of the theory.
(a)
(b)
(¢)
I (d)
I
Fig. 55.1H spectra of methylene protons for the products (a)-(d) of eqn. (13 l). S is a 1aC solvent satellite. Reprinted with permission from ref. 68.
Advan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
335
A second series of experiments designed to allow theoretical reproduction of spectra showing multiplets was also reported 68. Photoexcited substituted benzaldehydes were reacted with substituted diphenylmethanes according to p - X C o H 4 C H O + CHz (C6H4-p-Y)2 OH [p-XC6H4CH"
"CH(C6H4-p-Y)2 ]
XII
XIII
032)
OH
I ~"p - X C 6 H 4 C H C H ( C 6 H 4 - p - y ) z
where (a) X = B r ,
Y =H
(b) X = C l ,
¥=H
(e) X = H,
Y=H
(d) X = H,
Y =C1
(e) X = H,
Y=Br
Again, Ag = g x u - gxtH is expected to decrease in going from (a) to (e); however, here the protons in the radical pair are not equivalent and AB doublets should be observed (Fig. 56). The mixing coefficients for these systems with one spin on each component of the radical pair are shown in Table 25 where A~ refers to the hyperfine coupling constant of the benzylic proton in p-XC6H4CH(OH)" and A2 to that of (p-Y-C6H4)2CH'. Enhancement magnitudes can now be calculated from the mixing coefficients and eqn. (87) if values for A1, A2, Jee, ~, we and Ag are
Fig. 56. Observed and calculated spectra for the products (a)-(e) of eqn. (132). S is a 1aC satellite. Reprinted with permission from ref. 68. Advan. )Viol. Relaxation Processes, 4 (1972) 229-354
336
J. POTENZA
known. Values for A1 and A 2 were taken from the literature; J~e was assumed to be 108 rad./sec, z 10-9 sec, and it was further assumed that we > 50 w~. With these assumptions, Ag was varied to produce the best fit for the spectra in Fig. 56. As expected, A# decreased in going from reaction (a) to reaction (e), Further, the magnitude of Ag was approximately 10-3-10-4, in accord with what might be expected for radicals of this type. The calculated spectra shown in Fig. 56 agree remarkably well with experiment, demonstrating the validity of the approach. As stated above, reaction products produced from singlet precursors should show multiplet polarization opposite to that produced from triplet radical pair precursors 33, 64. This was demonstrated semiquantitatively for the production of 1,1,2-triphenylethane by singlet and triplet paths. The polarization shown in Fig. 16 can be understood with the aid of Fig. 21, which shows singlet and triplet manifolds for a radical pair containing two protons. If transitions labeled w0 are those of highest probability and if triplet radical pairs are produced first, states 14 and 15 will populate at the expense of 6 and 7. Since only the singlet radical pair can form product, product states with m z near zero will be overpopulated. With a singlet precursor, wo transitions will cause states 6 and 7 in the triplet manifold to populate at the expense of singlet states 14 and 15; thus the singlet radical pair will have nuclear states with mz furthest from zero overpopulated. For the same reaction product, then, singlet and triplet precursors should lead to opposite multiplet enhancements. The above considerations were made more quantitative with the KapteinCloss theory. Spectra of the reactions indicated in eqn. (133) were studied 1°~ and the results are shown in Fig. 57.
[(p-XC6H4)2C: ] + CH 3C6H4-p-Y
(a) X = C l ,
Y=H
(b) X = Y = H (c) X = H , Y = CI
] ]hv > [(p-XC6H4)2 CH" "CH2C6H4-P'Y] [
(p-XC6 H4)2 CHN=NCH2C 6H4-p-Y -1
(d) X = C 1 ,
1v
(l 33)
(p-XC6 H4)2 CHCH2C6 H4-p-Y
Y=H
(e) X = Y = H (f) X = H , Y
=C1
Reactions (a)-(c) differ from (d)-(f) in the multiplicity of the precursor. Mixing coefficients M j were evaluated for the benzylic protons of the product and eqn. (87) was used to reproduce the spectra. Agreement between theory and experiment is good, as shown in Fig. 57. Further, reactions (a)-(c) and (d)-(f) do indeed show opposite polarization as expected. Thus CIDNP may prove useful for determining radical pair spin multiplicities. Adoan. Mol. Relaxation Processes,
4 (1972) 229-354
DYNAMIC
(a)
NUCLEAR
POLARIZATION
337
(b)
'" '-, [l", _# (d)
(e)
Cf)
II
I
Fig. 57. Observed a n d calculated spectra for the products (a)-(f) o f eqn. (133), S is a ~aC solvent satellite. Reprinted with permission f r o m ref. 104.
It is important to note that the treatment here in terms of mixing coefficients does not differ in principle from that involving transition probabilities. These are merely different ways of describing the same physical situation. With Fig. 21, the nucleus-electron states are regarded as fixed and different transition probabilities between the states give rise to enhanced spectra. With the time-dependent theory, different states in one manifold change multiplicity more quickly than other states; this is equivalent to saying that there is a large transition probability between the states. Physically, both theories require that the components of the radical pair diffuse to a point where Aii ~ Jee, at which point singlet and triplet states can interconvert. In sum, the combined hyperfine, isotrooic g shift theory accounts semiquantitatively for all aspects of CIDNV spectra produced from radical coupling reactions. Only scalar coupling is assumed and only ~ and fl protons were considered. Many questions still remain to be answered before a complete theory of CIDNP applicable to all reactions at all field strengths can be said to exist. First, Advan. Mol. Relaxation Processes, 4 (1972) 229-354
338
J. POTENZA
there is the question of scalar vs. dipolar coupling. Closs interpreted his results in terms of scalar coupling, while Kaptein and Oosterhoff 64 used mixed scalar and dipolar coupling to generate expressions for the enhancement of products obtained from alkyl radicals. Protons ~ to the unpaired electrons were assumed to be dipolar coupled, protons fl scalar coupled. Second, there is some question as to how polarization arises in radical transfer reactions. Gerhart and Ostermann 7° assumed that polarization was produced when a free radical collided with a solvent molecule, while both Kaptein 64 and Fischer 6v assumed that polarization is produced as radical pairs form in the primary dissociation step. Nuclear polarization is then transferred to the product of the transfer reaction. Lastly, the field dependence of CIDNP requires elucidation. However, considering the results obtained to date, it seems only a matter of time before a unified theory is developed. C. Chain reactions Bargon and Fischer 14~ examined CIDNP spectra obtained from the addition of phenyl radicals to double bonds. In one experiment, benzoyl peroxide was used as a typical initiator in a solution of methyl methacrylate. Instead of the expected emission line from phenyl radicals, an enhanced absorption signal at 6 = 7.32 p.p.m, was observed. The positive polarization was attributed to phenyl protons of radicals such as O ~bCH2-(~COCH3
I CHa which form when th" reacts with the solvent. Multiplet effects were also observed for the aliphatic protons, indicating that methyl methacrylate is involved in the polarization-producing process. The positive enhancement was assumed to arise from long range coupling of the radical electron with the phenyl protons in analogy with EPR results from similar systems 62 where long range coupling is observed. The scalar field would then be modulated by rotation about C-C single bonds, a possibility which does not exist for ~b" (but which does exist for 4~C(O)O'). To examine chain proton enhancements further, benzoyl peroxide was decomposed in styrene and CBr 4. Reactive CBr 4 was used to terminate the chain quickly in order to avoid complicated spectra. The NMR spectrum of the product ~CHBrCH2CBr 3 showed E/A multiplets for both the ~ and fl protons. By unraveling the details of these spectra, information bearing on the first steps in polymerization reactions may be obtained. Cocivera and Roth 15° applied optically induced DNP tO detect a chain mechanism. Methyl diazotate, XIV, was irradiated in both CC14 and CDC13. The C - H protons of the products XVI and XVII both showed E, as indicated. Advan. Mol. Relaxation Processes, 4 (1972)229-354
DYNAMIC
NUCLEAR
0 0 II k~ I[ N2CHCOCH3 ~ -'- :CHCOCH3 XIV
339
POLARIZATION
CI O CCI4
~" CC13C-COCH3
XV
H
XVI
t
E
C10 coc13 I 1I :" CI2C-C-COCH3 DH,
(134)
E
XVII A large longitudinal polarization might be expected since substituents on the components of the radical pair differ greatly in atomic number. What was not expected was the long time rate of decay of the emission signals. Typically, after irradiation stopped, emission was observed for approximately 3 min. This can be understood if Ta of the product protons showing enhancement is about 70 sec, a time which is much too long. Having ruled out a long T~, it was assumed that products form via a chain process after irradiation ceases. CIDNP, then, may prove to be a sensitive tool for investigating chain processes. D. Reactions involvin9 lithium alkyls - characterization of radical intermediates
Many of the early ODNP investigations by Ward et al. 26'31'152 and by Lepley and Landau 30. ~53- ~s6 involved reactions of lithium alkyls. These were investigated both to study the CIDNP process and to characterize reactive intermediates. Typically, ethyl or butyl lithium was reacted with an alkyl or aryl halide; the reaction between LiR' and RX may be considered to proceed as follows ~52 (R'Li)x R X + R ' L i ~- [R-, R'., XLi] ~ R L i + R ' X
(135)
Coupling and disproportionation products Here electron transfer gives a caged radical pair which can either react to form coupling and disproportionation products or to give exchanged halide and lithium alkyl, q~hese reactions are complicated further in some cases by the addition of various Lewis bases which are required to depolymerize the alkyl lithium. Since the base is presumably in the vicinity of the alkyl lithium, it can enter into the reaction. We shall consider this later. Experimental results from several systems are summarized in Table 26. Not all of the possible products were observed as enhanced spectra, although in some Advan. Mol. Relaxation Processes, 4 (1972) 229-354
340
J. P O T E N Z A
TABLE 26 C I D N P R E S U L T S F O R H A L O G E N - - M E T A L E X C H A N G E REACTIONS
Reaction mixture
NMR spectrum a
Comments
Ref.
26
~(p.p.m.)
Assignment
n-BuLi, n-BuBr diphenylacetylene, diethyl ether
4.8 5.8
Butene (=CH2) Butene (CH)
[E and A[ IobservedJ
n-BuLl, n-BuBr, np-entyne, diethyl ether
4.8 5.8
Butene (~CH2) 8utene (CH)
(A and E ]observed }inverse of [ kabove systemI
t-BuLi, n-BuBr
4.8 5.8
EtLi, EtI, benzene
n-BuLl, sec.-BuI, benzene
Butene (~CHz) Butene (CH) Isobutylene (vinyl)
E and A
1.0--1.6 1.85 3.2
Butane EtI (CH3) Etl (CH2)
E and A A/E A/E
3.2 4.2
CH3CHzCHICH3 (methyne) CHaCHzCHICH3 (methylene)
A/E E/A
152
Etl (CH2)
E/A
152
1.83 4.26 5.1-5.9
CH3CHICIi3 (CH3) CHaCHICH3 (CH) Vinyl
E/A E/A E and A
155
3.17
n-BuI
A/E
155
CH3CHzCH=CH2 (vinyl) Et2NCH=CHz (vinyl)
E/A A/E
153
EtLi, ~1 n-BuLi, 2-iodopropane
n-BuLi, 1-iodobutane, tetramethylene diamine
26
n-BuLi, 1-bromobutane, EtaN
26 E/A 152
a Some multiplets also have a longitudinal effect superimposed. A/E means low-field absorption, high-field emission.
cases all peaks were not characterized completely. These are not included in the Table. The observation of polarized products indicates the presence of radical pairs. In some cases, polarization of the halide initially present was also observed, indicating a reversal of the initial cage formation in eqn. (135). No polarization of lithium compounds was observed, presumably because the lithium alkyl polymer acts as a radical trap. R ' + (RLi)x = R(RLi)x"
(136)
If reaction (136) occurs appreciably, signals from lithium-containing compounds would be too broad to observe. 7Li NMR results might help clarify these observations. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
341
The type of spectrum observed is extremely sensitive to the reaction mixture. An excellent example of this is provided by the first two entries in Table 26. There the systems differ only by an added unsaturated hydrocarbon which was found necessary to observe CIDNP. With diphenyl acetylene, the product butene showed both E and A; with 2-pentyne under the same conditions, the emission and absorption was reversed. According to current theories, this might indicate different radical pair multiplicities for the two systems or different signs for A. The system n-BuLi, 1-bromobutane and triethylamine is interesting because ClDNP is observed in 1-butene and in N,N-diethylvinyl amine. 1-Butene can form by disproportionation of two n-butyl radicals which is not unusual. However, the appearance o f enhanced N,N-diethylvinyl amine shows that the Lewis base is
5 = 2.61(A)
~
CI
b e n z e n e : e t hemrr ( 3 0 : 1 ) 40o/*
+EtLi
CI
(a) XVlll
3k"X-
CI 42*/.
~
2°I°
~M3
7°/°
6=4.45 (A'
/CI~C~CH
6 = 1 . 4 - - 1 . 9 (E)
~
C[
+
2 44~,o
3U3~-
EtLi
CI xviil
.
(b)
+
A
.
- reaction
EtCI
xxii
: LiC
EtLi ~
H+
~, 2 °to
xxIII
--
+
LiCl
.XIX . 4 4 " / *
Fig. 58. (a) Net reaction of l,l-dichloro-2,2-dimethylcyclopropane with ethyl lithium. (b) Reaction scheme for the system in (a). Reprinted with permission from ref. 31. Advan. 34ol. Relaxation Processes,
4 (1972) 229-354
342
J. POTENZA ¢
-~ . . . .
?,. . . . ~
;~
~ . . . . ~. . . . . . . . .
6
-i
" p.p.m.
Fig. 59. (a) IH Nr~ spectrum of ethyl lithium and 1,1-dichloro-2,2-dimethylcyclopropane in benzene; (b) the same system after addition of ether (composite); (c) the spectrum after completion of the reaction. Reprinted with permission from ref. 31. taking part in the reaction, presumably via the scheme ~53 Et2NCH2CH 3 + C 4 H 9 - --o Et2N(~HCH 3 + C4Ha0
(137)
Et2NI2HCH a + C4H9" ~ Et2NCH=CH2 + C4H 10 Detailed analysis of the multiplet structure here might further characterize the radical intermediate. Several reactive lithium alkyl systems have been studied with the aim of characterizing reactive intermediates. In one case, Ward et al. 31 examined the reaction of 1,1-dichloro-2,2-dimethyl cyclopropane, XVIII, with ethyl lithium in benzene-ether. Products of the reaction and yields are shown in Fig. 58(a). Proton YMR spectra taken before, during and after completion of the reaction are shown in Fig. 59. Dynamic polarization was observed for several protons as indicated in Fig. 58(a). The C H 3 protons of X I X showed E only, while the vinyl protons of the same product showed A. The only other clearly assignable portion of the spectrum was that for the proton e to C1 in XX, which showed a doublet of doublets positively enhanced at 6 = 2.61. S o m e of the intermediate absorption and emission in the region 6 = 0.25-0.6 was attributed to the remaining protons of XX, but additional transient lines were found in that region by comparison with pure XX. Lastly, it was noted that the methyl protons of X I X could not account for all emission in the region 6 = 1.4-1.9. The reaction sequence shown in Fig. 58(b) was advanced to account for these observations. As above, the reactants combine to form a caged radical pair in which polarization can occur. Disproportionation gives ethylene and XX, radical coupling gives XXI, while further electron transfer may result in lithium-halogen exchange to produce XXII, which can react further to produce XIX. Since X X I I is diamagnetic and is the product of a radical pair precursor, it may show CIDNI'. This may account for some of the unassigned peaks in the region 6 = 0.17-0.83. Advan. Mol. Relaxation
Processes,
4 (1972) 229-354
DYNAMIC
NUCLEAR
343
POLARIZATION
From the CIDNP data, we might expect to obtain some idea of the lifetime of the intermediate XX[I. Since polarization is observed in XIX, XXI[ should not live longer than the relaxation time of the protons in XIX if polarization is produced in the initial radical pair. However, polarization may also arise in the carbene XXllI and this would nullify the above argument. A second example of the use of CINDP to characterize reaction intermediates was given by Lepley 3°' 156. n-Butyl lithium was reacted with fluorobenzene and N,N-dimethyl benzylamine to give N-methyl-N(c¢-phenethyl)aniline as the major product (eqn. (138)). The Lewis base N,N,N',N'-tetramethyl ethylenediamine (TMEDA) was used as a catalyst and E/A was observed in the a-proton multiplet of XXIV.
(138)
n-BuLi +~bF+ (CH a)2NCH2~b 6 = 5.02(E/A) I
). C H 3 ]
hexane TMEDA
qSN-CHq5
I CH3 XXIV No other enhancements were reported; however, some spectral regions were obscured by solvent absorption. The reaction was assumed to follow the sequence outlined in Fig. 60. Butyl lithium reacts with q~F to produce benzyne which reacts further with (CH 3)2NCH2~b to produce the a ylide. The ylide rearranges via a radical path to give the product XXV. ÷1
I :
~ ylide
L~
CH3
t /,
I
+ :N--CH2
F"
~
F
~
+ n-C4HgL~ H
Fig. 60. Scheme for the reaction o f n-BuLi, fluorobenzene and N,N-dimethyl benzylamine. Reprinted with permission from ref. 30. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
344
J. P O T E N Z A
T A B L E 27 CIDNP RESULTS FOR n-BuLi-ARYNE-tert.-AM~NE REACTION PRODUCTS
Reprinted with permission from ref. 156. NR1R2 R a
Product chemical shifts 6 (p.p.m.)
Rl
R2
R3
~X
~bCH2
Me
Me
F, CI, P-Fz
5.02(quartet)E/A
ffCH2 ~6CH2 Me
F, CI
5.12(triplet)E/A;3.16(doublet)E/A
tfiCH2 Et
t~CH2 Et
Et Et
F F
4.95 (triplet)E/A; 4.44(singlet)N, 3.16(doublet)E/A 5.23 (singlet) N
n-Bu
n-Bu
n-Bu
F
5.78 N a, 4.82 N ~
a Vinyl p r o t o n s in 1-butene.
Additional evidence for caged radical pair precursors to products of the type described above is given in Table 27. Here eqn. (138) is followed but with different amines and halobenzenes. T M E D A was used as the catalyst and hexane as the solvent. The most interesting observation is that when two benzyl groups are present on the reacting amine, CIDNP is observed for more than one proton. With dibenzyl methyl amine, the triplet at 6 = 5.12 p.p.m, is assigned to the ~ proton of the product XXV[ while the doublet at 6 = 3.16 is assigned to the methylene protons of the migrating benzyl group. No polarization was reported for ~t5
= 5.12
l
q~N-CH~b CH2~b l XXVI
3 = 3.16
the methyl group. A similar effect was observed with dibenzyl ethyl amine. The observation of polarization in the migrating group was taken as further evidence for a caged radical pair intermediate. The possibility of a triplet carbenoid intermediate was eliminated since this might not be expected to produce Clr~NP at the fl protons. However, this interpretation might not be correct. If it is correct, it should be possible to use the Kaptein-Closs theory to determine the multiplicity of the radical pair and decide whether the reaction takes place by exciting the ylide to a triplet state or by homolytic bond cleavage. Advan. Mol. Relaxation Processes, 4 ( 1 9 7 2 ) 2 2 9 - 3 5 4
DYNAMIC
NUCLEAR
345
POLARIZATION
E. Radical pair intermediates in rearran#ement reactions
In several instances, CIDNP has been used routinely to test for the presence of radical pair intermediates in rearrangement reactions. An example was provided by Baldwin and Brown 32 who studied the thermal isomerization of XXVII. B,5 ~2.5-3.0__
/
[
~N/
(El?) ~ " " ~ ' i
A.5 =2.5-3.0
-~ ~"
(E/A) 140--170°C
xxvl[
"x x v.1
high yield
(139)
5%
Product XXIX was obtained in high yield along with 5 % of the dimer XXX. Proton NMR spectra at fi = 2.5-3.0 showed enhancements for both pairs of CH2 protons in XXIX. The low-field CH2 protons (labeled A in eqn. (139)) showed E/A; only one line of the CH2 fl protons could be observed and this showed E. These observations were taken as evidence for the intermediate XXVIII. No polarization of C methyl, N methyl or aryl protons was observed; only those protons nearest the migrating groups became polarized appreciably. Schollkopf et al. 1SAlSa studied lone pair rearrangements of sulfur and nitrogen ylides. With sulfur, the sulfonium ylide XXXI was decomposed thermally to give > 80 ~o of XXX[II as shown in eqn. (140). Small yields of XXXIV and XXXV were also reported.
o
[
H3C-S-C-HCq~
"
o
H3CS.--.C.-HCq5 ~ H3CS-CHCq5
I CH2q5
-CH2~b
XXXI
.CH20 _l
(140)
XXXIi
A--~ 0
0
II
II
•• H3CSCHC~b
I
+
CH2~b
~----A
H3CSCHC0
+ (~CH2):
I H3CSCHC~b
kl
t-E
o
XXXIII
XXXIV
XXXV
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
346
J. POTENZA
_
_
.
_
_
_
CH2-
CH2-. ~
Fig. 61. CIDNV spectrum for the reaction shown in eqn. (140). Reprinted with permission from ref. 157.
The proton NMR spectrum, shown in Fig. 61 and obtained during the reaction, shows the methyne proton in XXXII[ positively enhanced, the methylene protons of XXXIII negatively enhanced and the CH2 protons of XXXV positively enhanced. This is further evidence for the intermediate XXXI[. Perhaps the most interesting observation here is the enhancement of dibenzyl, which must escape the solvent cage. A similar treatment of the ammonium ylide XXXVI showed emission and absorption peaks for the methylene protons of XXXVIII (eqn. (141)). This was taken as evidence for the radical pair intermediate XXXVII in contrast to a previously proposed ion-pair intermediate. ~bCH2
O
CHa-N+-(ZHC~b
I
CH 3
~
"CH2~
> CHa
~CH2"
]
C~b ~ CH3- -(~H O
CH 3
XXXVI
CH.~ O
XXXV[I
q~CHz x
E and A
(141)
CH3-N-CHC~ CH30 XXXVHI Last, Lepley et al.159 studied the Meisenheimer rearrangement of a tertiary amine oxide. The oxide XXXIX was decomposed thermally to form primarily XLII. Some reduction occurred and N,N-dimethyl benzylamine was also found. As indicated in eqn. (142), proton emission peaks were observed both from the methyl and methylene protons of the product XLII, indicating the existence of XL and XLI. Note that here emission occurs for protons both ~ and fl to the migrating site. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR +
347
POLARIZATION
A
~CH2N(CH3)2----~
!
OXXXIX
"N(CH32] :o':- J XL
(142)
6 = 4.6(E) ~---6 = 2.5(E)
[
~bCH2" :N(CH3)2 ~
o
:~ q~CH2ON(CH3) 2
J
XLI
XLII
Overall, it seems that CIDNP is well suited for the detection of radical pair intermediates in intramolecular rearrangements of this sort. Detailed analysis of these spectra in terms of the theories above should yield additional information. F. Nuclei other than protons
Several CIDNP experiments involving 19F nuclei have been reported. The first mention was by Bargon and Fischer 14s who thermally decomposed benzoyl peroxide in three fluorine-containing solvents: p-fluorobenzaldehyde, p-fluorostyrene and p-fluoronitrobenzene. During the reactions, 40 MHz 19 F NMR spectra were recorded. With the first two solvents, strong absorption signals were recorded and attributed to products of the radicals F-C6H4C(O) • and F-C6H4(~HCHz~b; the former is produced in a radical transfer reaction, the latter in an addition reaction with qS.. In both cases, the polarization is long range, extending over at least four atoms from the nominal location of the unpaired electron. This suggests the possible use of 19F as a spin probe for aromatic radicals and radical pairs in much the same way that a 9F is used with non-reacting systems. Last, we note that fluorine polarization cannot be produced in the original radical (q~.) and transferred suddenly 67 to F-C6H4C(O)'; however, polarization in both systems can be understood in terms of the radical pair theory. Polarization was also observed with p-ftuoronitrobenzene and this polarization is more difficult to understand since it is not known for p-fluoronitrobenzene to react with pheny| radicals. If the product here is biphenyl and p-FC6H4NO 2 does not enter the reaction but only forms the solvent cage, this would provide the first example of solvent polarization, an effect not predicted by any theory to date. On the other hand ifp-FC6H4NO2 is involved in the reaction, nothing new is added. Obviously, additional data, including accurate product analyses, are necessary to understand this system completely. A second example of a9F CIDNP was given by Rakshys 16° who studied the reaction ofp-fluorobenzyl chloride with n-butyl lithium. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
348
J. P O T E N Z A
p-FC6H4CH2CI+n-BuLi EtOEt).(p-FC6HaCH2)z
(143)
XLII [ +p-FC6H4(CH2)4CH3 XLIV The reaction was catalyzed with diethyl ether and the major products were XLIII and XLIV. Fluorine signals from both products showed enhanced multiplets; that from XLIV had net negative polarization superimposed, as might be expected from the theory above. However, the 19F NMR of XLIII showed an effect not previously noticed with proton spectra (Fig. 62(a)). Here, the sign of polarization changes at least five times within the multiplet, in contrast to proton spectra where only one change from A to E or vice versa was observed. This complex
I
30 Ht
I
a (a-l) -1 2 a - l a * l l O ( a , 1 )
2al
(a-l)
Fig. 62. (a) ClDNPspectrum of bis(p-fluoro) dibenzyl. (b) Predicted relative intensities for the multiplet components in (a). Reprinted with permission from ref. 160. behavior may be understood by considering one p-fluorophenyl component of the radical pair as an AzB2X spin system where X is fluorine. We would therefore expect the fluorine NMR spectrum to approximate a triplet of triplets, the first triplet arising from F coupling with the m-protons of the ring (A2); this triplet is then split into three by the o-protons (B2). The observed nine-line spectrum was reproduced qualitatively (Fig. 62(b)) using the Kaptein-Closs theory assuming that the hyperfine coupling constant for the ortho protons (Ao) with the electrons of the radical pair is greater than that for the meta protons (Am) and opposite in sign. For many aromatic radicals, including benzyl ~61, spin densities at the ortho and meta positions are found to be opposite in sign. Thus, if the first triplet gives Advan. Mol. Relaxation Processes, 4 (1972) 229-354
349
DYNAMIC NUCLEAR POLARIZATION
E/A corresponding to A,~, the second will give A/E of different magnitude corresponding to Ao, and the general features of the spectrum will be reproduced. An interesting 19F CIDNP experiment was performed by Trozzolo et al. 162 who thermally decomposed fluorine-substituted benzoyl peroxides. rn, p -
C
2
A
b
2 o,m,p-
"
~4 .
2
F
(144)
The product fluorobenzene is formed from three different radical intermediates, each with fluorine at a different ring position. All systems exhibited proton polarization but only the meta-substituted fluorine precursor led to fluorine polarization These results again suggest the possible use of F as a probe for spin transmission effects in aromatic systems. To date, no detailed experimental work has been reported for nuclei other than H or F. However, Kaptein and Oosterhoff 163 have mentioned observing ~3C NMR enhancements during the thermal decomposition of enriched acetyl peroxide. Judging from the signal-to-noise ratio of previously reported spectra, it would seem possible to detect ~3C in natural abundance if l 3C enhancements are larger in magnitude than those of protons. Nuclei such as 31p and 7Li should also be observable. G. Gas Phase CIDNP?
The possibility for observing C1DNPduring gas phase radical reactions should depend on the radical pair lifetime. This is seen most easily from eqns. (85) and (87). If ~ is sufficiently small, the individual w/s, which govern the rate of product formation with nuclear spin state j, should become small and nearly equal. Thus, the enhancement factor Gjk which depends on differences in w, will be small regardless of the magnitude of the mixing coefficients Mj. Kaptein and Oosterhoff 64 used this argument to predict a negligible multiplet effect in the gas phase.
APPENDIX
Since this review was written, there have been major advances both in CIDNP and DNP. With CIDNP, the radical pair theory has become fully established (refs. 164-167) and has been reviewed 16s'169. Multiplet intensities have been considered ~7° and a graphic method for multiplet spectra analysis was given by Miiller TM. A theory of CIDNP equivalent in many ways to that of Closs, Kaptein and Oosterhoff was developed by Adrian 172-174. This theory assumes that encounters between radicals in a radical pair take place via diffusive steps with correlation times of the order of I0-11 sec. A number of these steps in succession then gives the total encounter. Several articles have appeared t65' 175.176 treating Advan. MoL Relaxation Processes, 4 (1972) 229-354
350
J. POTENZA
the anomalous EPR spectra of transient radicals in terms of radical pairs. Theories to account for low field polarization via T~. t - S mixing were proposed and tested (refs. 177-179). Two simple rules 18o for predicting the sign of net enhancement and the phase of multiplet spectra were advanced by Kaptein. These depend on the signs of A, A#, Jis, and whether the polarized product is formed from a singlet or triplet precursor and whether or not the product forms from cage collapse. Kaptein's rules are especially suited for applications of ClDNP. Enhanced 13C and ~5N NMR spectra have also been reported t81' 182 and these may be used to supplement ~H data. Lastly, a number of investigators have reported applications of Clt)NP, some of which are mentioned here 183-195. For DNP, Richards and co-workers have developed a theory 196 relating NMR enhancements to AE, the average electronic excitation energy of the receptor molecule and r, the polarity of the bond containing the receptor nucleus. The theory w a s u s e d 196'197 to interpret high field 3 1 p and ~3C DNP data. Solvation and hydrogen bonding was examined ~9s at five fields and various temperatures using 1H t~NP. With 19F, extrapolated enhancements for substituted fluorobenzenes were related ~99 to the chemical shift, to 7r-n* absorption frequencies and to Hammett's a constant, while another study 2°° gave values for intermolecular hyperfine coupling constants and correlation times. In addition, the effect of radical structure upon low field enhancement was examined TM. The pulse model was applied 2°2 to tri- and pentavalent phosphorus using multifield measurements. With 13C, in addition to a high field s u r v e y ~97, multifield results for benzene and methyl iodide were reported 2°3. Lastly, 7Li salts in solution were examined 204 at low field to study complexation and aggregation.
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U. SCH~LLKOPF,G. OSTERMANNAND J. SCHOSSIG, Tetrahedron Lett., (1969) 2619. U. SCH6LLKOPF, U. LUDWIG, G. OSTERMANNAND M. PATSCH, Tetrahedron Lett., (1969) 3415. A. R. LEPLEX', P. M. COOK AND G. F. WILLARD, J. ,4mer. Chem. Soc., 92 (1970) 1101. J. W. RAKSHYS,JR., Chem. Commun., (1970) 578. S. V. KULKARNIAND C. TRAPP, Mol. Phys., 17 (1969) 209. A. M. TROZZOLO,S. R. FAHRENHOLTZAND F. HEATLEY,,4bstr., 159th ,4CS Meet., Houston, Texas, Feb. 1970, O R G N No. 42. 163 R. KAPTEIN AND J. OOSTERHOFF,,4bstr., I59th A C S Meet., Houston, Texas, Feb. 1970, O R G N No. 73. 164 H. FISCHER, Z. Naturforsch..4, 25 (1970) 1957. 165 H. FISCHER AND M. LEHNIG, Y. Phys. Chem., 75 (1971) 3410. 166 G. WARD AND J. CHIEN, Chem. Phys. Lett., 6 (1970) 245. 167 G. L. CLOSS, d. Amer. Chem. Soc., 93 (1971) 1317. 168 H. R. WARD, ,4ccounts Chem. Res., 5 (1972) 18. 169 R. G. LAWLER, Accounts Chem. Res., 5 (1972) 25. 170 K. Mi3LLER AND G. L. CLOSS, J. ,4mer. Cheat. Soe., 94 (1972) 1002. 171 K. MOLL~R, Chem. Commun., (1972) 45. 172 F. J. ADRIAN, J. Chem. Phys., 53 (1970) 3374. 173 F. J. ADRIAN, J. Chem. Phys., 54 (1971) 3912. 174 F. J. ADRIAN, Chem. Phys. Lett., 10 (197l) 70. 175 F. J. ADRIAN, J. Chem. Phys., 54 (1971) 3918. 176 P. ATKINS, R. GURD, K. MCLAUCHLANAND A. SIMPSON, Chem. Phys. Lett., 8 (1971) 55. 177 J. CJARST,R. Cox, J. BARBAS,R. ROBERTS,J. MORRISAND R. MORRISON,d. Amer. Chem. Soc., 92 (1970) 5761. 178 J. GARST, F. BARTON AND J. MORRIS, J. Amer. Chem. Soc., 93 (1971) 4310. 179 J. CHARLTONAND J. BARGON,Chem. Phys. Lett., 8 (1971) 442. 180 R. KAPTE1N, Chem. Commun., (1971) 732. 181 E. LIPPMAA, T. PEHK, A. BUCHACHENKOAND S. RYKOV, Chem. Phys. Lett., 8 (1970) 521. 182 E. LIPPMAA, T. PEHK AND T. SALUVERE,lad. Chim. Belge, 36 (1971) 1070. 183 R. KAPTEIN, M. FRATER-ScHRODERAND L. OOSTERHOFE, Chem. Phys. Lett., 12 (1971) 16. 184 R. KAPTEIN, F. VERHEUSAND L. OOSTERHOFF, Chem. Commun., (1971) 877. 185 J. DEN HOLLANDER,R. KAPTEIN AND P. BRAND, Chem. Phys. Lett., l0 0971) 430. 186 G. L. CLOSS AND D. R. PAULSON, d. ,4mer. Chem. Soc., 92 (1970) 7229. 187 B. BLANK AND H. FISCHER, HelD. Chim. Acta, 54 (1971) 905. 188 J. BARGON, J. ,4mer. Chem. Soc., 93 (1971) 4630. 189 N. A. PORTER, L. J. MARNETT,C. H. LOCHMi.JLLER,G. L. CLOSSAND M. SHOBATAKI,J. ,4mer. Chem. Soc., 94 (1972) 3664. 190 M. TOMKmWlCZ, A. GROEN AND M. COClVERA, J. Chem. Phys., 56 (1972) 5850. 191 T. KOENIG AND W. R. MABE¥, J. Amer. Chem. Soc., 92 (1970) 3804. 192 H. D. ROTH, J. Amer. Chem. Soc., 93 (197l) 4935. 193 H. D. ROTrL J. Amer. Chem. Soc., 93 (1971) 1527. 194 S. R. FAHRENHOLTZAND A. M. TROZZOLO, d. Amer. Chem. Soc., 93 (1971) 251. 195 S. R. FAlqRENHOLTZAND A. M. TR(3ZZOLO, d. Amer. Chem. Soc., 94 (1972) 282. 196 R. A. DWEK, R. E. RICHARDS, D. TAYLOR AND R. A. S~tAW, J. Cheat. Soc. ,4, (1970) 1174. 197 T. C. CANNON, R. E. RIC8ARDS AND D. TAYLOR, J. Chem. Soc. A, (1970) 1180. 198 W. Mi3LLER-WARMUTH,E. OZTEKIN, R. VILHJALMSSONAND A. YALqINER, Z. Naturforsch. ,4, 25 (1970) 1688. 199 W. M/2LLER-WARMUTrtAND A. YALg1NER,Ber. Bunsen#es. Phys. Chem., 75 (1971) 763. 200 W. Mi2LLER-WARMUTH,R. VAN STEENWINKELAND A. YALglNER, Mol. Phys., 21 (1971) 449. 201 R. L. GLAZER AND E. H. POINDEXTER, J. Chem. Phys., 55 (1971) 4548. 202 W. MidLLER-WARMUTH,H. GRi3TZEDIEK AND R. VAN STEENWINKEL, Z. Naturforsch. A, 25 (1970) 1696. 203 H. GRi3TZED1EK, W. Mi3LLER-WARMUTHAND R. VAN SXEENWINKEL, Z. Natur/brsch. A, 25 (1970) 1703. 204 J. POTENZAAND J. LINOWSKI, or. Chem. Phys., 54 (1971) 4095. 157 158 159 160 161 162
Advan. Mol. Relaxathm Processes, 4 (1972) 229-354
Advances in Molecular Relaxation Processes Elsevier Publishing Company, Amsterdam.
MEASUREMENT
AND
P r i n t e d in t h e N e t h e r l a n d s
APPLICATIONS
OF
DYNAMIC
NUCLEAR
POLARIZATION
JOSEPH POTENZA
School o f Chemistry, Rutgers University, N e w Brunswick, N.J. 08903 (U.S.A.)
CONTENTS 1. I n t r o d u c t i o n
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230
II. T h e o r y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. The single resonance experiment . . . . . . . . . . . . . . . . . . . . . . 1. S o m e f u n d a m e n t a l p r o p e r t i e s o f n u c l e i . . . . . . . . . . . . . . . . . . 2. S p i n s t a t e s in a m a g n e t i c field . . . . . . . . . . . . . . . . . . . . . . 3. B o l t z m a n n t h e r m a l e q u i l i b r i u m p o p u l a t i o n d i s t r i b u t i o n . . . . . . . . . . . 4. S a t u r a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. R e l a x a t i o n t r a n s i t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . B. T h e d o u b l e r e s o n a n c e e x p e r i m e n t . . . . . . . . . . . . . . . . . . . . . C. S y s t e m s w i t h s h o r t - l i v e d i n t e r m e d i a t e s - ¢ior~P . . . . . . . . . . . . . . . . 1. B a s i c o b s e r v a t i o n s - c h e m i c a l p u m p i n g . . . . . . . . . . . . . . . . . . 2. T h e m u l t i p l e t effect . . . . . . . . . . . . . . . . . . . . . . . . . . 3. F i e l d d e p e n d e n c e o f ¢IDNP s p e c t r a - " z e r o - f i e l d p o l a r i z a t i o n " . . . . . . . . III. I n s t r u m e n t a t i o n a n d e x p e r i m e n t a l a s p e c t s o f DNP A. Electronically induced oNP . . . . . . . . . . . . . . . . . . . . . . . . 1. E x t r a p o l a t e d e n h a n c e m e n t s . . . . . . . . . . . . . . . . . . . . . . . 2. S a m p l e p r e p a r a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . 3. R a d i c a l s u s e d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. I n s t r u m e n t a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. CIDNP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. Q u a n t i t a t i v e CIDNP e n h a n c e m e n t s . . . . . . . . . . . . . . . . . . . . 2. H i g h - f i e l d p o s i t i v e e n h a n c e m e n t s . . . . . . . . . . . . . . . . . . . . . 3. R a d i c a l l i f e t i m e c o n s i d e r a t i o n s . . . . . . . . . . . . . . . . . . . . . 4. R e a c t i o n c o n d i t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . .
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IV. E x p e r i m e n t a l r e s u l t s a n d c h e m i c a l a p p l i c a t i o n s - DNP . . . . . . . . . . . . . . A. Physical factors affecting enhancement . . . . . . . . . . . . . . . . . . . 1. S p e c t r a l d e n s i t y c u r v e s - d i p o l a r vs. s c a l a r c o u p l i n g . . . . . . . . . . . . 2. E f f e c t o f v i s c o s i t y . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. E f f e c t o f t e m p e r a t u r e v a r i a t i o n . . . . . . . . . . . . . . . . . . . . . 4. P h y s i c a l p a r a m e t e r s o b t a i n a b l e f r o m DNP m e a s u r e m e n t s . . . . . . . . . . B. E x p e r i m e n t a l r e s u l t s f o r p r o t o n s . . . . . . . . . . . . . . . . . . . . . . 1. L o w - f i e l d m e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . 2. H i g h - a n d m u l t i f i e l d m e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . 3. E x c e p t i o n s to t h e r u l e - s c a l a r c o u p l i n g f o r p r o t o n s . . . . . . . . . . . . C. E x p e r i m e n t a l r e s u l t s f o r f l u o r i n e n u c l e i . . . . . . . . . . . . . . . . . . . 1. L o w - f i e l d m e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . 2. P o s s i b l e i n t e r p r e t a t i o n s f o r s c a l a r c o u p l i n g . . . . . . . . . . . . . . . . 3. M u l t i f i e l d m e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . D. Experimental results for phosphorus nuclei . . . . . . . . . . . . . . . . . 1. L o w - f i e l d r e s u l t s . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. H i g h - f i e l d m e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . E. E x p e r i m e n t a l r e s u l t s f o r c a r b o n n u c l e i . . . . . . . . . . . . . . . . . . .
232 232 232 235 237 239 241 244 254 254 258 270 273 273 273 275 276 280 289 290 291 291 292 292 293 293 296 297 298 298 298 300 302 304 304 306 309 313 313 318 321
Advan. MoL Relaxation Processes, 4 ( 1 9 7 2 ) 2 2 9 - 3 5 4
230
J. POTENZA
V. E x p e r i m e n t a l r e s u l t s - CIDNP A. Alkyl and aryl radicals . . . . . . . . . . . . . . . . . . . . . . . . . . B. P h o t o c h e m i c a l a p p l i c a t i o n s - t e s t s o f t h e K a p t e i n - C l o s s t h e o r y . . . . . . . . C. Chain reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Reactions involving lithium alkyls - characterization of radical intermediates . . E. R a d i c a l p a i r i n t e r m e d i a t e s in r e a r r a n g e m e n t r e a c t i o n s . . . . . . . . . . . . . F. Nuclei other than protons . . . . . . . . . . . . . . . . . . . . . . . . . G . G a s p h a s e CIDNP? .
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Appendix
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324 324 329 338 339 345 347 349
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349
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
350
I. I N T R O D U C T I O N
The subject to be discussed in this review is called by a variety of names. It is called the Overhauser effectI, after the author who first predicted it in 1953; it is called nuclear-electron double resonance 2, in analogy with electron-nuclear double resonance (eNDOR); and it is called dynamic nuclear polarization 3 (DNP), the notation we shall use. Whatever the name, ONV is a double magnetic resonance technique, and, as such, requires the presence of two non-identical spins. Basically, the population distribution of one type of spin is changed while that of the other is observed. Under these conditions, the magnitude of the resonance signal of the second spin is increased. Thus, if in a solution containing protons and unpaired electrons, the EPR signal is stimulated by light, an increase in the size of the NMR signal, known as an enhancement, is observed. Enhanced NMRsignals may be several hundred times larger than unenhanced signals and may be either positive or negative. In addition, the sign, magnitude and structure of the enhanced signal is extremely sensitive to the chemical composition of the system and the type of reactions occurring. Therein lies its chemical utility. The following historical abstract of work in the field will serve to demonstrate the type of information obtainable by DNV and the interest it has for chemists. In 1953, Overhauser predicted 1 that by stimulating the conducting electrons in a metal, it should be possible to increase the size of the NMR signal. This was verified experimentally a year later by Carver and Slichter4 who showed that appreciable nuclear polarizations could be achieved for lithium, sodium and hydrogen nuclei. Since that time, a variety of enhanced NMR signals has been observed in materials as diverse as chars 5, tars 6, metals 7-9, solutions containing transition metal ions 1°-~2, and solid free radicals t3-t5. Most of these systems have been investigated from a physical point of view with the aim of understanding spin-spin interactions. The first mention of chemical applications for DNV was by Richards and White16, J v. In a series of papers beginning in 1962, they suggested the possibility Advan. Mol. Relaxation Processes, 4 ( 1 9 7 2 ) 2 2 9 - 3 5 4
DYNAMIC
NUCLEAR
231
POLARIZATION
of using DNP tO increase the size of unobservable NMR signals, and to determine mean distances between and association times for species in solution. Simultaneously, other groups, including those of Miiller-Warmuth 18 and Poindexter 6 were using DNP as an experimental means for investigating molecular motions and collision dynamics in liquids. The greatest chemical possibilities for DNP have emerged in the last few years, and these have been in two distinct areas: solutions containing stable free radicals and systems with short-lived radical intermediates. With stable systems, ordinary, or electronically induced DNP, has been used for studying weak molecular complex formation 19' 20, as between two aromatic molecules, as a probe for stereo-specific collisions in liquids 21, as a probe for aromaticity in non-benzenoid compounds 22, and to measure NMR signals which cannot ordinarily be seen with a high resolution NMR spectrometer 23. In this area, DNP has the promise of contributing to the understanding of liquids on a microscopic level. Applications of DNP important to organic chemistry began in 1967 with the discovery of chemically induced dynamic nuclear polarization (CIDNV) by Bargon et al. 24' 25, and by Ward and Lawler 26' 27. Using only a high resolution NMR spectrometer, they observed that certain systems, such as organic peroxides and azo compounds, which are known to decompose via free-radical intermediates (refs. 28, 29), gave rise to transient NMR emission signals, whose magnitude changed as the reaction proceeded. With the same systems, no EPR signal from the radical intermediates could be observed. During the past few years, CIDNP has been used routinely to test for the presence of short-lived radical intermediates in several reactions including: (1) The rearrangement of a benzyne adduct to N,N-dimethyl benzylamine 3° (2) The reaction of gem-dihalocyclopropanes with alkyllithium compounds
(ref. 31). (3) The sigmatropic rearrangement of I to II (ref. 32) N N I
1I
In all these cases, enhanced NMR signals were observed and the presence of radical intermediates was ascertained. For the organic chemist, then, CIONP provides a powerful, routine, experimentally simple test for the presence of radical pair intermediates. Further, it has recently been shown 33 that CIDNP is capable of determining the spin multiplicity (singlet or triplet) of radical intermediates. Thus, the decomposition of an acyclic azo compound known to proceed via the singlet state gave an enhanced NMR spectrum predictably distinct from that of the same reaction product formed via a triplet intermediate in a different reaction. As Advan. Mol. Relaxation Processes, 4 (1972) 2 2 9 - 3 5 4
232
J. POTENZA
more reactions are studied and their spectra interpreted in detail, it is expected that additional insight concerning radical reactions will be gained. The purpose of this review is to introduce organic chemists to the principles and experimental techniques underlying DNP. No previous knowledge of magnetic resonance is assumed except for some familiarity with chemical shifts and coupling constants. For the sake of brevity, some items are not treated rigorously. Wherever possible, the reader is referred to standard textbooks and articles for a more complete treatment. In the theory section to follow, electronically induced DNP, applicable primarily to systems containing stable free radicals, is treated in some detail because of its intrinsic interest and because many of the concepts developed pertain also to CIDNP.
II. T H E O R Y
A. The single resonance experiment 1. Some fundamental properties o f nuclei
Fundamental particles such as electrons and protons have certain intrinsic properties, including charge, mass and spin. However, a spinning charge creates a magnetic field and so these particles also have associated with them a magnetic moment; that is, they behave like tiny magnets whose strength is described by a magnetic moment p, also an intrinsic property. The magnetic moment is a vector quantity proportional to the spin angular momentum of the particle (hi) and is given by
(1)
la = 7hi
where ~, the magnetogyro ratio, is the constant of proportionality. Figure 1 shows
N
p ((1)
(b)
Fig. 1. Relationship between spin angular momentum and magnetic moment for a particle with (a) positive, (b) negative gyromagnetic ratio. Advan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
233
POLARIZATION
the relationship between the spin angular momentum and the magnetic moment for particles with positive and negative magnetogyro ratios. Figure 1(a) depicts a positive rotating charge and corresponds to most nuclei. Figure I (b) shows a net negative circulating charge as found for the electron, neutron and certain nuclei. North and south poles are also shown for the magnetic moments. The magnetic moment is also given by the expression (2)
la = g i l l
Here # is a dimensionless constant called the nuclear # factor for nuclei 34 and the Lande # factor for electrons 3s. For a spinning sphere with its charge and mass uniformly distributed over its surface, the # factor would be unity; hence, the # factor is related to the charge distribution of the particle. For nuclei, fl is called the nuclear magneton (fiN); for electrons, the Bohr magneton. In either case, it is l given in terms of fundamental constants as eh
-
(3)
2mc
where h is Planck's constant divided by 2n, c is the velocity of light and m is the mass of the particle. Combining eqns. (2) and (3), we find that particles with small mass should have large magnetic moments and particles with large mass small moments. This is shown in Table 1, which contains the magnetic properties of TABLE 1 MAGNETIC PROPERTIES OF SELECTED PARTICLES
Particle
Spin I (h)
g
In 'H 2H 7Li 11B 12C
½ ½ 1 ] ~ 0
--3.826 5.585 0.857 2.171
-- 18,326 26,753 4,107 10,398
13C 15N t80 19F 3~p 3SCl Free e -
.~ ½ 0 ½ ½ ] ½
1.405 --0.567
6,728 --2,712
5.257 2.263 0.456 -- 2.002319
y Q (rad/sec.gauss) (10 -24 cm 2)
25,179 10,840 2,184
Resonance freq. at 10,000 gauss (Mc/sec)
0 0 0.00274 0.02 0.0355
29.165 42.577 6.536 16.547 13.660
0 0
10.705 4.315
0 0 -- 0.062 0
40.055 •7.235 4.172 27,994
P l a n c k ' s c o n s t a n t h = 6.6252 × 1 0 - 2 7 erg.sec B o l t z m a n n c o n s t a n t k = 1.38044 × 10-16 erg/deg Bohr m a g n e t o n fl = eh/2mec = 0.92731 × 10 -20 erg/gauss N u c l e a r m a g n e t o n fl = eh/2mpc = 0.50504 × 10 -23 erg/gauss
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
234
j. POTENZA
TABLE 2 V A L U E S O F ,q F O R SOME O R G A N I C R A D I C A L S
Radical
9
Ref.
Vinyl Anthracene cation Coronene cation Allyl Anthracene anion
2.00220 2.00249 2.00249 2.00254 2.00266 2.00437
37 38 38 37 38 38
2.00507
38
2.00512 2.0052
38 39
2.00568
38
1,4-Naphthasemiquinone anion 2,3-Dichloro- 1,4-naphthaserniquinone anion 2-bromo- 1,4-benzoserniquinone anion Tri-t-butyl phenoxyl 2,3,5,6-Tetrachloro- 1,4-benzosemiquinone anion
some fundamental particles and representative nuclei 36. The free electron magnetic moment is some 658 times larger than that of the proton. This factor is not the ratio of the masses because of the different g factors. For electrons, values of g vary from radical to radical depending upon how the spin angular m o m e n t u m interacts with the orbital motion of the electron. This "spin-orbit" coupling causes g to depend upon the chemical environment of the unpaired electron. Typical g values are shown in Table 2 for several organic free radicals. Larger lists may be obtained elsewhere 35' 40. Although deviations from the free-electron value are not large, they have some chemical significance and are important for describing CIDNP. For example, halogen atoms substituted on a radical generally lead to high g values. In general, g values increase as the atomic numbers of the substituents increase. F r o m Table 1, we notice that the magnetic moment of the neutron is not zero. Even though it has no net charge, the neutron does have a charge distribution, hence a magnetic moment. Also, the magnetic moment of the neutron, like that of the electron, is negative, indicating that it behaves magnetically like a negative particle. The magnetic moments of complex nuclei (ZH, 11B, x9F, etc.) are similar in magnitude to those of the neutron and proton because they are composed of these particles. Any nucleus with odd mass number will possess a magnetic moment since not all the nucleons are paired. In addition, some nuclei with even mass numbers will have spin (e.g. ZH) due to unpaired nucleons, while others will have zero magnetic moments. Carbon-12, for example, with all neutrons and protons paired, has no net spin angular momentum. Further, we note that the magnetic moment of the neutron and proton do not quite give that of the deuteron. The magnetic properties of each particle, then, are distinct and characteristic of only that particle. They are determined solely by the 9 value and the spin angular Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
235
POLARIZATION
momentum (equivalently by ~, and I), and cannot be obtained by any simple theory 41. Although we shall not be directly concerned with them, mention should be made here of nuclear quadrupole moments (eQ) (which are also related to the spin of the particle). These are tensor quantities related to the shape of the nucleus (ref. 42). Spherical spinning nuclei have no quadrupole moment, prolate nuclei (shaped like an egg) have a positive quadrupole moment, oblate (doorknob) nuclei a negative quadrupole moment. Hence, if an electron approaches a nucleus with non-vanishing quadrupole moment, the magnitude of the electrical interaction will depend on the direction of approach. Nuclear quadrupole resonance spectroscopy is an area of research in itself~3; however, for our application, quadrupole moments introduce only a complication. We shall not concern ourselves further with them.
2. Spin states in a magnetic field In the absence of other magnetic fields, a single nucleus, such as that shown in Fig. 1, can be oriented in any direction with equal energy. If, however, the nucleus is placed in an external magnetic field H (Fig. 2), there will be preferred
N
/
I t~-" 1
/ 1
Eint
2
Eint
=
-I/dJ
IHI cos 8
,
I
= -I/u [ IH/ c o 5 8'
2
\ Fig. 2. Allowed orientations and energy levels for a particle of spin ~ in a magnetic field. Only one value of 0 and 0' is allowed. orientations. For a classical magnet, all relative orientations are allowed and the energy of interaction between the two magnets is given by E~., = - ~ .
H = - I ~ l IHI cos 0
(4)
where 0 is the angle between the magnetic moments. Thus, the orientation with highest energy corresponds to north poles repelling, the orientation with lowest energy to north and south poles attracting. But nuclear and electron spins are quantized and, for these particles, there will be preferred orientations in the magnetic field. The energy of interaction is again given by eqn. (4), and we must look more closely at eqn. (2). For a given nucleus, g, and ft, are constant, while I, the spin angular momentum, is restricted. In general, only the magnitude of the ddvan. MoL Relaxation Processes,
4 (1972)
229-354
236
J. POTENZA
magnetic moment and one component (say along the external field direction, z) can be measured. The magnitude of the magnetic moment is given by I~1 = y[I(I + 1)]{h
(5)
and its component in the field direction by Pz = I, I - 1 , . .
", - I
(6)
in units of 7h. A particle of spin ½, therefore, has only two allowed energy levels (/~= = + ½7h, -½?h) characterized by the spin quantum number ms = +__½ and the z component may be aligned with or against the field, as shown in Fig. 3 for a proton. The magnetic moment itself will precess about the field direction defined by the laboratory magnet and the z component will remain constant.
\
,__/
(1)
\
,
/
(2)
Fig. 3. Precession o f p r o t o n magnetic m o m e n t in a n external field. T h e z c o m p o n e n t of/~H is c o n s t a n t for a given orientation. Since ~'n is positive, the state characterised by m~ = -}-½ lies lowest.
Since the states are discrete, transitions between them may be observed by shining light (dipole radiation) on the system. If the frequency of the light corresponds to the frequency of precession, light will be absorbed and spins will change their orientation. For nuclei, this is nuclear magnetic resonance (NMR); for electrons, electron paramagnetic resonance (EPR). These techniques are similar except that different instrumentation is required for each since the magnetic moment, the separation between the states and the frequency of radiation required for resonance are much larger for the electron than for any nucleus (Table I). At this point, we note that the resonance frequency is a function of the external field, viz. A E , . t = hv,os = ½ o ~ n - ( - ½ ) g ~ H
= g~H
(7)
for a particle of spin ½. As the external field is increased, the transition frequency increases linearly as shown in Fig. 4. Using the information in Table 1, we may now calculate the resonance frequency of any spin ½ particle at any field. Consider Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
237
POLARIZATION ngz =-~/2
energy~
I
A
E=hu=g~nH
m Z =+I//2
6
.u
Fig. 4. Energy levels for a positive spin ~ particle in a magnetic field.
1H at 10,000 gauss. From eqn. (7), ~'H - -
ON//NIHI h
Inserting appropriate values, we obtain v(10,000 gauss) = 5.585(5.0504 × 10 -24 erg/gauss) × 6.6252 × 10 - 2 7 erg.sec
104
gauss
= 42.575 × 106 c/sec = 42.575 MHz which is the value entered in Table 1.
3. Boltzmann thermal equilibrium population distribution Consider an assemblage of spins in the magnetic field, as, for example, in a 1 ml sample of water which contains some 7 x 1022 protons (Fig. 5). If we assume that the individual protons interact only with the external magnet and not
\
N
/
/\/'I \I\
grin
I n+
Fig. 5. A s s e m b l a g e o f non-interacting spins in a m a g n e t i c field. T h e energy levels s h o w n are highly degenerate.
with each other, there will be only two energy levels for each spin. Because of the large number of spins in the sample, each level will be highly degenerate. We may now ask how many spins are aligned with the field, how many against. Offhand, we might expect all the spins to be in the I+ ) state since that corresponds to lower energy. Indeed, this would be true at zero temperature or for an infinitely Advan. Mol. Relaxation Processes, 4 (1972) 229-354
238
J. POTENZA
strong external field. For other cases, the thermal motions in the liquid will populate the upper level with a consequent increase in spin entropy. When the spins are in thermal equilibrium with their environment, the populations of the individual levels will be governed by a Boltzmann distribution, such that the ratio of spins in the upper state to that in the lower is given by N_ N+
- exp ( - hv/kT)
(8)
where k is Boltzmann's constant and T is the absolute temperature. For protons in a field of 10,000 gauss at 27 °C, N_ _ exp - [(6.625_x 10 -27 ~ c ) ( 4 2 . 5 7 7 × 106_c/sec)7 [_ 1,3805 )< 10-16 erg/OK)(300 OK) j
N+
= exp [ - 6 . 8 1 × 10 -6] ~ 1/(1.00000681) Similar values will be obtained for other nuclei at this temperature. The result shows that at ordinary temperatures, ½ of the spins are aligned with the field, ½ against the field to six significant figures. Nonetheless, it is the difference in the seventh figure that allows NMR signals to be observed. It is not surprising that relatively sensitive apparatus is required to observe NMR signals. A similar calculation for the free electron shows that more spins are in the lower state, as compared with nuclei, because of the large magnetic moment of the electron. Other things being equal, we expect an EPR signal to be much easier to detect than an NMP, signal, if the size of the signal depends only on the relative populations of the spin states. For a spin ½ positive particle, the strength of the NMR signal is proportional to N+ - N _ . The individual populations, N+ and N_, can be calculated from eqn. (8), if the total number of spins, tiT, in a sample is known, since N + + N _ = nT
(9)
For nuclei with spin > ½, the situation is slightly more complicated and the NMR signal is proportional to 44 ~-E mzNm
/tnz
z
(10)
where 1 is the spin of the particle and mz is the quantum number characteristic of the state (for protons rnz = +½). The NMR signal strength also depends on the temperature and it is instructive to examine the ratio (N_/N+) at infinite and zero temperature. As T ~ 0 °K, N_ - - -~ exp [ - h v / 0 ] = 0 N+ Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
239
POLARIZATION
regardless of the strength of the external field which characterizes v. Thus, at 0 °K, all the spins are in the lower state. This is not surprising since at absolute zero there is no thermal energy to reorient the spins. As T ~ aD, N_
exp [ - h v / o o ]
= 1
N+ and exactly ½ of the spins are in each spin state. These results are indicated graphically in Fig. 6. We see that the room temperature population distribution is quite close to the high temperature limit, and that as the temperature changes, so does the expected strength of the NMR or EPR signal. Hence the need for constant temperature in magnetic resonance experiments. I ->
I -->
T---~-O
T -.-=.o o
Fig. 6. Schematic p o p u l a t i o n distribution for p r o t o n s in a magnetic field at zero a n d infinite temperature. T h e r o o m t e m p e r a t u r e distribution is close to the high temperature limit.
4. Saturation
A magnetic resonance signal is generally obtained by shining light (an oscillating electromagnetic field) at the resonance frequency on an assemblage of spins and varying the magnetic field slightly to pass through the value of H which satisfies eqn. (7). An absorption of radiation in and around the calculated resonance frequency is observed. The absorption is not an infinitely narrow line for several reasons 36. These include: (1) Dipole-dipole broadening which occurs primarily in solids and viscous liquids. We have previously assumed that each nucleus feels the effect only of the external field; however, other nuclear magnets are in the vicinity and are in constant motion. A given nucleus will therefore experience a time-dependent fluctuating magnetic field in addition to that from the permanent magnet. The result is a slightly different field for each nucleus and a broadened line. (2) Inhomogeneity of the applied magnetic field, which causes nuclei in different parts of the sample to experience different fields. (3) Spin-lattice relaxation, which will be discussed below. Essentially relaxation reduces the time a given nucleus spends in one state. This contributes to line broadening via the uncertainty principle AE. At ~ h. If At is long, AE will be small and the line will be narrow. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
240
J. POTENZA
(4) Quadrupole effects which afford an additional path for relaxation and affect At. To understand why absorption occurs, we consider the effect of light at the resonance frequency impinging on a collection of spins initially at thermal equilibrium. Three types of transitions are possible: absorption, stimulated emission and spontaneous emission. These are depicted in Fig. 7. In Fig. 7(a), a photon whose frequency corresponds to the energy difference between the I + ) and I - ) nuclear states is absorbed by a spin in the lower state. This raises the spin to the upper state and the photon is annihilated. In Fig. 7(b), an equivalent photon causes a downward transition. Since energy is given off in the process, two photons result, one from the energy loss and one corresponding to the original photon.
a)
~
¢
+ •
hv
•
• •
•
o,m
•
•
_>
•
+>
•
t->
•
•
e
¢
•
•
•
•
->
+>
•
->
I i
I+>
o e
•
c]
~_
•
•
t o o
I+>
~
D
-
I -'~ -
I
-
I
->
¢
+ I+>
°
° ° ' l
I
~
l
w
-
+>
Fig. 7. Schematic representation of (a) absorption and (b) stimulated emission, and (c) spontaneous emission.
With spontaneous emission, a spin in the upper state reverts to the lower state and the energy is emitted as a photon. Spontaneous absorption does not exist. For a given intensity of radiation (number of photons), the number of spins going from the I + ) state to the [ - ) s t a t e (n+_) via absorption is proportional to the number of spins in the lower state multiplied by the probability for the transition
(P+-): n+_
= N+P+_
(11)
Similarly, the probability for stimulated emission is given by n_+
= N_P_+
(12)
For any time-dependent perturbation, U ( t ) , in this case the oscillating magnetic field, applied to this system of discrete energy levels, the transition probability at the resonance frequency is given by 2re Pu = ~- I(ilU(t)lj)l 2
(13)
where (il and IJ ) are the wave functions of the discrete states. The matrix element Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
241
POLARIZATION
(il U ( t ) l j ) m u s t be non-vanishing for transitions to occur. In effect, the perturbation U(t) must mix the states. From the Hermitian property of the matrix element, it can be shown that KiiU(t)lJ>l 2 = [
(14)
whence P i j = eji, or, in our case, P+_ = P_ +. It can also be shown that, for all external fields obtainable in practice, spontaneous emission is negligible .5. Ignoring spontaneous emission, and using the fact that P + _ = P_ ÷, the rate of population change for the [ + > level is given by dN+ _ ( N _ - N + ) P dt
(15)
Recalling that N+ + N _ = rtT, the total number of spins, and defining the population difference N+ - N _ = no, it follows that N+ - (nT+nD) 2
and
N _ - (nT--n°) 2
(16)
Now, since dN+/dt = ldno/dt, we may rewrite eqn. (15) and solve for no, which governs the size of the resonance signal. Thus, dnD
--2nDP
(17)
no = riD(0) exp [ - 2 P t ]
(18)
-
dt
-
whence
Here, no(O) is the population difference at zero time (the thermal equilibrium value calculated above). Equation (18) predicts that, at zero time, the NMR signal reflects the thermal equilibrium population difference between the states, but that as time goes on, the difference is reduced to zero and the resonance signal disappears; viz. as t ~ oo no ~ no(O) exp [ - 2 P o o l
= 0
This is known as saturation, and if complete, the number of spins in the lower state equals that in the upper state, the same effect that would be obtained at infinite temperature. One usually tries to avoid saturation when obtaining quantitative spectra, since if even partial saturation occurs, the resonance signal will not reflect the true thermal equilibrium population distribution. Saturation is usually avoided by keeping the density of radiation small. For DNP, we shall use intense radiation and purposely try to saturate electron spin levels. 5. Relaxation transitions Suppose that, having saturated the resonance signal of a sample via RFAdvan. Mol. Relaxation Processes, 4 (1972) 229-354
242
J. POTENZA
induced transitions, we removed the source of light. Ignoring spontaneous emission, we have no mechanism by which spins in the upper state can return to the lower state. This is unacceptable, since, when saturated, the spin system is not in thermal equilibrium with its surroundings. In addition, we could follow experimentally the return to equilibrium by watching the NMR signal grow to its original value. The spin system returns to thermal equilibrium via relaxation transitions 46. These are radiationless transitions by which the fluid, acting as a thermal bath, absorbs the energy released by the spin transitions (Fig. 8). For relaxation transi-
I I
energy
+
llh i •
•
•
•
molecular motion
absorbed
•
+
I+>
•
•
•
*
by fluid
•-I+>
Fig. 8. Schematic representation of a downward relaxation transition. tions to occur, there must be molecular motions in the liquid at the resonance frequency and the spin system must be coupled to other degrees of freedom. It is this process of relaxation that originally produces the excess of spins in the lower state, and so the downward transition probability for relaxation (w_ +)nmst be greater than the upward transition probability (w+_). We may now write an equation for the rate of population change of the lower spin state as dN+ _ dt
N+ w+_ + N _ w_+
(19)
At equilibrium, dN+/dt = 0 and we find that N_(eq)
-
N+(eq)
w+ _
- exp [ - h v / k T ]
(20)
w_+
The relaxation transition probabilities are in the ratio of the equilibrium populations of the states. Again using eqn. (16), the rate equation describing the change in the population difference due to relaxation transitions can be written as dnD _ nT(W- + -- W+_)-- nO(W- + + W+_) dt
(21)
This can be rewritten as
dnD dt
-
no--riD 7"1
(22)
where W_+ --W+_) /'/0 ~
nT
(w_++w+_)
and
--1 = ( w + _ + w _ + )
TI
Advan. Mol. Relaxation Processes, 4 ( 1 9 7 2 ) 2 2 9 - 3 5 4
DYNAMIC
NUCLEAR
243
POLARIZATION
The solution to eqn. (22) is nD = no + C exp [ - t/T1]
(23)
Now, it is easily seen that n o is the equilibrium population distribution (let t ~ Qo) and that T~, which has units of time*, is characteristic of the approach to equilibrium. It may be regarded as the half-life of the nucleus in the upper spin state. Notice that T 1 is the reciprocal of the total relaxation rate. This will be true in general. For our completely saturated spin system at t = 0, the system is unpolarized; that is, half of the spins are in each level and no = N+ - N _ = 0. In this case, no = no(1 --exp [--t/Tl])
(24)
from which we see that the population difference should increase exponentially to its equilibrium value. By measuring the size of the NMR signal as a function of time after turning off the stimulating radiation, we may measure 7'1, the spin-lattice relaxation time. TABLE 3 PROTON SPIN--LATTICE RELAXATIONTIMES
Compound
T1
Re].
(sec) 11 ~ benzene in CS~ Benzene T o l u e n e (ring) T o l u e n e (CH3) H20 Ethanol H2SO4 Glycerine
60 l 9.3 16 9 3.6 2.2 0.7 0.023
47 47 47 47 48 46 46 46
Spin-lattice relaxation times for several protons in different compounds are shown in Table 3. In general, values for organic compounds are in the range milliseconds to seconds. They decrease with increasing viscosity (compare ethanol, H2SO4, glycerine), and this has been interpreted theoretically. Further, values of T1 depend upon the magnetic field at which the measurement is made, generally increasing with increasing field. This increase results from the field dependence of the relaxation transition probabilities which will be discussed below. Other factors, including temperature, soNent and paramagnetic impurities, also strongly affect the magnitude of T1. The addition of paramagnetic impurities, including O2 * T h a t Tt h a s units o f time is seen f r o m its definition as the reciprocal o f a relaxation rate. If w is given by transitions/sec then the units o f T~ are seconds.
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
244
J. POTENZA
from the air, reduces/'i markedly. Values of 7"1 of the order of 10 -4 sec are not unusual when paramagnetic impurities are present. The measurement and interpretation of T1 in terms of molecular motions in liquids is itself an area of research (ref. 49). We can now obtain a more complete description of the spin system by considering simultaneously the effects of radiation and relaxation. From eqns. (17) and (22), we obtain the rate equation drip _ _ 2 n o p + (no - riD) dt T~
(25)
In a steady state, dno_ dt
0
and
nb
_
no
(26)
1 + 2PT~
Thus, if 2PT1 << I, nD is the equilibrium value, and the NMR signal will reflect this distribution. Alternatively, if P, which is proportional to the square of the resonance radiation amplitude, becomes large, no < no and saturation occurs. For samples with large values of T1, indicating inefficient thermal relaxation, saturation is easier to obtain for a given intensity of radiation than for samples with small 7'i. Overall, since the availability of molecular motions required to induce relaxation transitions varies as the chemical composition of the system changes, we expect T~ and the ease of saturation to be a function of the system chosen. B. The double resonance experiment
We consider the simplest case of a nucleus of spin ½ and an electron of spin ½, each on different molecules, placed in an external magnetic field. In practice, this may consist of a solution of a stable free radical in a proton-containing solvent. When the spins are far apart, each will feel only the influence of the external field. In this case, the spins are uncoupled, and it is possible to observe separately an EPR transition and an NMR transition (Fig. 9(a)). The spin Hamiltonian for this 3
1
I*>
N i ** >
1
2
3
\
4 -4-I->/
(a)
S
~.
q
4
i -.>
(b)
Fig. 9. Energy level d i a g r a m s h o w i n g possible transitions for a system o f two (a) u n c o u p l e d a n d (b) coupled spins. T h e large arrows correspond to electrons, the small arrows to nuclei.
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
POLARIZATION
245
uncoupled system is given by (27)
oY" = - hYl Ho I ~ - hVs Ho Sz
where I~ refers to the nuclear spin quantum number and S~ to the electron spin quantum number. The four energy levels in Fig. 9 are obtained using eqn. (27) and the appropriate values for S, and I~ (+½). The - ½ state lies lowest for the electron since it is a negatively charged particle. The conditions for which this energy level diagram applies have been discussed by Abragam 5o. Owing to Brownian motion, the spins will diffuse into proximity of each other and therefore the nucleus will be affected by the electron and vice versa. The spins are said to be coupled and the possible states are shown schematically in a simplified way in Fig. 9(b). State 1, with both electron and nucleus aligned against the field, is obviously highest in energy, followed by states 2, 3 and 4. Transitions 1-3 and 2-4 labeled p in Fig. 9(b) correspond to the EPR transition since only the electron spin changes. Similarly, q refers to the NMR signal, while r and s are double spin transitions. The symbols p, q, r and s are transition probabilities. Hence, transitions between states 1 and 2 in Fig. 9(b) occur with probability q, etc. The size of the ~MR signal will be proportional to (N2 + N 4 ) - ( N l + N 3 ) . If now we saturate the EPR signal with light of appropriate frequency and intensity, we may enquire as to its effect on the NMR signal, which we shall observe. For complete saturation, N1 = N 3 and N2 = N4, and the question arises as to whether N~ > N2 ; that is, are the spin states on the left-hand side of Fig. 9(b) more highly populated than those on the right or is the reverse true? This will depend on the magnitude of the relaxation transition probabilities q, r and s. Ignoring q for the moment, we may examine the limiting cases qualitatively. If r >> s, we may ignore s, obtaining the spin energy level diagram shown in Fig. 10. Some of the spins entering state 1 will return to 3 via stimulated emission and relaxation, while some will go to state 4 via relaxation transitions. The net effect of this is to populate states 2 and 4 at the expense of 1 and 3. Thus, with r >> s, 1 2
I-->
-
I-÷>
-
-
-
4
I-*>
Fig. 10. Spin energy level d i a g r a m for a two-spin system a s s u m i n g r ~, s.
Advan. MoL Relaxation Processes, 4 (1972) 229-354
246
J.
POTENZA
N~ << N2 and N 3 << iV,. The observed NMR signal will now be larger than the equilibrium value, resulting in a positive enhancement. Alternatively, if s >> r, N1 >> N2 and emission will occur across the q gap, corresponding to a negative enhancement of the NMR signal. Examples of positive and negative enhancements are shown in Fig. 11.
/40:745
Galvinoxyl
Enhonced signal
--~,.
BDPA +
C6F6
CeF6
Enhanced signal
Fig. 11. Examples of negative and positive 19F enhancements obtained at 74 gauss using C6Fe with the stable free radicals galvinoxyl and bisdiphenylene phenyl allyl.
Following Solomon 51, we may now determine a quantitative expression for the enhancement factor by considering the rate of population change for the individual energy states. From Fig. 9(b), it follows that dN+ _
constant
-
pN_ _ + rN_ + + qN+ + - (p + q + r)N+ _ +
-
pN_+
-
pN + _ + sN + + + qN _ + - (p + q + s)N_ _ +
constant
pN+ + + rN+ _ + qN_ _ - (p + q + r)N_ + +
constant
dt
dN++
+sN__
+qN+_
-(p+q+s)N++
+constant
dt dN__ dt
dN_+ -
(28)
dt
The constants may be obtained by considering the system at thermal equilibrium where dN+ _/dt = 0, etc., and inserting the appropriate values for the populations. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
247
POLARIZATION
Experimentally, we can observe the net z component of the nuclear magnetic moment (i~, proportional to the NMR signal strength) or the net z component of the electron moment (Sz, proportional to the EPR signal strength). These are given by (N+ + + N_ + ) - ( n + _ + N _ _ ) = kt z
(29)
(N_+ + N _ _ ) - ( N + _ + N + + ) = kS z
(30)
We can now calculate the rate of change of both nuclear magnetization (dlz/dt) and electron magnetization (dSJdt) by combining eqns. (28)-(30). Thus d(N + + + N _ + N + _ dt -
-
N
_ _) = k di_~ = k[ dt
-
(2q + r + s)t z - (r
-
s)$z + C] (31)
At thermal equilibrium, diz/dt = 0 and we evaluate the constant as C = (2q + r + s)l o + ( r - s)So
(32)
where I o and So are given by eqns. (29) and (30) respectively. Inserting the constant and rearranging, we obtain dlTz _
dt
(2q + r + s)(i z - I o ) - ( r - s ) ( S . - So)
(33)
If the EPR signal is saturated completely, the electron magnetization ~ is reduced to zero, and, in a steady state, the nuclear magnetization is constant, i.e. diJdt = O. Under these conditions, eqn. (33) reduces to 0 = - (2q + r + s)(l~ - Io) + ( r - s)So
(34)
Solving for Tz, we have
t2 = io+
(r-s)So (2q+r +s)
(35)
The enhancement factor G corresponds to the increase in nuclear magnetization over the thermal equilibrium value and is given by
G - 1~-I° (r-s)So Io (2q + r + s)Io
(36)
That G indeed represents the enhancement can be seen most readily by considering the system initially. Then, i z = I 0 and G = 0. Overall, eqn. (36) comprises two factors. The first, [(r-s)/(2q+r+s)] is essentially the ratio of polarizing relaxation transitions to the sum of all possible relaxation transition probabilities. The second factor, So/Io, is the equilibrium ratio of electron to nuclear polarization, which is equal to ~s/~i, the ratio of the magnetogyric ratios of the two spins. Later, by considering the possible magnitudes of the various relaxation transitions, we shall Advan. Mol. Relaxation Processes, 4 (1972) 2 2 9 - 3 5 4
248
J. POTENZA
show that for electronically induced DNP, if ~,~ > 0, the maximum positive signal enhancement is given by I~s/~tl, the maximum negative enhancement by -½1~s/hl. Table 4 lists values of these ratios for several spin systems. We see that maximum enhancements of the order of 0-3 should be obtained for systems of coupled nuclei, while for an electron coupled with a nucleus, enhancements of several hundred to several thousand are expected, depending upon the nucleus in question. TABLE 4 SCALAR AND DIPOLAR LIMITS FOR SELECTED SPIN SYSTEMS
System
Saturate
Maximum negative enhancement a (½es/7l)
laC/1H 19F/1H 19F/1H alP/1H alp# H ~H/exaC/e19F/e3tP / e -
1H 1H 19F IH aap Free Free Free Free
+1.99 +0.53 -~0.47 +1.23 +0.203 -- 329 -- 1305 --350 -- 813
eeee-
Maximum positive enhancement
+658 +2610 + 700 + 1625
" Nuclear enhancements are positive because the sign o f 7 is the same for both nuclei.
The exact limits of the enhancement for this intermolecular case will depend on the magnitude of the relaxation transition probabilities q, r and s in accord with eqn. (36). These in turn will depend on the type of coupling between the spins. Two types, dipolar and scalar, are possible. Dipolar coupling is classical in nature, and is approximately the same as the interaction between two bar magnets (Fig. 12) If the magnets are in relative motion, an oscillating magnetic field due to one magnet will be established at the second. The electron and nucleus may be con-
Fig. 12. Dipolar interaction between two bar magnets. I f the magnets oscillate, so will their energy of interaction.
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR
POLARIZATION
249
sidered similarly, except that now if the molecular motion between magnets is at the resonance frequency, relaxation transitions will be induced. Mathematically, the dipole-dipole interaction is given by the following term in the Hamiltonian.
J f a'
= [_ F#'r~Is"l~s 3 (l~," r,s)(~s"
(37)
where/u, and/~s are the magnetic moments of the nucleus and electron respectively and rts is the distance between them. In practice, ~ should be summed over all magnetic particles in the system. By writing Jd~, in component form 52 and by expressing Pt and Ps in terms of raising and lowering operators ss, it is possible to show that transitions p, q, r and s are allowed. We shall return to dipolar transitions later, after examining scalar coupling. Scalar coupling is quantum mechanical in origin, and for a system in rapid motion, is governed by a term in the Hamiltonian, viz.
~t°; = A i s I " S
(38)
1" S in eqn. (38) represents the overlap between the electron and nucleus, while A~s, the hyperfine coupling constant, is related to the probability of finding an unpaired electron at the nucleus in question. In fact, A~s is given by 34 4zr A's = --3 gs fls g, fit p(O)
(39)
where p(0) is the square of the electron wave function (the electron density) evaluated at the nucleus. For Ats to be non-vanishing, there must be some unpaired s-electron density at the nucleus, since the probability of finding p, d, and higher electrons there is identically zero. In practice, many orbitals may become slightly unpaired during a molecular collision and it is more proper to think of p(0) as the net unpaired spin density at the nucleus. Again, as the molecules move with respect to each other at the resonance frequency, the spin density, hence the electric field, at the nucleus fluctuates periodically with time, inducing relaxation transitions. We shall now show that scalar coupling can only induce transitions of the type } + - ) ~ - I - + ) ; that is, transitions parallel t o t in Fig. 9(b). In general the transition probability, w, between any two states, is given to first order by 5t w=t~ 1
fl
< m j l ~ ( t, ) l,m , > e -ita.fl ' dt t 2
(40)
where ~ ' ( t ) is the perturbing Hamiltonian, mi and mj are two eigenstates (say I + - > and 1+ +>), and ~oij is the angular resonance frequency between the states
colj = 27~v,j = ( E i - Ej)/h
(41) Advan. Mol. Relaxation Processes, 4 (1972) 229-354
250
s. POTENZA
To show that the probability is non-zero, we need only show that the matrix element ( m j l ~ ' l m ~ > does not vanish for the perturbing Hamiltonian A ( t ) l • S. To do this, we express I • S in terms of components, viz. (42)
I. S = I~Sx+IySy+lzSz
and make use of the raising and lowering operators I+ and I_ defined by 52 I+ = I ~ + i I ,
S+ = S ~ + i S y
I_ = I~-iIy
S_ = Sx-iSy
(43)
By Solving eqn. (43) for I~, Iy, S~ and Sy we obtain Ix = ½[I+ + I - ]
Sx = ½ [ S + + S _ ]
(44)
1 [i+_i_]
S,
1 [S+-S_]
The raising operator has the property of connecting an eigenstate characterized by mz, the z component of the spin, to one characterized by mz + ~. In particular, I+ Irnz> = (1(1 + 1 ) - m~(m~ + 1))~lm~ + 1 >
(45)
I-ling> = ( I U + 1 ) - mz(m=- 1))~lmz - 1> For the spin ½ system being considered, I = ½ and m~ = _+½. Therefore, we have
I÷l+ -)
= (½(~)-(-½(½)))~1+ +> = I+ +>
and 1+ I + + > = 0, since the + ½ state cannot be raised further. Similarly for the electron, S + I - + ) = (½(9-(½(-½)))~1+ + ) = l+ + )
etc.
We can now express I • S in terms of the raising and lowering operators: I • S = IxS~+IySy+I~S z
= ¼[I+ + I _ ] [ S + + S _ ] - ¼ [ I + - I _ ] [ S + - S _ ] +I~S~
(46)
= ½(s_I++s+I_)+szt~ Recalling that I~1+ - >
= -½J+->
LI++>
= +½1++>
S,I+-)
=½1+-)
etc.
we can evaluate all terms in (rn~lS • l l m j ) . As an example, to determine whether scalar coupling can induce transitions l+ + ) r a I - - ) , we must evaluate .4doan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
251
POLARIZATION
( + + IS" I I - - ) . Using eqn. (46) this is shown to be ( + + 1[½(S- I+ + S + I - ) + Szlz]l- - ) = ½(+ + i S _ I + I - - ) + ½ ( + + I S + I _ I - - ) + ( +
+lS=I~l--)
=0 The first term is zero because S - I - - ) = 0. The second term vanishes similarly, while for the third we obtain ¼ ( + + 1 - - ) which is zero because of the orthogonality of the spin wave-functions. Similarly, all transitions except I + - ) ~ I - + ) are forbidden via contact relaxation. Inclusion of scalar coupling leads to the following expression for the enhancement. G = 7s
(r + c-- s)
(47)
Yt (2q+r+s+c) Here, r refers to the dipolar transition probability between the I + - ) and I - + ) states, while c refers to the scalar transition probability between the same states. Equation (47) is equivalent to eqn. (36) except that the [ + - ) ~ - i - + ) transition probability has been divided into scalar and dipolar components. We can easily determine a maximum value for the enhancement by assuming that c, the scalar relaxation component, is much larger than any dipolar component q, r or s. In the limit as c ~ ~ , G becomes G -~ ~_s c-~o
(48)
7I
Hence, the maximum possible positive enhancement may be read from Table 4. The limit for pure dipolar coupling (c ~ 0) is more difficult to treat, for here we need to know relative values for q, r and s. For a pure dipole-dipole interaction, these have been determined by Solomon 51 as ze
1
1 +ohz¢ r
2 % 8h " ( F - )
s
1
(49)
1 + ( c o , - co
2z~ 2 1 --h2 ( } F z l ) 1 + (t~t + COs)2.r~2
where CO~ = 27tv~is the resonance frequency of the nucleus, COsthat for the electron. (F02), (IFll 2) and (IF2[ 2) are average (expectation) values for various parts of the dipole-dipole perturbing Hamiltonian and will not concern us further. %, the correlation time, is an important parameter in magnetic resonance. Unfortunately, it is difficult to give it a precise physical definition. It may be regarded Advan. Mol. Relaxation Processes, 4 (1972) 229-354
252
J. POTENZA
as that length of time shorter than which the motion of the two spins is negligible. For dipolar coupling, % is generally found s< s5 to be approximately 10 - ~ sec. Several points are worth noting regarding eqn. (49). First, as the external magnetic field is increased, both COs and cot increase (Fig. 4), such that q, r and s tend to zero at high fields. This is plausible physically, since at high fields molecular motions of extremely high frequency are necessary to induce transitions and these become less available. In addition, since the electron resonance frequency is much larger than any nuclear frequency, r and s will decrease more rapidly with increasing applied field than will q. As Ho ~ m, all the relaxation transition probabilities approach 0, but since r and s decay faster than q, the enhancement approaches zero. Maximum values of q, r and s are obtained near zero field where cotr 2 ~2 << 1 and Wsr~2 2 <~ 1. In this region, which is generally called extreme motional narrowing, eqn. (49) reduces to sl 222 3h ~,YsZc q 2066 222
,-
-
h ~,7s% 10b 6
S --
(50)
5b 6
where b is the distance between spins. While it is not possible to calculate q, r and s directly without knowledge of % and b, relative values o f q, r and s can be obtained directly from eqn. (50). Thus, in the zero-field limit, q: r : s = 3: 2 : 1 2
(51)
Using this result, we can determine the maximum value for the enhancement assuming pure dipolar coupling. F r o m eqn. (47), with c = 0 Gdipolar
__
TS (2-- 12) -~t ( 6 + 2 + 1 2 )
1 YS 2 7t
The negative sign corresponds to an emission signal, while the magnitude is half as large as that expected for pure scalar coupling. Maximum possible zero-field dipolar enhancements are shown in Table 4. As the external field increases, q, r and s decrease as indicated above. For small applied fields ( < 100 gauss), it is possible to obtain relative values for q, r and s from dipolar enhancement curves aS, assuming that the spin-spin interaction is modulated by diffusion and that no scalar coupling is present. For hydrogen nuclei at 74 gauss, the values 3.0, 1.6 and 9.6 have been used 56 for q, r and s. Using these values in conjunction with eqn. (47) and a measured enhancement G, it is possible to calculate the scalar rate c relative to the total dipolar relaxation rate ( 2 q + r + s ) . At higher fields, relative Adman. )Viol. Relaxation Processes, 4 ( 1 9 7 2 ) 2 2 9 - 3 5 4
DYNAMIC NUCLEAR POLARIZATION
253
values for q, r and s have not yet been obtained. Nonetheless, by measuring the sign of the enhancement at high field, it is possible to determine whether dipolar or scalar coupling predominates. The exact form of the scalar transition probability will depend upon the model chosen for the spin-spin interaction. For intermolecular radical-solvent encounters, two models have been used: sticking and diffusion 57. The sticking model assumes that c = 0 except when a free radical and solvent molecule are stuck together. The sticking time, zs, is a random variable described by a correlation function. This model leads to a scalar transition probability, viz. c(~o) -
A2~s
(52)
1 ~- O~2T2
where z~ is the scalar correlation time and A is the hyperfine coupling constant. At zero field, eqn. (52) reduces to
c(0) = a2~s The diffusion model leads to a more complicated expression for c which reduces to c(0) - ns ~A2zs d 222
(53)
at zero field. Here, ns is the number of spins/ml and 2 is a parameter related to the intermolecular pGtential function by
Ad Aii(t ) = - - - exp [ - A(rij d)] -
-
(54)
/'U
where r,3 is the instantaneous distance between the electron and nuclear spins and d is the distance of closest approach. A~j is a function of time because as the molecules containing the electron and nuclear spins move with respect to each other, the overlap between them changes. Both theories give c(0) proportional to AZz~. By studying the field dependence of scalar coupling relative to dipolar coupling, it should be possible to deduce values for A, the intermolecular hyperfine coupling constant, and %, the sticking time for the scalar interaction. The former may be related to the degree to which an odd electron delocalizes over solvent nuclei during a molecular collision. Hence, it is a useful parameter for examining weak complex formation. z~ is also useful for this purpose, in that it gives the time during which the spins, hence presumably the molecules, are associated. Additional DNP theory will be presented before experimental results are offered. Here, we merely note that: (1) Because of cross-relaxation transitions involving two spins, enhanced NMR spectra may be observed if one spin system is saturated electronically. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
254
J. POTENZA
(2) The enhancement may be positive or negative depending upon whether scalar or dipolar coupling dominates the interaction. (3) The enhancement is expected to decrease with increasing magnetic field in a manner consistent with the frequency spectrum of molecular motions. (4) By studying enhancement spectra, information concerning the time of contact between spins (Q and the amount of unpaired electron density at the nucleus observed (A) may be obtained.
C. SYSTEMS WITH SHORT-LIVED INTERMEDIATES - CIDNP
1. Basic observations - chemical pumping
The first mention of CIDNP occurred in 1967. In pioneering experiments by Bargon and Fischer 2~' 25 and independently by Ward and Lawler 26' 27, the appearance of emission signals in the NMR of products obtained from rapid radical reactions was reported. A typical example is the thermal decomposition of benzoyl peroxide in cyclohexanone, which is well known zS' z9 to proceed via radical intermediates. O
O
II
I[
c00¢
O A
[I
2 c0.
-CO~
2 "H
>2¢r
(55)
If the NMR signal of the product benzene is observed as a function of time, the single NMR signal starts out as emission, becomes larger, then smaller and finally passes through zero to become an absorption signal as the reaction proceeds. Figure 13 shows the results obtained for the above reaction at three proton resonance frequencies 25. ~6._4-M-"-z~--u-*k 7"-v-"-'"
Fig. 13. Amplitude o f 1H benzene NMR signal during the thermal decomposition o f benzoyl peroxide at 40, 56.4 and 100 MHz. Reprinted with permission from ref. 25. Advan. Mol. Relaxation Processes, 4 (•972) 229-354
DYNAMIC NUCLEAR POLARIZATION
255
The nuclear polarization observed has been attributed to DNP as follows. Because of the conservation of spin, exactly half of the radicals formed in eqn. (55) by breaking the peroxide bond must initially have spin up, while the other half have spin down. This is exactly the situation obtained by saturating transition p artificially in Fig. 10. Since the reaction is performed in a magnetic field, when the radicals are formed, the electron spin populations are not their equilibrium values, The electrons will relax to their equilibrium distribution given by the Boltzmann Law. This will occur in a time T~e characteristic of electron relaxation (usually about 10-5-10 -6 sec for organic radicals). But the nuclei on the radical, in this case the protons of the phenyl radical, may be coupled to the electron and scalar and/or dipolar relaxation transitions, similar to those considered above, may be induced, causing DNP. From this point of view, ClDNP arises a s a r e s u l t of double spin relaxation transitions analogous to those occurring with stable systems, while the driving force for the polarization is the tendency for the electrons to reach a thermal equilibrium population distribution in the applied field. Later, we shall see that this mechanism cannot totally account for all observations without severe restrictions. Nonetheless, it may apply to some systems and it is instructive, following Bargon and Fischer 25, to develop a quantitative interpretation based on this mechanism. Consider a reactant R which decomposes to give two radical intermediates I . , which in turn react in an abstraction reaction to form a product P whose NMR spectrum is monitored. Rff-~ 2 II .+M%
(56) P+M.
For simplicity, we assume that only a single proton is coupled to the unpaired electron of the radical intermediate. The [I.] will depend upon the rate of decomposition of R (rf) and the rate of production of P (rp). With these assumptions, the energy level diagram for the reacting system is that shown in Fig. 14. The energy levels for the radical intermediate are labeled according to the spin quantum r,-
~
I+-> '~ ,
S
r--
I~-÷
r'~-
S"
,.
-
o >>
L,
"-3- t-,> reQctont
free rodicOl
intermediQte
product
r'-*
Fig. 14. Spin energy level diagram for a radical intermediate and product molecule assuming a single electron coup|ed to a sJng|c nuc|¢us. Advan. Mol. Relaxation Processes,
4 (1972) 229-354
256
J. POTENZA
number of the electron and that of the nucleus. In the diamagnetic product, only nuclear spin states are relevant. The individual levels of the coupled spin system are populated at rates r + _ , etc., and depopulated at r ~ _ , etc. We have also added a term parallel to p to account for electron relaxation transitions other than those caused by the electron-nucleus coupling. In principle, it is possible to observe the NMR signal of the radical, the EPR signal of the radical and the ~MR signal of the product. These are proportional to ANs = (N~ + N , ) - ( N , + N~) a N , = (N~ + N , ) - (N~ + N,) ANp
(57)
= N+--N_
respectively. We are primarily interested in the size of the product NMR signal ANp. As with the simple two-spin case treated above, we may write equations for the rate of change of the populations N+ and N _ . This is best done using the relaxation transition probabilities shown in Fig. 15. Downward transition probabilities are indicated by p, q, r, s, while the upward ones are smaller by a Boltzmann factor, in accord 34 with eqn. (20). r:
-,.l÷->-- -
r2
~.
~
~-~V'/kr
~
\ "\,\
2 I÷÷~.
22TI
- - I - >
p e -hlls//kT
-
-
4
-
-
I-*>
Int er rnediate
Product
Fig. 15. Spin energy level diagram and relaxation transition probabilities for a radical intermediate and product molecule. The upward transition probabilities are shown smaller than the downward ones by a Boltzmann factor. For the rate of change of N+ and N _ , we have dN+ dt dN_
-
r'z+r'4+qpN_-qpN+ entering + state
exp
[-hv,/kT]
leaving + state
- r'x + r ~ + q P N + e x p [ - h v f f k T ] - q P N _
dt Advan. Mol. Relaxation Processes,
4 (1972) 229-354
(58)
DYNAMIC
NUCLEAR
257
POLARIZATION
Similar equations may be developed for the rate of change of N 1 to N4. These may be combined to give expressions for dANp/dt, dANs/dt and dANg/dt which are similar to eqn. (31). In a steady state, these differentials equal zero and the three equations can be solved to give an expression for the observed enhancement G. ( 1 + p'ZL) +
G
_
ANp-AN°AN ° - NRNP TIP i - (I q - p ~ - a 2 z
aZL ~S TI
2]
(59)
Here, Tip is the spin-lattice relaxation time of the nucleus in the product, Np is the total number of protons, NR is the total number of radicals present, while p', p and a are combinations of relaxation transition probabilities.
p = 2q+r+s p' = 2p+r+s+ws
(60)
O" ~ s - - r
The magnitude of the enhancement can be measured only with difficulty in CIDNP experiments, mainly because of problems associated with estimating the zero NMR signal strength (because a chemical reaction is occurring, the number of product molecules and the NMR signal associated with them changes with time). By adding paramagnetic impurities to the reaction system (Fig. 13), it is possible to reduce TI of the product and observe only absorption of radiation at the NMR frequency. The area under the absorption curve at a time corresponding to that for maximum enhancement may then be used as a measure of the zero signal. In this manner, observed enhancements may be obtained. These may then be compared with values calculated using eqn. (59). To calculate a magnitude for the enhancement from eqn. (59), several quantities, including T~, r, z L, p, etc. are necessary. None of these is easy to come by experimentally. Estimates for p, q, r and s can be obtained from equations similar to (49). Values for the remaining parameters can be obtained from the CIDNP experiments or from independent studies of similar systems. We shall return to this point later when experimental results are discussed. At present, we simply state that eqn. (59) assumes that CIDNP enhancements arise as a result of relaxation transitions within a coupled spin system analogous with the ordinary Overhauser effect. The theory predicts smaller enhancements with increasing field because of the frequency dependence of the relaxation transitions (Fig. 13). The Fischer mechanism assumes the existence of free radicals and well defined stationary states. It has recently been criticized 5a and replaced by theories which explicitly involve radical pairs for the production of CIDNF spectra. As of now, there exist grave doubts that this mechanism applies to any CIDNP system. We consider now the alternative proposals. Advan. Mol. Relaxation Processes, 4 (1972) 2 2 9 - 3 5 4
258
J. P O T E N Z A
2. The multiplet effect
From the first experiments involving CIDNP 26'59, it was apparent that additional processes other than those described above were required for a complete analysis. The most apparent discrepancy between theory and experiment was the interpretation of the multiplet effect. We assume that the reader is familiar with multiplet structure in NMR spectra and proceed to describe the effect by means of an example. As shown by G. L. Closs and co-workers 33' 60, the reaction product 1,1,2triphenylethane can be formed by photodecomposition of either the azo compound (~b)ECHN=N-CH2~b or diphenyldiazomethane. For the azo compound, the following reaction is relevant. ~b2CHN=NCH2t~ byor a•
Vradical pair 1 I_intermediate_]
• q~2CH-CH2~b
(61)
In the case of t~2CN2, we have ~b2CN2+~CH3 --, [~b2CH • • CH2~b] ~ ~2CHCH2~b
(62)
The NMR spectra of th2CHCH2~b obtained during the reactions (61) and (62) are shown in Fig. 16. In the absence of CIDNP, we expect to find the normal N ~ absorption spectrum. What is observed is positive and negative enhancements
(o)
5,6 ] I 13
IIc.3
Fig. 16. aH NMR spectra of 1,1,2-triphenylethane obtained during (a) thermolysis of ~2CHN=NCH2~ and (b) photolysis of diphenyldiazomethane in toluene. The downfield multiplets strikingly display positive and negative enhancement. Reprinted with permission from ref. 33. within a given multiplet. Further, the sum of the enhancements within a given multiplet is near zero, indicating that the net z component of the magnetization is not far removed from its equilibrium value. Sometimes, as in the case of the multiplet on the lower right in Fig. 16, a net polarization is superimposed. Last, we note that in some cases the high-field portion of the spectrum is positively Adcan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
259
POLARIZATION
enhanced, while for other cases the reverse is true. In particular, the product from eqn. (61) shows the former behavior, in contrast to that from eqn. (62). Several attempts have been made to interpret this phenomenon. The first is based on the analysis given above and involves special assumptions concerning the populations of the free radical states 6x. For example, with a radical intermediate containing two non-equivalent protons, the energy level diagram shown in Fig. 17 would apply. The diagram consists of the four possible nuclear spin states, split by a single electron. For simplicity, we assume that these states are 4
'5
Intermediate
Product
Fig. 17. Spin energy level diagram for a reacting doublet radical coupled to two non-equivalent protons. F o r clarity, the allowed relaxation transitions are n o t labeled.
2_1`4_3
3_1`4-2 ~/o ~
I 2-1
I ,4-3
3-1
Ho Ca)
`4-2
,,
(b)
Fig. 18. Idealized A B doublets arising f r o m the product in Fig. 17. (a) T h e n o r m a l NMR spectrum, (b) a possible CIDNP spectrum.
retained in the product and give rise to the two AB doublets shown schematically in Fig. 18(a). An observed ClONe multiplet might appear as that in Fig. 18(b), where the low-field lines are negatively enhanced and the high-field lines positively enhanced. The observation of emission of radiation for the 2 ~ 1 transition corresponds to state 2 more highly populated than state 1 in the product. Enhanced absorption for the 4 ~ 3 transition indicates that N3 > N4. Thus, this pattern is consistent with abnormally high populations in nuclear spin states with I z close to zero. If the pattern were reversed, abnormally high populations would be inferred for nuclear levels with I z furthest from zero. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
260
J. POTENZA
The situation depicted in Fig. 18(b) could be obtained if the rates of population of the individual spin states in the radical intermediate rij were different. Fischer and Bargon found no compelling reason to assume such restrictions. On the other hand, they noted that certain restrictions on the rate of population of the radical states would lead to transient emission signals in the ~PR which should be observed immediately after the radicals are formed and before they reach a thermal equilibrium population distribution. Such transient emission signals have been observed for short-lived radical intermediates produced by pulse radiolysis techniques 37, 62. Recently, the idea of different population rates was given foundation by Kaptein and Oosterhoff 6 a, 64. By considering singlet and triplet states within a radical pair, they showed how differences in population rates could arise and how these could lead to transient EPR spectra as well as multiplet effects in the NMR. An alternative explanation for the multiplet effects involving the formation of radical pairs coupled with singlet-triplet crossover was given by G. L. Closs 65. Before describing this, we mention some basic properties of singlet-triplet encounters. Consider two electron spins, each on different molecules. When the spins are far apart, each can be described in the usual way as a spin ½ particle. However, when the radicals approach each other, two possibilities exist: the total electron spin angular m o m e n t u m can either be one or zero. This corresponds roughly to the molecules colliding with spins parallel or antiparallel. The former is called a triplet state, because it consists of three distinct levels characterized by the component of the spin angular momentum Sz about a chosen axis. That three levels must exist for a system with spin angular momentum can be seen from eqn. (6). For a triplet molecule in a magnetic field, the three states are shown in Fig. 19.
\
.o/
N
/
~
Sz=l
\
s
\
Sz=O
- -
& ( ~
s~=-I
- -
I-->
I÷->÷1-+>)=
N
7"0
= E~
\
I++>
~(1.->+1-+>~1
/
li: / I-->
Fig. 19. Allowed spin orientations a n d energy levels for a triplet molecule in a s t r o n g magnetic field.
The spin wavefunction for the upper state may be designated t+ + ) or T 1 and corresponds to both electrons repelled by the external field. Similarly, the lowest state T_ 1 corresponds to attraction. For the Sz = 0 state (To), the wavefunction can be obtained by applying the appropriate lowering operator to [ + + ) . Since a triplet state has net spin, triplet encounters between molecules cannot by themselves lead to the formation of a chemical bond in which all electrons are paired. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
261
DYNAMIC NUCLEAR POLARIZATION
In addition to the triplet encounter, it is possible for two electrons to approach each other in such a way that there is zero spin angular momentum. This leads to a singlet state S whose spin wavefunction is given by ~ks = (l/v/2) (I + - ) - I - + ) ) . Singlet encounters can lead to bond formation. For organic radical pair intermediates at high field, the To and S states should have approximately the same energy. TI should be much higher in energy than either TO or S, while T_ 1 should be much lower. F o l l o w i n g Closs 65, we consider the reaction of diphenyl carbene with toluene to produce 1,1,2-triphenylethane (eqn. (62)). If diphenyl carbene is produced as a triplet, the initial encounter between q~2C: and OCH3 is singlettriplet. This leads to the formation of a radical pair initially in the triplet state which may convert to a singlet and then to product. The situation for the two electrons is shown schematically in Fig. 20. /'I ~
~
Rp(rl)
v~
\ ro rf
~
RP(To)
------S~
\
RP(S)
ws
rf
~
RP (Z~)
triplet
/
crossing or
recombinotion
singlet
product
]Fig. 20. Electron spin energy levels corresponding to the reaction of ~2C: with ~CH3. Reprinted with permission from ref, 65.
Diphenyl carbene in the triplet state is characterized by the wavefunctions T1, To and T_I. Calculation of the electron relaxation rate showed that the populations of these levels are probably in thermal equilibrium before hydrogen abstraction occurs to form the triplet radical pair intermediate. If the rate of formation of radical pairs rf is assumed independent of the electron spin states, the triplet radical pair energy levels RP (Tins) will initially have the same equilibrium distribution as the precursor. These states are also connected by relaxation transitions which are indicated by unlabeled arrows. The downward transition probbilities will be larger than the upward probabilities in accord with the requirements of thermal equilibrium. Singlet radical pairs RP (S) can be obtained from the triplet pairs via two mechanisms: intersystem crossing, or by separation of the triplet components by Advan. Mol. Relaxation Processes, 4 (1972) 229-354
262
J. P O T E N Z A
diffusion and recombination with the appropriate singlet wavefunction. The net probabilities for crossover are given as r l , ro and r_ 1 respectively, and are not equal. Finally, the singlet radical pair produces the product at a rate % . To understand the origin of the rnultiplet effect, we examine the singletriplet crossover in more detail. The simplest case is that of a radical pair containing one proton on each component. Sixteen energy levels result from the two electrons and the two protons. To a good approximation, these are determined by the Zeeman spin Hamiltonian Jt~ = - (/Is, + Psi)" Ho - (/t,, + p,=). H 0
(63)
They are shown in Fig. 21 and labeled according to the z component of the nucleus (rnt.) and that of the electron (ms.). The states are also labeled 1-16 for convenience. In this rather complicated case, the complete Hamiltonian should also take into account scalar and dipolar components which induce the relaxation transitions. Here, we shall consider only scalar contributions (dipolar may be treated similarly) and inquire as to the possibility of obtaining NMR signal enhancement via transitions such as 6 --* 15 and 7 ~ 14, etc., which correspond to r ~ , r o and r_ 1 in Fig. 20. ~_~z
'
o-,1~ -
o
-'1'
o
sz
o -,
4
I LL~ ~,~,
,,,,
~ "-" "-~
_ "-,'-'~" .-'~..,.~6
13/~'/".y7 /
//// ///¢ / / / ,
///." //// #/ / /
'~ f
-~
--
o
1-6
#'--12
iT
Fig. 21. Spin energy level diagram for triplet and singlet radical pair intermediates containing two equivalent protons. Triplet and singlet states are connected by relaxation transitions wo and wo' which do not vanish. Reprinted with permission from ref. 65.
The complete scalar Hamiltonian for this four-spin system is given by Jt°~
= AlxS1
" I1+A12S~
"/'2+A21 82 " /1 + A 2 2 S 2 " / 2 +JeeSt
" S2 + J n n l l " 12
(64)
The first four terms correspond to electron-nucleus coupling, the fifth to electronelectron scalar exchange and the sixth, which we shall neglect because of its small size, the nuclear spin-spin coupling. Equation (64) takes into account all possible unique overlaps between the four spins. It can be s h o w n 66 that if J~e = 0, or if Adcan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
POLARIZATION
263
[J.I >> IAijl, singlet-triplet transitions will not occur. Indeed, Je~ = 0 corresponds to two non-interacting electrons or two doublet states, while IJool>>l,41/ implies that the electrons are coupled strongly to each other and not to the nuclei. On the other hand, if {J~,l m IA ij[, the singlet and triplet states are connected by transitions such as w~ and wo in Fig. 21. This can be verified hy the somewhat tedious evaluation of matrix elements of the form (6]Jt~dl5). This gives expressions such as +¼(All+A22-A12--A21 ) which do not vanish. If the electrons and the nuclei were identical, they would vanish and no transitions would be observed. t Further.• it has been shown 6~ that Wo~>.> Wo, for the diphenyl carbene reaction, leading to the preferred relaxation transitions w0 which connect triplet states of zero nuclear spin to singlet states of the same kind. Now when the singlet radical pair forms a product, the nuclear spin states with rex, = 0 will be overpopulated, leading to the multiplet effect. This development is different from the previous treatment of ONP in several ways. First, the driving force for the enhancement comes from the requirement of spin pairing to form products and not the generation of an equal number of radicals in upper and lower doublet states. Thus, for the multiplet effect to be observed, we would expect radical lifetime requirements to be somewhat different from those based on the attainment of equilibrium in the electron spin system. Here, it would seem that the radical pair need only live long enough for the relaxation transitions connecting triplet and singlet states to establish themselves. Closs used lifetimes z of the order of 10 -8 sec. Secondly, with the multiplet effect, no net z component of spin is obtained. Thus, the assemblage of spins showing only a multiplet effect is in thermal equilibrium with the liquid as a whole, and the process of singlet-triplet interconversion corresponds to a transverse effect in which the x and y components of the singlet and triplet pairs interchange. It has been suggested that this phenomenon, which corresponds to an ordering of spins in the x, y plane or entropy polarization, be termed the transverse Overhauser effect. An ordinary, or longitudinal, Overhauser effect, can also be superimposed on the transverse effect (Fig. 16). The present treatment allows for this in that when product formation occurs with electron spins originally in thermal equilibrium, a net fraction of molecules must undergo upward transitions for all spins to pair. This gives rise to a net change in nuclear z components of spin and an energy polarization. Note that this interpretation is directly the opposite of the previous interpretation which assumed that nuclear polarization occurred before the electron spins reached thermal equilibrium. Last, with regard to x, y polarization, we note that constraints as to the possible magnitude for the polarization need not be the same as those for longitudinal polarization. Thus for protons it would be possible to observe enhancements in excess of ?s/?n = 658. Indeed, proton polarizations greater than 700 have been reported 6 o for multiplets and the theoretical maximum obtainable enhancement remains unknown. Advan. MoL Relaxation Processes, 4 ( 1 9 7 2 ) 2 2 9 - 3 5 4
264
J. POTENZA
The theory developed by Kaptein and Oosterhoff is similar to that given by Closs in that both require singlet-triplet mixing and scalal electron exchange for the multiplet effect to be observed. The major difference involves the manner in which the singlet-triplet mixing is considered. Closs considered the mixing in terms of transition probabilities between well-defined states while Kaptein and Oosterhoff developed the theory in terms of the time evolution of coupled spin states. A review of the latter theory in its simplest form is instructive. The simple theory applies to multiplet effects as observed in EPR spectra immediately after radicals are produced by the breaking of chemical bonds. Consider the dissociation of H-X, where X has no nuclear spin. Although dissociation is continuous, electrons in the H-X bond unpair gradually to produce two doublet radicals. The process may be approximated by a two-step sequence involving a radical pair intermediate (eqn. (65)). The radical pair may be either singlet or triplet; its formation is assumed to take place suddenly. H-X -~ t H ' " X] -~ H " + X -
(65)
The energy level diagram consists of eight states, three triplet and one singlet electronic state, each split by the single proton. As above, we assume that mixing is appreciable only between the singlet (S) and triplet To states, since states with ms, = +_1 differ considerably from the singlet state in energy. The Hamiltonian is given by eqn. (66). = ~ ' ~ . . . . . + Jf~x~ha,~o+ ~ s ~ = o~(S1 + $ 2 ) - d,~(½+ 2S1" S2) + A I . ($1 + S=)
(66)
The first term gives the electron Zeeman splitting, the second corresponds to scalar electron exchange and the third to scalar hyperfine coupling. Angular frequency units are used. Again, it is assumed that Je~ ~ A for significant mixing. For a given H - X molecule, the proton can have only one spin quantum number at any given time. If the radical is initially in a singlet state and the proton has e (or + ) spin, the state of the radical pair would be Se, while for the triplet, the corresponding state would be Toe. These states may evolve in time, one converting to the other. The wavefunction describing this time evolution is given as linear combination of the singlet and triplet wavefunctions. 4~(t) = [Cs(t)S + Cr(t)To]e
(67)
Here ICs(t)l 2 gives the probability at time t that the nuclear spin is e, the electronic state singlet, while ICr(t)l 2 gives the corresponding probability for the triplet electronic state. A similar equation can be written for ~ ( - ) spin. Equations for q~(t) and ~ba(t) in terms of deo and Aij can be obtained from the above Hamiltonian and the time-dependent Schr~Sdinger equation. )f'qS,, a - iO~b~,a 3t Advan. Mol. Relaxation Processes, 4 (1972) 229-354
(68)
DYNAMIC
NUCLEAR
265
POLARIZATION
Substitution o f ¢ , , p into eqn. (68) gives the following differential equations:
idCs(t)
JeeCs(t) + A CT(t)
~t
iOCr(t) _ A dt
4
(69)
C s ( l ) -- gee C T ( t )
These may be solved simultaneously for Cs(t) and Cr(t) in terms of J¢o and A. If the radical pair is initially in a singlet state, Cs(O) = 1, Cr(O) = 0 and
Here, D = (Jee2+A2/16) ~. The important point is that ~t and ,6 wavefunctions change with time regardless of the initial state of the system and that the nuclear spin states influence the electronic spin states as suggested by Bargon and Fischer. This leads to a fluctuating spin density at the H nucleus which may be integrated over the radical pair lifetime to yield electron polarization and transient EPR signals. For the multiplet effect, we are interested in the reverse process ofeqn. (65), that of forming product from a radical pair. As with the Closs treatment, the simplest case involves two protons and two electrons. A typical reaction sequence would be A (p...... o,)
kl
ka
> [RH~ • • RH2] > RHt " + R H 2 • I P* 1/Tt I k2 •
•
(polarized product)
(71)
P
(unpolarized product)
Again, radical pair formation and destruction is assumed to take place suddenly. The precursor A yields radical pair with rate kl ; the radical pair can then either diffuse to form two free radicals (k3) or combine to form polarized recombination and/or disproportionation products (k2). Polarized products become unpolarized with rate 1/T 1 , where T~ is the nuclear relaxation time. An approximate scalar spirt Hamiltonian is
= ~oe(S~t+S~)-Jee(½+2S~" S2)+A, IZ~S~ +A2I~ S~z
(72)
Here, nucleus one is coupled only to electron one, nucleus two to electron two. Further, z components of S and I are used because only these will mix To with So. The state of the radical pair prior to bond formation can be described as above: ¢,(t) = [C~(t)S+Cir(t)To]X,
(73) Advan, Mol. Relaxation Processes, 4 (1972) 229-354
266
s. ~POTENZA
where X~ are the nuclear spin wavefunctions I + + ), J- - >, etc., for two nuclei. From the time-dependent Schr6dinger equation, it was shown 64 that for a radical pair initially in the singlet state
C~s(t) = cos (Di t ) - iJe~ sin (D, t) Di
(74)
and
C~r(t) =
iM, sin (D, t) Di
where D, = (Jee2+M~2) ~ and M~ are hyperfine mixing coefficients dependent upon the nuclear spin states X~. For example, if X = l+ + ), M = ¼(A~-A2), while if X = } + - ) , M = ¼(AI+A2). Since diamagnetic products form only from singlet encounters, the rate of product formation will be proportional to iCs,(t)12 and will be different for the various nuclear states. Hence polarized spectra will result, A quantitative expression for the maximum observed enhancement can be obtained by calculating the population rates wj of the nuclear levels for the polarized product P*. For an originally singlet radical pair, these are given by the average of Cj(t) over the lifetime of the radical pair z.
w i = 1-- 2M~'c2 1 +D~z z
(75)
Use of the steady state approximation for the reactions occurring in eqn. (71) gave the following expression for the maximum enhancement G~j.
I0
~w,
\ k 2 + k 3 NgNflNHolN[Pm]]
Here, the k's are the rate constants given in eqn. (71), l is the total number of nuclear states in the product, [Am] is the concentration of the precursor A at the time of maximum enhancement and [Pm] is the corresponding concentration of product. Using eqn. (76), multiplet enhancements may be calculated if the following parameters are known: [Am], [Pm], kl, k2, k3, TI, A1, A2, Je~ and z. Equations (75) and (76) show that polarized multiplet spectra will arise from the above reaction scheme since M~ and D~ depend upon the nuclear spin states. For example, if A 1 and A2 have the same sign, 1+ +> and [ - - > nuclear states will be populated more quickly than J + - > and I - + > levels. If the nuclear spin-spin coupling constant is positive and the two protons are nonequivalent, one should observe two E/A doublets as shown in Fig. 18. Both this theory and that given by Closs predict a reverse multiplet effect for radical pairs generated in triplet states, and the mechanisms are subject to test. A third explanation for the multiplet effect was given by Fischer 6v and Advan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
267
POLAR1ZA'IrlON
applied to combination, disproportionation and radical transfer reactions. Equation (71) applies except that radicals R" liberated from the solvent cage can react suddenly with other molecules in a transfer reaction of the type R-+X-R' ~ RX+R'.
(77)
A major difference between this and previous theories involves the time scale for polarization production. Previous theories assumed that polarization was produced during the life of the radical pair which was approximately 10-s sec for the Closs mechanism and 1 0 - 9 - 1 0 - 1 0 sec for the Kaptein mechanism. Fischer assumed a smaller time scale, that corresponding to the correlation time z for molecular motions in liquids (10-11-10 -12 sec). The precursor is assumed to form a radical pair continuously with consequent decreasing Je¢. In a time t ~ z, the radical pair will either react to form products or separate to give two free radicals. Destruction of the radical pair is assumed to occur suddenly and may be induced by collisions with solvent or other molecules. Nuclear polarization occurs when the radical pair forms and may be transfered to all products. Using the above ideas and that of singlet-triplet mixing, equations were developed which gave the probability of product formation by recombination, disproportionation or radical transfer. The major new point subject to direct experimental verification was that if transfer products show A/E, disproportionation and recombination reactions should show E/A and vice versa. A unified theory capable of yielding both longitudinal and transverse Overhauser effects within a given multiplet was advanced by Closs and Trifunac 5s. The treatment is based on electron y factor changes within a radical pair and involves electron spin-orbit coupling explicitly. To show how isotropic 9 shifts in radical pairs can lead to net polarization, we consider the simplest case of one proton coupled to the electrons in a radical pair, Precursor
kl
~- [HR~ .- R2] I ~2 ~
k3
> HRI"+Rz"
(78)
HRt-R2+RI+REH
The radical pair can dissociate to give two doublet radicals or polarized products can form via combination or disproportionation. For this three-spin system, the scalar Hamiltonian is given by ~-- ~ ' ~ ..... -4- ~z~eexchange -'1-J~Sl-~~SL
(79)
The first three terms are those in eqn. (66); the fourth term describes the interaction of the electron spin with its orbital motion. If the two electrons have different degrees of spin-orbit coupling, their y values will differ from that of the free elecAdvan. MoL Relaxation Processes, 4 (1972) 229-354
268
J. POTENZA
tron and from each other. For organic products, these differences are expected to be small but significant (cf. Table 2). With the inclusion of spin-orbit coupling, the scalar Hamiltonian becomes
= flno(g~ Sl +g2 Sz)-Joo(½+2S~. S 2 ) + A I . S 1
(80)
Again, this is equivalent to eqn. (66) except that the electrons are non-equivalent and only electron 1 is assumed to be coupled strongly to the nuclear spin (At • S~ vs. A I . (St +$2)). Use of the time-dependent Schr~Sdinger equation for a triplet precursor led to the following expressions for Cs(t) and Cro(t). (t) = - i
Ag + l a
si,
( o ± t)
(81)
D± iJee . sin (O+-t)
C~o(t ) = cos (O+-t) - ~ where
The rate of product formation is proportional to IC~ (t)12 = (½flHo Ag +¼A) 2 sina (D +-t) D-+2
(82)
Therefore, products with nuclear spin state I + ) will form with a rate governed by IC~-(t)12 while products with nuclear spin i - ) will form with rate proportional to ICs(t)l 2. These rates will not be equal unless gl = g2As above, the total rate of product formation will be the average of the singlet coefficients taken over the radical pair lifetime. For a triplet precursor, the product rate is given by w_+ = k 2(½flHo Ag +__¼A)2z 2 1 +4D+2z z
(83)
where k is the rate constant for product formation from the radical pair singlet state. For a radical pair formed as a singlet, w ! is given by I w+ = k
1-
2(½flHoAg +_¼A)2z2-] ~+4D+2 -]
(84)
Triplet and singlet precursors should lead to opposite polarizations. The important point is that differences in electron g values can lead to net polarization, the magnitude and sign of which depends upon the relative magnitude and signs of Ag and A. For systems with more than one nuclear spin, the above arguments may be
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
POLARIZATION
269
amplified 6a to give:
k 2M2z 2
(85)
wj = 1 + 4(M~ + J~e)zz Here, wj gives the rate of population of nuclear spin state j as a function of the radical lifetime v, the scalar electron exchange coupling constant Jee, and a tripletsinglet mixing coefficient Mj. Mj is given by n
My = ½flHo AO + ¼ Z eij A i
(86)
i=1
where eij = __+1. The enhancement factor Gjk for NMR transitions between states j and k then becomes
wk - wj
6jk
(87)
(Wk+ Wj+2Wo)IOk
Here, 1jR ° is the thermal equilibrium population difference for nuclear statesj and k while we describes all relaxation transition probabilities independent of the nuclear spin states, lfJee, Ai, z, we and A# are known, eqn. (87) can be used to calculate enhanced spectra. Comparisons between theory and experiment are quite good and will be presented later. The current status of cioNv theory, then, is this: with the Fischer mechanism, net or longitudinal enhancements arise from Overhauser considerations because of cross relaxations within a coupled spin manifold. Transverse polarization is then accounted for by different population rates for nuclear spin levels. The magnitude of the polarization is limited by the Overhauser mechanism. Further, polarization is assumed to arise when radicals are formed and electrons relax to their thermal equilibrium population distribution in the applied feld. This places limits on free radical lifetimes. On the other hand, the Closs-Kaptein theory accounts for both transverse and longitudinal polarization in terms of singlet-triplet crossover within radical pairs. Transverse polarization arises from scalar nuclear-electron hyperfine interactions while net polarization is explained in terms of # differences between the radical pair components. No limit is placed on the possible magnitude of polarization by this mechanism. Although free radical lifetime considerations are unimportant here since polarization occurs within radical pairs, the lifetime of the radical pair is important. Times varying from 10-11 to 10 -8 sec have been used to compare theory with experiment. The question as to which mechanism applies to a given reaction has not yet been answered completely. However, at the time of writing, the Closs-Kaptein theory appears to have won widespread acceptance. Advan. MoL Relaxation Processes, 4 (1972) 229-354
270
J. POTENZA
3. Field dependence of CIDNP spectra - "zero-field polarization"
The third interesting facet of CIDNP concerns the field dependence of the enhancement. For the decomposition of benzoyl peroxide at several high field strengths 25, the magnitude of the enhancement increased with decreasing field (Fig. 13). Similar observations were reported by Kaptein 59, who studied the thermal decomposition of several alkyl peroxides at 1H resonance frequencies of 15, 60 and 100 MHz. There, multiplet enhancements increased with decreasing field. Both theories above are capable of explaining these observations qualitatively. With the Fischer mechanism, enhancements should decrease with increasing field because of the field dependence of the relaxation transition probabilities (eqn. (49)). With the Kaptein-Closs mechanism, nuclear polarization is also field-dependent since the rates of population of nuclear states depend on Ho (eqns. (76) and (87)). Definitive tests of the latter theory should be forthcoming ss.
f5 20 ~5 30 35 do 4'5 ~0 time (see) Fig. 22. The 1H NMR spectrum of the e-triplet (6 = 4.4-4.8 p.p.m.) of 1-chloro-l-phenyl propane obtained from the reaction of ethyl lithium with e,c~-dichlorotoluene. Spectrum (a) was obtained after mixing reactants in the spectrometer probe. For spectrum (b), reagents were mixed outside the spectrometer and placed in the probe 12 sec after mixing. Reprinted with permission from ref. 69.
Recently, Ward et al. 69 reported nuclear polarization for reactions occurring in the absence of an external magnetic field. An example of such zero-field polarization is shown in Fig. 22 for the reaction of a,~-dichlorotoluene with ethyl lithium (eqn. (88)). C1
\
CH 3CH2Li + C12HC4~--* Fradical pair 1 I_intermediateJ
--* H C C H 2 C H 3
/
(88)
q~ Spectrum (a) shows a positively enhanced nuclear triplet from the a-proton of 1-chloro- 1-phenylpropane. The ratio of peaks in the multiplet is very nearly 1 : 2 : 1, the ratio expected for pure longitudinal polarization. On the other hand, spectrum (b), obtained by placing the sample in the spectrometer 12 sec after mixing the Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
271
reactants shows net negative enhancement and a superimposed multiplet effect. Further, calorimetrfc measurement showed that the reaction was more than 95 complete in 5-6 sec, such that nuclear polarization took place in the absence of an external field and was measured before the nuclei had relaxed completely. Apparently the NMR spectrometer was used only to detect the enhancement. A second example of the zero-field effect was reported 69 for the reaction of benzoyl peroxide in 2-iodopropane and o-dichlorobenzene. Enhancement of the 1H NMR spectrum of 2-iodopropane was observed even though it undergoes no net change during the reaction. The following reaction scheme was advanced to account for polarization observed in C H a C H I C H 3 . ~ C ( O ) O O ( O ) C ~ -~ 2 ~ * - + 2 CO2 ~b*. + i - P r I
~ ~b*I+i-Pr*.
i-Pr*" + i-PrI
~ i-Pr*I + i-Pr*.
~b*.+i-Pr*.
~ Coupling and disproportionation products
(89)
Here, the asterisk indicates species with polarized proton spin levels. (In view of the theory above, reactions (89) should probably be written with radical pair intermediates.)
(b)- ~ p.pm. Fig. 23. Proton NMRspectra of 2-iodopropane (1.48 M) in o-dichlorobenzene containing 0.61 M benzoyl peroxide. Spectrum (a) was taken at 140 °C during the decomposition ofbenzoyl peroxide. Spectrum (b) was taken approximately 5 sec after quenching the reaction which was conducted at 140 °C outside the spectrometer. Reprinted with permission from ref. 69. Observed spectra are shown in Fig. 23 for this reaction both in the presence and absence of a magnetic field. Qualitatively, for the reaction in the field, the doublet expected for the methyl groups of isopropyl iodide shows an E / A multiplet with a positive enhancement superimposed, while the septet for the remaining proton shows a similar multiplet effect and a net negative enhancement. In the absence of the field, the doublet remains approximately the same, while the septet shows almost no multiplet effect. Advan. Mol. Retaxation Processes, 4 (1972) 229-354
272
J. POTENZA
Two points require consideration. First, how may isopropyl iodide become polarized and secondly, how can any polarization arise at zero field? The first point was considered by Gerhart and Ostermann ~°, who regarded the transition state of a transfer reaction as an array of three radicals, viz. R . + X - R ' -~ [R-X'R"] ~ R - X + R ' .
(90)
I f [R'X-R'.] is approximated as a radical pair [R-R'-] split by the spin of X., eight electronic energy levels are obtained (Fig. 24). The six states on the left for [R.X.R'.] correspond to the triplet radical pair state split by X., while the two on the right come from S of the radical pair. It was assumed that only symmetric ms z * 3/2
T1 s
..... S
a
//~
....
~"
/ / / ~
s"
_ ~
-
a'
*112
"~";~%" / ' - -
- - . r
o
-lt2
~-
-3•2
~-.
(
)
[R.V.R ']
t _ _
[R.
v
)
X. R:]
Fig. 24. Electronic spin states for [R • • R] and [R • - X • R']. Reprinted with permission from ref. 70. electronic states with ms= -- +_½ are populated. Following Closs 65, crossover to states arising from S was assumed to occur. Now, if mixing occurs most readily for nuclear states with mr. near zero, E/A multiplets will be observed. The electronic transitions occurring in Fig. 24 can be visualized in a simplified manner, viz. RI"X~R'I" --* RI"X~R'$
(91)
Before crossover, the electron of X is equally bonded to R" and R'. ; after crossover, bonding occurs only between R. and X.. This mechanism, which could account for polarized i-PrI, was criticized 58 on chemical grounds since it requires three uncoupled electrons and transition state lifetimes of about 10-1 o sec. Most likely, polarized i-PrI arises from non-reactive encounters in radical pairs of the type IX..i-Pr] and is transferred to the product in an abstraction step before it has time to decay. N o explanation has been offered for the zero-field experiments. However, we note that at very low fields, the theories presented above will not hold. As the field is decreased, states T1 and T_ 1 of the triplet electronic manifold will have to be considered sS. Experiments similar to those of Ward et al. 69 have been performed by AbragamTa, 72, but with solids. A crystal of LiF at 2 °K was allowed to equilibrate in a weak magnetic field Ho (0-40 gauss). The crystal was then removed from the Advan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
POLARIZATION
273
magnet and placed in a stronger field (4840 gauss). The resonance signal of 7Li was found to depend only on the strength of the initial weak field and did not approach zero as Ho ~ 0. Scrutiny of Abragam's experiments may provide some insight concerning the zero-field experiments mentioned above. However, for a liquid in rapid motion, it is difficult to see how polarization or net magnetization can arise at zero field. The interesting results obtained so far with CIDNP point towards a wealth of chemical information stored within polarized spectra. The interpretation of these spectra should contribute heavily to the development of free-radical chemistry and mechanistic interpretations in organic chemistry. In the next section, we summarize the experimental procedures and instrumentation required to obtain enhanced NMR spectra. IlI. INSTRUMENTATION AND EXPERIMENTAL ASPECTS OF DNP
A. Electronically induced DNP 1. Extrapolated enhancements
We consider first the quantitative measurement of NMR signal enhancements. From eqn. (36), the enhanced NMR signal amplitude G is given by G - i ~ - I o _ Vs (r-s+c) Io Vt ( 2 q + r + s + c )
(36a)
Two difficulties are encounteted if one tries to apply this equation to experimental observations. First, the derivation of eqn. (36) tacitly assumed that S~ = 0; i.e. that the electron spin levels of the coupled spin system (Fig. 9(b)) were completely saturated. In practice, this would require an infinite intensity of radiation at the radical EPR frequency, which is impossible to obtain. For any finite intensity, the magnitude of G would be less than that given by eqn. (36). Second, the relaxation transitions p, q, r, s and c were assumed to be the only relaxation transitions occurring in the fluid, leading to the factor ( r - s + c)/(2q + r + s + c) in eqn. (36). This factor gives the ratio of polarizing transition probabilities (those which simultaneously change an electron and nuclear spin) to the total relaxation rate. If other relaxation processes not involving the electron spin occurred (e.g. nuclear or electron relaxation via spin-spin coupling), the total relaxation rate would be larger than that expected from eqn. (36). These considerations lead to two additional terms in the expression for the enhancement, the saturation factor and the leakage factor 73 The electron saturation factor S~(P) is given by: Se(P) - (So - Sz)
(92)
So Advan. Mol, Relaxation Processes, 4 (1972) 229-354
274
J. POTENZA
and the leakage factor by
f=
(2q+r+s+c) (2q+r+s+c+w)
(93)
where w is the total probability for relaxation transitions other than those of interest for the coupled spin system. Inclusion of these factors gives the following expression for the enhancement. G - Ysy,(2q+ +s +r(sr+- c) c)fSe(p)
(94)
For complete saturation, Sz = 0 (definition) and the saturation factor is unity as expected, while for zero intensity of radiation, S~ = So and Se(P) = O. That is, no enhancement is observed without saturating the EPR signal. Experimentally, one generally assumes that Se(P) is related to the power P applied to saturate the EPR signal in such a way that a plot of ]/G vs. 1/P should give a straight line whose value extrapolated to infinite power gives the enhancement for complete saturation. Typical plots 74 of 1/G vs. 1/P for hydrogen and fluorine nuclei are shown in Fig. 25. Scatter of the points for these nuclei give errors of typically __.10 700. We note, however, that this relatively simple procedure has previously 0 . 0 7
,
f
r
J
,
,
-
f
,
o H y d r o g e n (TTBP in C<;H6) . j , 0.0(5 . Fluor'in¢ ( T T B P ooo °04
0.03 0.02 0.01 i
0
J
J
0.04
i
008 p-1
t
i
0.12
I
•
0.16
r
0.20
Fig. 25. Plot of I/G vs. 1/P for 1H nuclei in C6H6 and 19F nuclei in C6F 6. The abscissa is calibrated in reciprocal watts. The sample consisted of 50 vol. ~ C6H6, 50 ~ooC6F6 and O. 1 M tri-tert.-butyl phenoxyl. Reprinted with permission from ref. 74.
been criticized ~3 and should not apply in all cases. Corrections, which are beyond the scope of this review, are particularly important for quantitative work at high external magnetic fields and will depend on the type of ~MR detection circuit employed. For our purposes, we shall neglect these corrections and quote enhancements as reported in the literature. The leakage f a c t o r f m a y be rewritten as f = 1-
W
(2q+r+s+c+w)
- 1
W
wt
(95)
where wt is the total relaxation rate. Since the total relaxation rate is the inverse Advan. MoL Relaxation Processes, 4 (1972) 229-354
275
DYNAMIC NUCLEAR POLARIZATION
of the spin-lattice relaxation time 7"1 in the radical solution, while w is the inverse of T~ for the same solution without free radicals, f r e d u c e s to f = 1
TI
(96)
T,B
T~B, the bulk relaxation time, pertains to the diamagnetic solution. Thus, the effect of additional relaxation may be accounted for by measuring 7'1 for the paramagnetic solution of interest and for a similar solution without free radicals. This is the easiest way to correct for leakage. A second method sometimes encountered in the literature ~7' 7s assumes that q, r, s and c are proportional to the free-radical concentration [R] such that at infinite radical concentration/'1 = 0. Hence, a plot of 1/G vs. 1/[R] should give a straight line whose extrapolated value corresponds to f = 1. This method requires the preparation of many samples at different radical concentrations and generally is not employed for that reason. In sum, by measuring an observed enhancement as a function of saturating power and by measuring two relaxation times, an ultimate or extrapolated enhancement, U~, corresponding to eqn. (36), may be obtained. It is this value which must be used whenever quantitative comparisons between different systems are offered.
2. Sample preparation For the study of systems containing stable free radicals, it is imperative that molecular oxygen be removed from the samples. Oxygen is paramagnetic; therefore, it will give rise to additional relaxation mechanisms and will affect 7"1 of the sample and TIB of the bulk fluid used to correct for leakage. If the concentration of oxygen is unknown and varies from sample to sample, erroneous values for the extrapolated enhancement will be obtained. Further, because it is paramagnetic, oxygen will shorten the electron relaxation time in the radical of interest, thereby making its EPR spectrum more difficult to saturate. Finally, 02 may react with and destroy the radical. For instance, the lifetime of semiquinone radicals is known to increase with the removal of oxygen 17. A simple vacuum apparatus, such as that shown in Fig. 26, generally suffices
VOcuu pumpm
~~
Dewar
Trop
II ~- StOpcOck ~--Dewor -
~Sam
pie
Fig. 26. Vacuum line for sealing samples. Advan. Mol. Relaxation Processes, 4 (•972) 229-354
276
J. VOT~NZA
to remove oxygen. The sample is frozen in liquid nitrogen, after which it is evacuated. A vacuum of the order of 10 pm Hg is usually sufficient and this can be supplied with an ordinary oil-filled vacuum pump. After pumping, the stopcock is closed and the sample is allowed to melt. This freeze-pump-thaw procedure is repeated five times and the sample is sealed while frozen. An alternative method for obtaining oxygen-free samples consists of bubbling dry nitrogen through the sample tube, followed by sealing. The sample size is governed mainly by the ease of detecting the unenhanced NMR signal. Since the strength of the NMR signal is proportional to ( N + - N _ ) , which in turn is related to the Boltzmann factor, low field measurements will require larger samples than high field measurements. For hydrogen nuclei, which are the easiest to detect, 6 ml samples have been used for fields in the range 50-300 gauss, while at earth's field, pint-sized samples are required. At these low fields, the sensitivities of nuclei other than ~H and 19F are such that unenhanced signals cannot be seen. As an example, at 74 gauss, the a ~p zero signal of neat triethylphosphate, which contains approximately 6 M phosphorus, lies buried in the noise; enhanced signals, however, are plainly visible. If quantitative measurements are desired for a~p, 7Li ' etc., at low fields, some way must be found to obtain quantitative zero signals. This could be accomplished by increasing the sample volume with the disadvantage of severely limiting the number of samples which can be examined because of cost. Generally, for low-field studies, a computer of average transients (CAT) is used to detect zero signals. This is a device which divides a given signal into a large number of parts (generally 256 or larger). The signal is repeatedly scanned and the total intensity at each point remembered. For random noise, this total increases as the square root of the number of scans, while the signal increases linearly. Typically, one may increase the signal-to-noise ratio by about a factor of 10 using this method before instrumental instability leads to erroneous results. This allows 31p and 7Li to be examined at 50-100 gauss. To study 13C in natural abundance conveniently, a minimum field of about 500-800 gauss will probably be required. Limitations on sample size also arise from the type of double resonance spectrometer used. For high resolution, because of the stringent requirements for field homogeneity, small samples give better resolution. High-resolution DNP spectrometers operating at 3300, 8500 and 12,500 gauss have been employed 73 with sample volumes ranging from 0.1 to 1 ml. 3. Radicals used
The most important factors governing the choice of radical are stability, solubility in the solvent of interest, and ease of saturation of the EPR signal. Generally, dilute solutions (0.001-0.05 M) are employed and solubility is not a great problem except when it is desired to compare the effects of the same radical Advan. 54ol. Relaxation Processes, 4 (1972) 229-354
TABLE 5 SELECTION OF STABLE RADICALS USED FOR D N P EXPERIMENTS
Name
Abbreviation
1. 2,4,6-Tritertiary butyl phenoxyl
TTBP
2. Galvinoxyl
GALV
Formula
~
6
NO 2
3. Diphenylpicryl hydrazyl
DPPH NO 2
4. Tetrachloroserniquinone
CI
CI
CI
CI
TCSQ
5, Bisdiphenylene-phenyl allyl
BDPA
6, Peroxylamine disulfonate
PODS
7. 2,4,6-Triphenylphenoxyl
TPPO
q)
4~
~\~/® 8. Triphenylverdazyl
xPv
9. Triphenylpyrylyl
TPPY
N
N
I
I
CH
10. Wurster's blue perchlorate
WBPC
C~I3 /N--~
CH 3
11. Naphthalene negative ion
NNI
12. Ditertiarybutylnitroxide
DTBN
~
N
I
O° O.
13. 2,3-Dichloronaphthaquinone
DCNQ O"
/'t::=z N ~CH3
CIO 4-
278
J. POTENZA
in a wide variety of solvents. On the other hand, radical stability is often a criterion for deciding which samples may be examined. In favorable cases, radical solutions will last for months, especially if they are kept frozen when not in use; more generally, lifetimes of the order of days are obtained. Many stable radicals have been used for DNP studies, some of which are shown in Table 5. Space does not permit a description of the advantages and disadvantages of each. Rather, the following discussion is intended to acquaint the reader with the considerations involved in choosing an appropriate radical. A large number of stable radicals were described by Buchachenko 76, and recently by Forrester et al. 77. (a) Commercial availability. Of the radicals shown, only DPPH, GALV and PODS can be obtained commercially as the radical. However, radicals derived from commercially available quinone or phenol precursors may be generated quite easily via simple, one-step syntheses. For instance, TTBP is readily generated in a variety of hydro- or fluorocarbons by oxidation of 2,4,6-tri-tert.-butyl phenol with excess PbO2. o
while TCSQ may be obtained either from tetrachloro-p-quinone by reduction in base with glucose or by air oxidation of the corresponding hydroquinone. For the reduction
0 C,~C,
,oco o
O° C,~C,
NaOMe C,
I] 0
C,
C,
1 o-
(98)
"el
Other quinone and phenolic radicals may be prepared similarly. The major disadvantage with these radicals is that the reactions do not go to completion, and it is therefore difficult to reproduce a given radical concentration. This increases the difficulty of a concentration extrapolation in that the radical concentration must be measured independently by EPR techniques. (b) Nitrogen-eontainin 9 radicals. WBPC, D P P H and TPV* all contain nitrogen, and all have relatively broad EPR spectra (Fig. 27). For this reason, they are almost impossible to saturate completely. This is a general feature of nitrogencontaining radicals and can only be corrected for conveniently at low applied field. For high-field work, these radicals should be avoided unless care is taken to ensure an EPR line narrow enough to be saturated completely. (c) Semiquinone radicals. Except for TCSQ and DCNQ, the majority of semiquinone radicals are not of great value for double resonance work 74. p-Benzo* Many verdazyl derivatives were reviewed by Kuhn and Trischmann7s.
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
GALV
NUCLEAR
279
POLARIZATION
TCSO TPV
TTBP
@DPPH TPP~, BDPA@ Fig. 27. EPR spectra o f selected free radicals used for DNP studies. T h e EPR spectra were taken at 3400 gauss with a p p r o x i m a t e l y 0.01 M solutions. Reprinted with permission f r o m ref. 74.
semiquinone, for example, yields stable solutions in many cases, but the EPR spectrum contains 5 lines (one electron coupled to four equivalent protons) and is difficult to saturate. As a final observation, we note that semiquinone radicals are produced as the anion, such that if they are generated in relatively non-polar solvents, they should exist as ion pairs. This adds an additional complication for the interpretation of enhancement data. A procedure for obtaining stable solid semiquinone radicals for DNP work was described by Richards and White z. (d) Perchloro radicals. O f these, TCSQ has been the most widely used. Because the chlorine nuclei possess a quadrupole moment, no hyperfine coupling of C1 with the radical is observed. Instead, the EPR signal (Fig. 27) is a sharp single line which is extremely easy to saturate. Because they should have similar desirable properties, perchlorohydrocarbon radicals, as they become available, should be widely used in DNP. A general synthesis for highly chlorinated compounds 79 and radical derivatives a° has been reported by Ballester et al. As more of these radicals become available, they will likely be used for DNP because of their favorable EPR parameters. R
(e) Nitroxide radicals'. Radicals of the type
R'
\N j
, although they have
O" not been widely used in the past for DNI-, will probably be used more in the future for several reasons. First, the unpaired electron is highly localized on the N - O group, in contrast to many of the radicals above where it is highly delocalized. Second, the groups R and R' can be varied to give almost any organic functional group without destroying the radical. Third, at least one of these radicals (diAdvan. Mol. Relaxation Processes, 4 (1972) 229-354
280
J. POTENZA
tert.-butyl nitroxide) is a liquid at room temperature which should permit a wide range of radical concentrations to be studied easily. Lastly, several of these radicals are water soluble, which will foster the development of DNP in aqueous solutions, perhaps those containing biologically important macromolecules. The only apparent disadvantage of nitroxide radicals is a relatively broad EPR line, but the advantages mentioned above may compensate for this. Since their discovery s~' s2, a large number of nitroxide radicals has been prepared and their properties examined (refs. 83-85). Some are available commercially 86. ( f ) Hydrocarbon anions. Radical anions, such as NNI, may conveniently be prepared by reaction of the hydrocarbon with Na metal. Procedures for preparing radical cations of hydrocarbons have also been described 87. Both anions and cations have been studied extensively by EPR 35. For DNP, these radicals have the disadvantage of being relatively unstable. Further, an excess of sodium metal must sometimes be maintained in the sample and this causes NMR signals to be difficult to detect. In addition, the effects of counterions must be considered. On the positive side, hydrocarbon radicals are for the most part planar and the unpaired electron is easily accessible to solvent molecules. Nonetheless, because of the disadvantages, it is unlikely that these species will find widespread applicability for DNP. At present, the radicals most favorable for DNP include TTBP, GALV, DPPH, TCSQ, TPPY and BDPA. The synthesis of BDPA has been described by Koelsch 88, and a large number of pyrrilium salts were examined by Dimroth 89. For TPPY, the radical may be obtained from the fluoroborate salt by reduction with zinc. TTBP and TCSQ, although their concentration cannot be easily reproduced, are easily saturated. GALV gives a broader Et'R line which can still be saturated. D P P H is convenient to weigh, but difficult to saturate, while the major difficulty with BDPA is its lack of availability. Most of the results to be presented will refer to these six radicals. 4. Instrumentation (a) The NMR spectrometer. Before considering DNP spectrometers, we should examine the phenomenon of resonance further. As shown in Fig. 3, nuclear magnetic moments precess in an applied magnetic field with an angular frequency proportional to the field strength. ~o = 2~rvr~ - gN fin Ho h
(99)
However, the z component of the magnetic moment is constant in time and may be measured, while the x and y components of ~ change with time as p rotates (Fig. 28(a)). For a large number of spins in the magnetic field, the total z component adds and leads to a permanent magnetization in the z direction. On the
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
\
.
/
281
\
/ Mx=My=O /
-,.~x z
.uy M z -i~ 0
/
s
\
\
/
(a)
(b)
Fig. 28. (a) The motion of a single nuclear magnet in an applied field. The z component of/~ is constant in time while ttx and/~r change; and (b) the motion of a collection of magnetic nuclei in an applied field. All the nuclei precess about the field direction. When plotted from a common point, the assemblage uniformly covers the surface of a cone. The macroscopic x and y components of the magnetization (M= -- ~k~x, My = 5~/~r) vanish, while the z components add to give the resultant magnetic moment shown. other hand, since the assemblage of nuclei is precessing randomly, the x a n d y c o m p o n e n t s will add vectorally to zero. T h a t is, there is n o net x or y c o m p o n e n t of the magnetic m o m e n t for a large n u m b e r of spins (Fig. 28(b)). The resonance experiment consists of i m p i n g i n g radiation on this assemblage of precessing spins in the x, y p l a n e a n d observing the effect produced o n the macroscopic c o m p o n e n t s of the magnetization. Consider r a d i a t i o n at a frequency v i m p i n g i n g o n the collection of spins shown in Fig. 28; this could be provided by the experimental a r r a n g e m e n t shown in Fig. 29. The a.c. oscillator sends a n alternating signal t h r o u g h the coil at a frequency which depends on the characteristics of the transmitter. The oscillator generates a magnetic field directed along the l a b o r a t o r y x axis. F r o m the geometric a r r a n g e m e n t of the coils, the signal amplitude increases a n d decreases in the x direction with the frequency v. However, this linear oscillating magnetic field (called H ' as c o m p a r e d with H o , the p e r m a n e n t magnetic field), is equivalent to two fields, one rotating clockwise in the x - y plane, one rotating counterclockwise
\
N
/
z
-N'
Oscillator Oscillator output
Sample NO
Fig. 29. A simple NMRprobe consisting of a coil of wire wound around a sample vial. The oscillator connected to the coil provides an alternating current of frequency ~ which causes a secondary field H ' to be directed along x. This field increases and decreases in the x direction with the frequency of the oscillator. ,4dvan. Mol. Relaxation Processes, 4 (1972) 229-354
s. POTENZA
282
((:1)
(b)
(c)
Fig. 30. (a) T h e H ' field m a y be regarded as the s u m o f two fields rotating in the x, y plane with a n a n g u l a r frequency co c o r r e s p o n d i n g to that o f the oscillator. O n e o f the rotating fields (H1) precesses in the s a m e direction as the magnetic m o m e n t s . (b) T h e rotating fields in the laboratory f r a m e o f reference at a later time. (c) T h e HI field interacts with the nuclear magnetic m o m e n t s a n d exerts a torque T = ft × H1 on t h e m which tends to change their orientation.
in the same plane. This is shown in Fig. 30(a). The vector sum of the two rotating fields gives the linear field generated by the coil arrangement. In effect, then, one has a magnetic field H~ perpendicular to the static field H 0 and precessing in the same direction as the spin magnetic moments of the nuclei. The second field is precessing in the opposite direction and will be ignored. Classically, the effect of the rotating field is to exert a torque (T -- M x H1) on the magnetic moment which tends to reorient the spins (Fig. 3 0 ( C ) ) 36. I f the oscillator frequency is not at the resonance frequency, this component of torque will vary in time and will exert little net effect on the total nuclear moment (actually it will cause it to wobble). When the applied frequency corresponds to that given by eqn. (99), the applied and nuclear frequencies will be the same and the component of torque will always be such as to reorient the nuclear spin. This will result in a decrease in the z component of magnetization and a change in the x and y components as they attempt to follow or stay in phase with the H~ field. The net Oscillator
output
z
resonance Mx , My-4:0
Mz~O Amplitude
IL
(a)
(b)
Fig. 31. (a) A t resonance, # a n d H1 are precessing at the s a m e frequency. T h e torque is c o n s t a n t a n d spins are reoriented. (b) T h e energy required to reorient the spins c o m e s f r o m the H1 field. T h e oscillator o u t p u t is reduced a n d absorption o f energy is observed.
.4dvan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
283
POLARIZATION
result is a decrease in the z component and an increase in the x and y components of the magnetization. Pictorially, the individual magnetic moments may be considered to bunch up at resonance as shown in Fig. 31 (a). Quantum-mechanically, the constant torque exerted on the nuclear moments corresponds to spin flips of the individual nuclei. The energy required to flip the spins comes from the alternating H 1 field provided by the oscillator (Fig. 31). At resonance, the output of the oscillator is reduced because the nuclei absorb energy; this change in amplitude may be amplified and the result displayed on a recorder or oscilloscope. The usual method for observing resonance consists of varying the magnetic field Ho by means of sweep coils wound about the magnet pole caps while the oscillator frequency is kept constant. As the field increases, the frequency of nuclear precession given by eqn. (99) changes. When the resonance frequency is reached, the oscillator and precession frequencies are the same and a net absorption occurs. A block diagram for this simplified NMR spectrometer 9° is shown in Fig. 32. The sweep coils which vary the H o field strength are connected to the x axis of an oscilloscope such that
~mpLe .
fo,o,,,o,or } ] ome ''''or rectifier
Oscilloscope
~Sweep coiI Sweep generotor ~ _
Ho
Fig. 32. A simplified NMR spectrometer. The sweep generator slowly increases and decreases the Ho field and hence gives a measure o f the external field strength. The signal from the oscillator is rectified, amplified and displayed vertically on the oscilloscope.
the x direction is a measure of the field strength. Output from the oscillator is rectified, amplified and fed to the y channel of the oscilloscope which then gives a measure of the NMR signal strength. In actual practice, more complicated arrangements of coils and detection equipment are used. In particular, many high resolution NMR spectrometers employ both a transmitter coil for stimulating the NMR signal and a receiver coil at right angles to the transmitter coil to detect the NMR signal. This procedure has the advantage of isolating the NMR signal from background noise in the transmitter. The reader is referred to standard texts 9°- 92 for a thorough discussion of spectrometer design and characteristics. In principle, EPR may be observed in a like manner with the exception that at a given field, a much higher oscillator frequency is required for the electron. Usually, however, EPR spectrometers are designed to display the derivative of the Advan. Mol. Relaxation Processes, 4 (1972) 229-354
284
J. POTENZA
absorption curve aS' 93. Resonance frequencies for the various nuclei and for the different electrons at any given field may be calculated from eqn. (7). For fields less than 1000 gauss, NMR and EPR frequencies fall in different regions of the radio spectrum. For fields between 1000 and 25,000 gauss, which includes most commercial NMR and EPR spectrometers, the NMR signal is in the radio region, while the EPR signal corresponds to microwave radiation. The basic problem in designing double resonance spectrometers is to permit detection of the NMR signal while simultaneously stimulating an ~PR signal. (b) DNP spectrometers For a DNP spectrometer, the question of introducing radiation at the appropriate EPR frequency to an ordinary NMR spectrometer is the one we consider first. In principle, this can be accomplished by inserting an additional set of coils at the EPR frequency in the double resonance probe. A schematic arrangement of a DNP spectrometer might then look 9° like that shown in Fig. 33. The permanent magnet (usually a large electromagnet) supplies the H o field while the sweep EPR c o i l s ~ , , , ,\
Power meter \\
~,r
--JJ Sweep coil
//
jNMR coil
TransmiterEPR ~ at frequency /
..L. /
Sweep col I
_//.~ ]'-,~
z
Fig. 33. A simplified DNP spectrometer. The diagram is similar to Fig. 32 except that a set of EPR coils has been introduced perpendicular to both sweep coils and the NMR coils. The EPR coils are powered by a radio transmitter or microwave generator and the amount of power is measured with a meter M.
generator slowly increases H o to pass through resonance. The NMR transmitter and coil provide an oscillating H1 field in the x direction which induces nuclear transitions in the solvent. Similarly, the EPR transmitter, which is at a much higher frequency, provides an oscillating field in the y direction which induces EPR transitions if the solution is paramagnetic. Since the EPR and NMR coils are at right angles, the two H1 fields should interact minimally. Consider now what is occurring in the solution. When a free radical collides with a solvent molecule containing a magnetic nucleus, an energy level diagram such as that given in Fig. 10 applies. The two spins are coupled via the relaxation transitions, and an attempt to saturate the EPR signal will result in a change in the NMR signal amplitude. The Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
POLARIZATION
285
exact design of a DNP spectrometer will depend on several factors, including: (1) whether high or low NMR resolution is required, and (2) whether qualitative or quantitative enhancement data are required. A wide variety of DNP spectrometers has been employed for various purposes and an excellent review of DNP, including high-field DNP spectrometer design, has appeared recently 73. We shall detail the experimental requirement for a low-field low resolution spectrometer, then mention some considerations in going to high field and high resolution.
Magnet and probe ~
I
Coaxial lead to EPR coils ,
Power supply for Frequency counter
1
\
\
/ l o c k - i n amplifier ' Sweep generator
Power supply .....
transmitter
~
'~
,,,afar
Mogoe,
" Oscillator,"
Lock-in a m p l i f i e r
Fig. 34. A low-field DNP spectrometer.
A schematic of a DNP spectrometer designed to operate at 74 gauss is shown in Fig. 34. In this apparatus, the EaR transmitter, contained in the left-hand rack, is designed to operate at 210.7 MHz. The circuit design is standard and may be found in a UHF--VHVmanual. The top portion of the rack contains the oscillator and several amplification stages, while lower parts contain power supplies and regulators to control the power output. Unfortunately, simple transmitters and usual probes will operate conveniently at only one EPR frequency. This determines the magnetic field strength at which resonance will occur and so the entire spectrometer will operate at only one field (here, 74 gauss) with this transmitter. Since the magnetic field required for resonance with organic free radicals (g = 2.00) is fixed by the EPR transmitter, the NMR frequency for any nucleus is determined. Thus, protons will resonate at 319.7 kHz, 19F nuclei at 300.8 kHz, 3tp nuclei at 129.4 kHz, etc. Attached to the cage shielding the magnet is a wattmeter which is connected to the RF transmitter and then to the EPR coil. This serves to measure the power used to saturate the EPR signal. At low field, in apparatus similar to that shown, considerable amounts of power (50-200 watt) should he used if quantitative measurements are desired. This level of power corresponds approximately to 1 watt of power per milliliter of sample volume. The reason for this large power Advan. Mol. Relaxation Processes, 4 (1972) 229-354
286
J. P O T E N Z A
requirement may be seen by considering Fig. 25. There, the reciprocal of the signal enhancement decreases as the power P is increased. If high powers are available, the extrapolation to infinite power is short and therefore more reliable. Secondly, if the plot of 1/G vs. 1/P is not precisely linear, as is sometimes observed, the high power values will lead to a more accurate extrapolated enhancement. Lastly, high powers give large enhancements, and if an experiment is designed only to detect a given nuclear species, high powers will be desirable. The transmitter shown will generate 70 watt maximum which provides an Hie field of 1 gauss peak and this is usually sufficient to obtain extrapolated proton enhancements reproducible to about _+ 10 ~o- For high-field work, less power (about 1-5 watt) is generally required to obtain comparable saturation, because more efficient probes may be constructed. Often, however, plots of G - 1 vs. P - 1 are not linear at high field, and elaborate correction procedures 73, 94, 95 are required to obtain quantitative extrapolated enhancement data. The N~R transmitter is shown on a stand protruding from the front of the shielded electromagnet. In this spectrometer, the transmitter is actually a marginal oscillator, and the NMR coil forms part of the oscillator circuit. Essentially, an oscillator is an amplifier in which part of the amplified output signal is fed back to the circuit as input. This maintains continuous oscillation. For a marginal oscillator, an additional automatic gain control feedback is adjusted so that oscillation is just barely maintained. As a result, the level of oscillation is very sensitive to the small changes which result from resonance. The marginal oscillator shown can be adjusted by means of tuning capacitors to oscillate anywhere in the range 80 kHz-2 MHz and is thus satisfactory for observing a large variety of nuclei over a wide range of field strengths. For example, by inserting appropriate capacitors, the resonance frequency may be changed from 319.7 kHz (for all) to 3C0.8 kHz (for 19F). Lower frequencies can be obtained by further increases in capacitance until the oscillator no longer oscillates. The point at which this occurs will depend upon the number of turns of wire in the NMR coil. Typically, 100 turns are used. By changing the appropriate capacitors and the numbers of turns on the coil, frequencies down to 80 kHz and up to several MHz can be obtained. The exact NMR frequency (to seven figures) may be continuously monitored with a standard frequency counter such as that shown in the center rack. This permits calculation of the field strength when resonance is observed and serves as a useful check on the oscillator. A 150 V d.c. power supply, directly below the frequency counter, provides the operating voltage for the oscillator. The modulated output of the oscillator is displayed on the oscilloscope next to the frequency counter. Before and after resonance only incoherent noise coming from the power supply is observed. During resonance, a sine wave pattern at the modulation frequency (to be discussed below) is displayed, and, if the feedback is appropriately adjusted, the maximum height of the wave gives the amplitude of the NMR signal. This type of detection is unAdvan. Mol, Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR
287
POLARIZATION
satisfactory for several reasons: the signal-to-noise ratio is poor and no permanent record of the NMR trace is obtained. To increase the signal-to-noise ratio, a phase-sensitive detector, shown on the bottom of the rightmost rack, is used. These commercially available devices reject noise from a large portion of the spectrum and amplify the remaining signal and noise. The output of the phase-sensitive detector has a large signal-tonoise ratio and this signal is fed directly to an x - y recorder, shown on the right, to obtain a permanent trace of the NMR signal. At the top of the right hand rack is the magnet power supply and the sweep generator. The power supply is current regulated and supplies a constant current through the coils of the large electromagnet. This produces the steady field Ho which increases with the current from the power supply. The sweep generator is connected directly with the magnet power supply in such a way as to increase and decrease periodically the current flowing through the magnet coils. By adjusting the sweep generator, the magnetic field strength may be made to vary over almost any desired range. For most applications, variations of about 1000 c/sec are usual, but larger sweeps (m the range 40 kc) are used for some applications. At 74 gauss, protons resonate at 319.7 kc and so 1000 c/sec corresponds to (74)(1000)/319,700 = 0.2 gauss. The sweep generator also controls the rate at which resonance is passed. Perhaps the most critical part of any magnetic resonance spectrometer is the probe into which the sample is inserted. A schematic of a probe used at 74 gauss for DYe studies is shown in Fig. 35. The probe is inserted between the poles of the magnet such that the Ho field is coaxial with the induced field of the large coils. This particular probe consists basically of three coils. The innermost white coil is used to stimulate and detect the NMR signal. Each notch in the coil contains the requisite number of turns (say 10) and the induced field H ' is directed along the coil axis (up and down in Fig. 35). With this arrangement, H' is perpendicular to the H o field. The EPR "coil" consists of two half turns of thick wire (one on either side of the sample) which are connected to each other in such a way that their induced fields are in the same direction. With this geometry, a minimum amount of EPR power is introduced directly into the NMR circuit. MoOulotion coils
\\\
NM R
coils
Tuning c a p o c i t o r ~.__~ f o r E PR CooxiQI lead D~tO oscilletor
Cooxiel leod to EPR t Pclnsrnitter
TuF3ing cQ pQci~or f o r EPR
Fig. 35. A low-field DNP probe. .4dvan. MoL Relaxation Processes, 4 (1972) 229-354
288
J. POTENZA
Extending from the NMR coil is a coaxial cable which is connected directly to the marginal oscillator. The coaxial cable extending beneath the NMR coil connects the EPR coil to the radio transmitter. It is interrupted three times by adjustable capacitors which are varied to minimize reflected power and tune the circuit. Consider what happens to radiation at the EPR frequency. It emerges from the transmitter, passes through the coaxial cable and into the EaR coils. Only if all the power transmitted through the cable is used to generate the EPR H ' field will a plot of 1/G vs. lIP be linear and accurate extrapolated enhancements obtained. If any power is reflected back from the coils to the transmitter, the probe circuit is not tuned and will be extremely temperature-sensitive. By suitably adjusting the capacitors shown, the reflected power can be reduced to zero. The large set of coils perpendicular to both the EPR and NMR coils have their induced field in the Ho direction. They are not sweep coils; rather, they are modulation coils which are used primarily to increase the signal-to-noise ratio of the NMR signal. The frequency fed through the coils is usually low and can be varied. For the spectrometer shown, 53 Hz is used. To understand the usefulness of modulation, consider only the N~R system near resonance. The field of the permanent magnet is slowly being increased by the sweep generator and the precession frequency of the individual nuclear magnetic moments is approaching that of the H1 field. Without the modulation coils, we would expect one pass through resonance with a decrease in oscillator energy as shown in Fig. 31. However, the modulation coils provide an additional small amplitude sweep field of 53 Hz with the result that durin9 resonance the Ho field is being varied at a rate of 53 c/sec. The output of the marginal oscillator, therefore, does not decrease regularly; rather, the steady decrease has superimposed on it an oscillation corresponding to 53 Hz (Fig. 36). The advantage of modulation is that now an audio-frequency amplifier, such as that found in a phase-sensitive detector, can be used to amplify the 53 Hz signal which is proportional to the NMR signal strength as defined above. This arrangement provides a convenient means for utilizing narrow band amplification combined with synchronous or lock-in detectors. x= c_S_
31g k.¢
Before resono.nce
During resonQnce
After resonance
Fig, 36. Oscillator output with modulation (schematic). The high frequency corresponds to
the NMRfrequency at resonance. The low, superimposed frequency is the modulation frequency. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
POLARIZATION
289
In sum, any DNP spectrometer will consist of the components considered above. Except for the probe and perhaps the NMR oscillator, all items are commercially available. Modifications of the probe shown in Fig. 35 are not useful for fields above about 500 gauss because as the EPR and NMR frequencies increase, the size of the corresponding coils should be decreased accordingly. Such coils become increasingly difficult to make in miniature at high fields, and the sample sizes which can be treated decrease drastically. ONP probes which have been used successfully at 3500 gauss and higher have been described in detail elsewhere 7s. Basically, the NMR coil still consists of a wire wound about the sample, but now the EPR "coil" is a resonant cavity (like an organ pipe), the length of which can be adjusted so that radiation at the EPR frequency resonates within the cavity. At high field, one may decide to employ high resolution NMR to examine chemically distinct resonance signals. A high resolution DNP spectrometer in principle does not differ from an ordinary high resolution NMR spectrometer, except that a microwave cavity must be used in conjunction with the modulation and NMR coils. Several high resolution t)NP spectrometers operating at about 3300 (refs. 3, 96, 97), 8500 (ref. 98) and 12,500 (refs. 99, 100) gauss have been described and reviewed in the literature. Low resolution spectrometers operating at about 15 (ref. 101), 175 (ref. 102) and 1070 (ref. 18) gauss have also been described. In practice, to obtain high resolution and quantitative data, a great deal of experimental ingenuity is required. We note that the resolution to be expected using any DNP spectrometer is less than that obtainable with commercially available high resolution equipment using diamagnetic samples because DNP samples of necessity contain paramagnetic additives which increase the NMR linewidth. At high field, linewidths of several Hz may be expected. The importance of high resolution DNP will be considered below when experimental results are described. B. CIDNP The experimental aspects of C1DNP are quite different from these governing electronically induced DNP. These differences arise in the main because ODNV inherently implies a chemical reaction producing radical intermediates, generally in a low steady state concentration ( ~ l0 -4 M). In addition, since the NMR signal of a diamagnetic reaction product is observed, the size of both enhanced and unenhanced NMR signals is a function of time. This makes quantitative enhancement data difficult to obtain. Further, because of the chemical reaction, it is diffÉcult to correct for leakage. Nonetheless, some idea of the magnitude of the enhancement may be obtained by one of several techniques 25'6° to be discussed below. The sign of the enhancement (emission (E) or absorption (A)) is usually evident by comparison with ordinary spectra. If ODNP is employed only to test for the presence of radical intermediates, the observation of an enhanced signal (E or A), or of a multiplet effect, is usually sufficient. On the other hand, to Advan. Mol. Relaxation Processes, 4 (1972) 229-354
290
J. POTENZA
obtain all the information relevant to the reaction mechanism contained in CIDNP spectra, quantitative measurements may be required. Finally we note that CIDNP differs from electronically induced DNP in that only a high-resolution NMR spectrometer is necessary for detection. The following paragraphs examine the above statements in greater detail. 1. Quantitative CIDNP enhancements
In the original C|DNP experiment 24, 2~, benzoyl peroxide was decomposed at 105 °C in cyclohexanone according to eqn. (55). As shown in Fig. 13, an emission signal was observed which grew to a maximum and then decayed through zero to give the absorption signal of the product when the reaction subsided. The zero signal at the time of maximum enhancement was estimated by decomposing benzoyl peroxide in the presence of FeC13 . Since Fe + 3 is paramagnetic, polarized benzene molecules were relaxed rapidly and only normal absorption signals occurred. The height of the absorption signal at a time corresponding to the maximum enhancement was then taken as a measure of the unenhanced signal strength. Enhancements so obtained will be accurate provided the added paramagnetic impurity does not affect the reaction sequence or broaden the NMR line of the product significantly. This will have to be determined for each experiment. A second approach leading to quantitative enhancements involves estimation of the steady state concentration of polarized product 6°. As an example, we consider the photodecomposition of diphenyldiazomethane in the presence of toluene (eqn. (62)). The product 1,1,2-triphenylethane showed a large multiplet effect (Fig. 16(b)). The magnitude of the multiplet enhancement was estimated by calculating the steady state [~b2CHCH2~b]* from [~b2CHCH2~b]* = n k T 1
( oo)
where n is the yield of triphenylethane, k is the zeroth-order rate constant for the decomposition of diphenyldiazomethane and 7"1 is the spin-lattice relaxation time of $2CHCH2~b. Each of n, k and T1 was measured independently and [~b2CHCH2¢]* was found to be 3.5 x 10 -4 M. The intensity of a separate standard solution of ~b2CHCH2~b was measured and compared with the CIDNP spectrum to obtain the enhancement, which in this case was 760+ 100 for one set of lines. Again, quantitative measurement of the CIDNP enhancement is not straightforward and depends on parameters obtained from other systems. Relatively large errors may be introduced if any of these parameters is inaccurate. For example, T1 is quite sensitive to the nature of the solution in which it is measured ~03 and care should be taken to ensure that 7'1 is measured for a solution closely approximating the reaction mixture. If possible, the yield of product should be obtained from the reaction mixture itself. Advan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
291
2. High-field positive enhancements The observation of enhanced signals during chemical reactions proves beyond a doubt the existence of free radicals or of radical pairs somewhere during the reaction sequence. Emission signals are easily detected and can arise from no other source. However, the observation of a small positive enhancement (ca. 2 or 3) at high external field leaves some ambiguity since this could arise from heating effects if the reaction occurs at elevated temperatures, from the transient formation of product, or from line narrowing. For protons, positive enhancements observed to date have either been extremely large or have had associated with them a multiplet effect which left no doubt as to their nature. When no multiplet effect is observed and the enhancement is too small to indicate the presence of radicals, the system should be rerun at a lower field, which should increase the size of the enhancement.
3. Radical lifetime considerations The range of radical lifetimes that can be detected by C1DNP depends on whether nuclear polarization is produced 25'27 when the radical is formed, when it is destroyed 6s, or by a radical pair mechanism. I f the former case prevails, the following considerations apply. We consider the simplest case of one electron and one nucleus each of spin ½ (Fig. 14). Because of spin conservation, when the radical forms, the ] + ) and I - ) electronic levels of the coupled spin system are equally populated if it is assumed that the electronic populations are independent of the nuclear spin states. Thus NI = N3 and N2 = iV,. The populations N1, N 3 and N2, N4 will tend toward their thermal equilibrium values with a time constant characteristic of pure electronic relaxation, T1,. I f the relaxation times for cross relaxation (1/r and 1Is) are much larger than TI~ (that is, if the relaxation rates r, s << p), no appreciable polarization will occur. Since electronic relaxation times for organic radicals are of the order of 10 .6 sec, the relaxation times for r and s transitions should be of this magnitude. Second, the rate of formation of product, kd, should be greater than the nuclear relaxation rate for the radical, q. I f ka << q, nuclear polarization will have decayed before the product is formed and observed. According to this condition. one would estimate 59 favorable radical lifetimes to lie between 1 0 - , and 10- a sec. For longer-lived radicals, the polarization would decay in the radical before observation. However, such long-lived radicals, if present in large enough concentration, should be detectable by EPR or electronically induced DNP. Finally, the steady-state concentration of radicals should be small ( ~ 1 0 - 3 - 1 0 - 4 M); otherwise, the radicals will shorten the relaxation time of the product and cause NMR detection to be difficult. I f polarization is produced via singlet-triplet crossover within radical pairs, Advan. Mol. Relaxation Processes, 4 (1972) 229-354
292
J. POTENZA
different considerations apply. For appreciable CIDNP tO be observed 65, 6 8, several conditions should be met. First, to observe net enhancement at high field, A# for the radical pair should be non-zero. This occurs, for example, when one component of the radical pair contains a heavy atom. Second, to observe multiplet spectra, the scalar electron-electron exchange coupling constant Jee should, at some point during the diffusion process, be of the same order of magnitude as the electron-nucleus coupling constant A~j, as discussed above. Finally, the rate of electronic relaxation must be small enough to permit appreciable polarization (eqn. (87)), and this polarization must be detected before it decays via spin-lattice relaxation in the product. For the systems studied by Closs 65, the ratio of polarizing transition probabilities (Wo in Fig. 21) to all transition probabilities was found to be ~0.01 and this gave large polarizations. At present there is no general consensus regarding the lower lifetime limit for the detection of radical pairs. Closs and Trifunac 1°4 have used • ~ 10-9 sec to reproduce observed spectra, Kaptein has used z > 10-10 sec, while Fischer 67 has used 10 -1~ sec. It seems safe to conclude that ~ ~ 10 - l ° sec can be detected. 4. Reaction conditions
Here, the usual conditions of kinetics apply. Concentrations of radical precursors and the temperature of the reaction mixture should be such as to provide a steady-state concentration of radicals which is neither too large or too small. For photochemical applications, the light intensity should be such as to satisfy this condition; a focused 500 watt super high pressure Hg lamp has been used successfully in many reactions 6°. In addition, the duration of the reaction should be approximately 5 min so that enhanced spectra can be recorded conveniently with commercial NMR equipment. For very fast reactions, it is possible to record NMR signals displayed on oscilloscopes photographically or with tape recorders. The latter technique has been applied 24. To conclude, we mention that, while observation of enhanced NMR signals definitely indicates the presence of unpaired electrons in the reaction vessel, the absence of such signals, because of what has been said above, does not preclude their existence.
IV. EXPERIMENTALRESULTSAND CHEMICALAPPLICATIONS-- DNP In general, the magnitude of extrapolated enhancements in solutions containing free radicals will depend upon a variety of factors, including (1) the external field strength; (2) the ratio of scalar to dipolar coupling; Advan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
(3) (4) (5) (6) (7) (8)
the the the the the the
293
temperature of the system; viscosity of the solution; free radical used; chemical environment of the receptor nucleus; type of receptor nucleus examined (e.g. 1H, 19F, sac, asp, etc.), and nature of any additional solvent.
These factors fall into two major categories: physical (1)-(4) and chemical (5)-(8). Many of these factors are also important, though in a different way, for the interpretation of high resolution NMR spectra. From a chemical standpoint, one aim of DNP measurements is to utilize observed enhancements which arise from relatively weak spin-spin interactions as a probe for the much larger electronic interactions which accompany molecular collisions in solution. Before presenting experimental results from a chemical point of view, we should examine some of the physical factors mentioned above. A. Physical factors affecting enhancement 1. Spectral density curves - dipolar vs. scalar coupling
We have already seen that the scalar transition probability c is a function of the external field strength. Depending upon the model chosen for the scalar interaction, one obtains more or less complicated expressions for c. The sticking model mentioned above gives 1°5 c(co)-
A2z~ 1 + O)2T2
(52)
while a scalar interaction modulated by molecular diffusion in the liquid gives 57 c(~o) - ns ~AEd 2 [1 +(sin/~-cos/~) exp (-/~)]
(101)
2~,2D# where # = (t~zs) ~ and o~ is the angular frequency corresponding to transition c. The other parameters involved are given by eqn. (53) except for D, the average diffusion constant of the radical and receptor nucleus. D is defined in terms of the radical-solvent distance of closest approach d and the scalar correlation time zs b y 57
z~ --
d2 D
(102)
In the zero-field limit, as ~o ~ 0, eqn. (101) reduces to eqn. (53). Different authors (ref. 106) use slightly different definitions of z. In a similar manner, expressions for the dipolar relaxation transition probAdvan. MoL Relaxation Processes, 4 (1972) 229-354
294
J. P O T E N Z A
abilities q, r and s as a function o f the external field strength may be obtained. If the dipolar interaction is modulated by rotation, one obtains 74 for q
q
3h 2 -
2 2
7~7"Zr
-
20
(103)
2 2) b 6(1 +~0nZr
where 0). = 2uv., the angular NMR frequency. Similar expressions may be obtained for r and s. Alternatively, if the dipolar interaction between the two spins is modulated by translational diffusion, q is given by s7 3r:
222
[ne h ~ v . ~ [p2 _ 2 + ((#2 _ 2) sin p + (#2 -t- 4# + 2) COS /~) exp (-- p)] q = iO \ dDp 5 ] (104) where/~ = (~o,ra) ÷ as above and the other terms are defined as previously. Similar expressions hold for r and s with the substitution o f o)e +__o9, and insertion o f the factors 2 and 4 before the right-hand side o f eqn. (104). Overall, then, the exact form of the relaxation transition probabilities will depend upon the model chosen for the spin-spin interaction (rotation, diffusion, (a) C) "rd long
eT,~l ,re(e)
( ~ I"d short
i
xi
i
I
i
ii
V2 =1 ~
i
~ ~ 1 1 1 ~ / i i i i
I
i
103 104 105 106 107 108 109 10101011 1012 ResonGnce frequency • to (b) -330 -300'
UC~H (~) -100.
I
I
I
I
I
10
102
103
10 `4
105
H (gouss)
Fig. 37. (a) Schematic dipolar spectral density plot. The n u m b e r o f molecular m o t i o n s is given as a function o f the resonance frequency o9. Curve 1 corresponds to a long dipolar correlation time, curve 2 to a shorter correlation time. (b) Anticipated extrapolated p r o t o n e n h a n c e m e n t as a function o f the external field. Scalar coupling is assumed to be absent.
Advan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
295
etc.). The choice of model then introduces certain parameters characteristic of the model such as radical-solvent distance of closest approach d, average diffusion constant D, etc. We need not concern ourselves immediately with the exact form of q, r, s and c. Rather, we will concentrate on similarities between the various formulations. All of the transition probabilities given above have several common characteristics. First, they all depend upon the quantity ~or, the frequency of interest multiplied by the correlation time between the two spins. Since the correlation time is a constant characteristic of the system, as the external field increases, co, and hence o)z, also increases. As cot ~ o% each of the transition probabilities given above approaches zero. Thus, a plot of transition probability vs. either external field strength, co, or cot would be large at low field and small at high field, as shown in Fig. 37. The correlation time for the interaction may be determined from such a plot. For the curve at half its maximum height, cot ~ 1 (ref. 45). Now, since (n is known, z may be calculated. From eqn. (102) and knowledge of the diffusion constant, one may obtain a distance of closest approach between the radical and receptor molecules. In general, individual relaxation transition probabilities cannot be measured. Rather, one measures the NMR signal enhancement or nuclear polarization 44' 73 as a function of external field. In the absence of scalar coupling, this is proportional to ( r - s ) / ( 2 q + r + s). But since s is greater than r for pure dipolar coupling, we expect large negative enhancements at low field which decay towards zero at high field (Fig. 37(b)). I f scalar coupling is also present, the situation is slightly more complicated because scalar coupling leads generally to positive enhancements. Further, since scalar and dipolar coupling are different in nature, they may have different correlation times. This is most easily understood by considering the radical solvent collision process. For a given system, the collision between radical and solvent is governed by electronic interactions between the two species and is largely independent of the external magnetic field strength, which acts as a small perturbation on the total energy. The external field, however, strongly influences the relaxation transitions which we monitor via the NMR enhancement. Now, dipolar coupling is long range while scalar coupling occurs at short range. Hence, the ratio of scalar to dipolar coupling will vary with the distance between the two spins. When the spins are far apart, dipolar coupling will predominate, while at closer distances, the ratio of scalar to dipolar coupling will increase as the electron-nucleus overlap increases. This is shown schematically in Fig. 38. Since the scalar and dipolar interactions sample the collision differently, different correlation times might be expected, and the two situations depicted in Fig. 39 arise quite naturally 2 o. More complicated behavior of the spectral density curves has also been reported 1°7 The upper part of the figure shows a dipolar spectral density such as r - s characterized by a dipolar correlation time za. Also shown are two scalar spectral densities, one for t~ < To and one for zs > zd. In terms of observables, the case z~ < Zd Advan. Mol. Relaxation Processes, 4 (1972) 229-354
296
J. POTENZA
T
I n t e h s i t y of interaction DipoLar ScaIQr
Fig. 38. Schematic comparison of scalar and dipolar coupling for bimolecular collision. For large electron-nucleus separations r~j, dipolar coupling dominates. As r~j decreases, scalar coupling becomes increasingly important.
0J "o •-
j
tt) J
c
•,oo!
I
rs>~a
L/I
j
10~ 104 109 106 107 10a 109 10~o10~110TM 101~ EPR frequency, Hz
Fig. 39. (a) Schematic scalar and dipolar spectral densities. (b) NMR enhancement curves expected from combinations of the spectral densities in (a).
would lead to a large negative NMR enhancement at low field and positive enhancements at high field (Fig. 39(b)). At zero field, the enhancement would not be the full dipolar value because of the presence of scalar coupling. With z~ > zd, the reverse would be true and we expect large positive enhancements at low field and negative enhancements at high field. By appropriately dissecting the observed enhancement spectrum, the ratio of ~ to zd may be obtained, while a single measurement at low field determines the presence of scalar coupling. 2. Effect o f viscosity I f the free radical and the solvent molecule undergoing collision are assumed to be spherical with radii r 1 and r2 respectively, the average diffusion coefficient mentioned above can be related to the viscosity of the solution t / b y the StokesAdvan. Mol. Relaxation Processes, 4 (1972) 229-354
297
DYNAMIC NUCLEAR POLARIZATION
Einstein equation. For a pure solvent, the diffusion coefficient is given by 42
O -
kT
005)
6zc~Ir
where k is Boltzmann's constant, Tis the absolute temperature and r/is the viscosity. For two species in solution DAy = (Dr +D2)/2, or DAv -- 12rtq Now, if we define a translational diffusion correlation time by za obtain 3, 10s -
121rd2 ( rl r22 1 k T \r t +r2/
=-
d2/DAv, we
(107)
whence the correlation time is directly proportional to the viscosity. Equation (107) implies that translational diffusion modulates the spin-spin interaction, that the colliding species are spherical and that chemical effects other than those contributing to viscosity are negligible. From eqn. (107), we expect an increase in viscosity to lead to longer correlation times. But since in the diffusion expressions for the relaxation rates the expression (¢oza)~ occurs as a unit, an increase in Zd has the same effect as an increase in ~o or an increase in external field strength. For pure dipolar coupling, then, we expect the extrapolated enhancement to approach zero with increasing viscosity.
3. Effect of temperature variation The effect of temperature variation upon enhancement may be treated most conveniently by considering the temperature dependence of viscosity. The typical dependence of q upon T is given by 42 =
exp
[AE/RT]
(108)
where v/o is a constant characteristic of the liquid, R is the universal gas constant, and AE is an energy barrier that must be overcome before the elementary flow process can occur. Thus, the exponential term in eqn. (108) is a Boltzmann factor related to the fraction of molecules with energy greater than that of the barrier. As the temperature increases, the viscosity of the liquid and the correlation time decrease. In fact, by combining eqns. (107) and (I08), we obtain ~°s ~a =
[_ k T
\rl +r2/
r/o exp (AE/RT)
(109)
Advan. MoL Relaxation Processes, 4 (1972)229-354
298
J. POTENZA
and, if we set the term in square brackets equal to %IT, we have TO
Zd = - T e x p ( A E / R T )
(11o)
Since a decrease in za is equivalent to lowering the magnetic field strength, an increase in T will give an increase in enhancement for pure dipolar coupling modulated by diffusion. The presence of scalar coupling and/or rotational contributions to the relaxation rate will lead to more complicated behavior.
4. Physical parameters obtainable from DNP measurements In principle, by utilizing the equations developed above in conjunction with DNP measurements, it is possible to determine values for electron nucleus correlation times z, radical-solvent distance of closest approach d, energies of activation AE, and average diffusion constants D. Further, DNP can yield information regarding the type of molecular motions in the liquid (rotational, translational, etc.). When scalar coupling is present, the intermolecular hyperfine coupling constant A and the scalar correlation time z~ may also be determined. The scalar correlation time may be related to the length of time molecules "stick" together in solution, while, in some cases, A may be governed by the intensity of the electronic interaction during collision. The manner in which these parameters are obtained is not straightforward since generally a given solution has more than one type of coupling or motion. As a result, one generally assumes a value for one parameter and calculates the remaining variables with respect to the one assumed. By iteration, a consistent set of parameters may be obtained. Overall, DNP measurements have the potential of yielding a rather detailed microscopic description of the liquid state.
B. Experimental results for protons In this and following sections, no attempt will be made to survey completely all experimental results. Rather, those results will be presented which serve to illustrate general trends and amplify points presented above.
1. Low-fieM measurements At low fields ( < 200 gauss), proton NMR enhancements generally extrapolate close to the dipolar limit. That is, regardless of the free radical or receptor molecule used, protons in organic solutions containing free radicals generally show no scalar coupling 3' 109. No value of lU® n[ smaller than 330 has ever been reported for intermolecular collisions. Typical results at 74 gauss for a variety of free radicals are shown in Table 6 for mixed hydrocarbon-fluorocarbon solutions TM. Several
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCELAR
299
POLARIZATION
TABLE 6 D Y N A M I C P O L A R I Z A T I O N IN HEXAFLUOROBENZENE S O L U T I O N S
Reprinted with permission f r o m ref. 74. Radical
Additional solvent
Relaxation time (sec) TH
Tv
Maximum observed Extrapolated enhancement enhancement Uoov
Contact component cv
Gn
Gv
Uoon
--22
-- 14
--310 a --200
2.6
PODS
D M S O (80 %)
GALV
None Benzene (50 9/oo) Acetone (90 %)
1.1 i.8
0.7 1.0 1.0
--225 --210
-- 165 --155 --120
--325 --315
-- 200 --200 --145
2.6 2.6 3.9
None Benzene (50 %) A c e t o n e (50 9/oo)
0.5 0.3
0.5 0.2
--295 --285
--115 --170 --120
--310 --315
--150 --190 --135
3.8 2.8 4.2
TPPO
Benzene (90 %)
6.7
5.3
--155
--16
--310
--32
7.3
PAC a
Benzene (50 ~ ) , CC1. (40 %)
2.6
1.7
--53
--7
--310
--40
7.0
None Benzene (50 %) A c e t o n e (50 ~ )
0.6 0.7
0.8 0.7 0.6
--55 --80
--0.3 --2.3 --9
--310 --310
--2 --13 --35
8.4 7.9 7.2
None Benzene (50 %/00)
4.7
<0.3 3.4
--210
--300
+20 +40
9.2 10.0
TTBP
DPPH
BDPA
+16 +30
PBSQ b
A c e t o n e (80 ~ )
--20
--5.5
--310
--75
5.9
"I-FSQ c
A c e t o n e (90 ~ ) E t h a n o l (90 ~o)
--4 --24
+0.5 --13
--310 --310
+35 --150
9.7 3.3
TCSQ
Acetone (90 ~ )
3.4
2.7
--210
+165
--280
+195
18.5
TPV
Benzene (50 ~ ) A c e t o n e (90 %)
1.0
0.3
--75 -- 105
+75 +95
--310 --310
+300 +270
28.0 24.7
TPPY
Benzene (90 9/00) A c e t o n e (90 %)
7.8 5.1
3.5 1.9
--140 --170
+170 +260
--270 --270
+210 +300
19.7 28.0
WBPC
A c e t o n e (90 ~ )
2.3
1.4
--130
+135
--300
+240
22.1
NNI
T e t r a h y d r o f u r a n (99 ~ )
--5
+I0
--225
+450
56
a P A C = picryl a m i n o carbazyl; b PBSQ = p-benzo-semiquinone; T F S Q = tetrafluoro semiquinone. n Figures in italics were obtained u s i n g the ratio m e t h o d TM.
points are worth mentioning with regard to proton enhancements. First, although the maximum observed 1H enhancements Gn cover a relatively large range, extrapolated enhancements U~a are all near the dipolar limit. The values for TCSQ and TPPY fall somewhat above this limit, but not outside the experimental error. Advan. MoL Relaxation Processes, 4 (1972) 229-354
300
J. POTENZA
Thus, the presence of scalar coupling is questionable. Second, we note that the radicals used in this study cover a wide range of chemical types. For example, GALV and TTBP both contain bulky t-butyl groups with little or no electron density as determined by EPR. Hence, for these radicals, the unpaired electron should be unable to effectively delocalize over the proton-containing solvent and little or no scalar coupling is expected. On the other hand, radicals such as TCSQ are not sterically well shielded and the unpaired electron, which is located primarily in the molecular 7t system, should be able to interact strongly with solvent electrons. In addition, we note that the chemical environment of the proton also has little or no effect upon the ultimate enhancement; e.g. the protons of acetone, benzene, etc., behave equivalently at low field 3. Because low-field 1H enhancements are purely dipolar in character, they are largely uninteresting except in their relation to highfield measurements, to which we now direct our attention.
2. High- and multifieM measurements Proton DNP measurements x09 for a variety of substituted methanes at 3300 and 12,500 gauss are shown in Table 7. As expected, all enhancements are negative and U~oHat both fields changes markedly as the receptor molecule is changed. The results shown were interpreted in terms of dipolar coupling only. A model for the electron-nucleus spin-spin interaction based on translational diffusion was assumed and a comparison of extrapolated enhancements with those expected on the basis of the model chosen gave values for the diffusional correlation time Za the radical-solvent distance of closest approach d, and the mean diffusion coefficient D. Notice that the values for zd increase with increasing viscosity as expected from eqn. (107). In addition, the values for D increase with decreasing viscosity as expected intuitively and from eqn. (106), although the agreement here is not exact. TABLE 7 PROTON DNP RESULTS AT 3300 AND 12,500 GAUSS USING T T B P R e p r i n t e d with p e r m i s s i o n from ref. 109.
Solvent
Uooa(3300) Uoon(12,500)
zd d (sec×lO u ) (/t)
D × 106 ~7a A# (cm2.sec -1) ( P x I O 2) (p.p.m.)
CHa*OH CHaOH* CHaI CH2Iz CH2Br2 CH2CI2 CHBra CHCl3 CHFCIz
--200d:30 --235±35 --2564-20 --102±8 --141+8 --2314-17 -- 674-5 --213d:10 --265±10
84-2 5il 3+1.5 244-2.5 15±2 54-0.6 364-1.5 6±1.5 2.4~0.5
15 19 28 5 9 12 9 11 18
-- 654-20 -- 905:40 --1214-30 -- 3 7 i 1 5 -- 5 4 ± 1 5 --1034-15 -- 214-4 -- 854-5 --134±20
a T a k e n from Handbook of Chemistry and Physics.
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
3.3 3.0 3.0 3.3 3.6 2.4 5.5 2.6 2.1
0.597 0.597 0.500 2.822 1.030 0.430 1.975 0.580 0.412
0 0 219.0 187.0 139.5 1.9 136.0 9.4 39.6
DYNAMIC
NUCLEAR
POLARIZATION
301
Two results from Table 7 are quite interesting. First, the diffusion coefficient for the methyl protons on methanol is smaller than that for the O H protons. To interpret this, it was suggested that chemical exchange contributes significantly to the diffusion of the O H proton. The second result of interest concerns the last column in Table 7 which gives solvent g shifts for the TTBP radical in parts per million. The values of Ag entered in the Table measure the extent to which the electron resonance of the free radical is shifted to higher g values. Since Ag values were corrected for nuclear resonance and bulk susceptibility effects 1°9, Ag indicates that some of the unpaired electron interacts with the solvent. However, even though the unpaired electron is perturbed, no scalar coupling for protons is observed. Since there would appear to be no lack of translational molecular motions to modulate the coupling, it would seem that the lack of contact coupling here arises because very little of the unpaired electron is actually present at the H nucleus. For most proton systems studied, translational motions describe the relaxation quite well. However, Kruger et al. 99 found that for solutions of toluene in p-chloroBDPA, a rotational contribution was required at low temperatures. This they determined by measuring Uoo. at five widely separated field strengths (15, 175, 1070, 3410 and 13,200 gauss) and several temperatures between 73 °C and - 120 °C. Their experimental results are shown in Fig. 40. At 15 gauss, proton enhancements all lie within experimental error of the dipolar limit. As the field is
"-, L "'i,""
'
:
'7,~/r<-1o T,/r<-2r,/r<~l
10 8
i
,
:
IC#
44MHz
i }
493MHZ
i"2 1(~° :
~\
\
] I 10"
I°
] ', S -~ 10 '2
3GHz ~SGHZ 37GHz CaS
Fig. 40. Extrapolated proton enhancements for toluene as a function of frequency and temperature. The radical used was bisdiphenylene-p-chlorophenyl allyl. Reprinted with permission from ref. 99. increased, U~n becomes more and more sensitive to temperature. At all fields, the enhancement decreases with decreasing temperature as expected. Analysis of the data showed that enhancement spectra between - 4 0 and 73 °C could be interpreted by translational diffusion alone. At temperatures below - 4 0 °C, rotation became important, and the curves could be fitted by assuming that the relative importance of rotation to translation was 0.3. This gave the ratios of rotational to translational correlation times Zr/Zt shown in Fig. 40. With decreasing temperAdvan. Mol. Relaxation Processes, 4 (1972) 229-354
J. POTENZA
302
ature T,/rt increases. It was further shown that both rotational and translational motions followed an activation law T t , r ~--- "t"0 e x p
[AE/RT]
(111)
By measuring the relaxation times T1 and 7"2 at various temperatures, the energies of translational and rotational activation were evaluated, Thus AEt = 3.1 kcal/ mole and AEr = 7.8 kcal/mole for toluene. In chemical terms, toluene does not solvate the free radical at high temperatures. As the temperature is lowered, complexes form, probably because of collisions between the n systems of the radical and solvent. On the average, the coordination number of toluene with the radical was 0.6, indicating extremely weak solvation. This may be contrasted with aqueous solutions where the coordination number is much larger and solvation effects much stronger.
3. Exceptions to the rule--scalar coupling for protons Proton scalar coupling has been observed in several cases. The first case reported was for MnC12 in aqueous solutions ~°. Here, Mn + ÷ was used to supply unpaired electrons and the proton NMR spectrum of water was recorded. At 10 gauss, large positive enhancements were observed (Fig. 41) for various concentrations of MnCI2. Very high RF power was required to saturate the Mn ÷ ÷ hyperfine multiplets because of the short relaxation time of Mn + +. Short relaxation times are characteristic of transition metal ions. 10.C
& X o [3
0.001M MnCI~aqueous Solution 0.0025M = ,, ,, o 0.005 M . . . .°x~ x 0.01M t3
GH 1C
9/°
o
/~ O/° 1"~.1 1,o Electron resonance s a t u r a t i n g
/4x & Ho-lOGQUSS Ternp~ 25"C 10 field Hle ~n GQU$S
Fig. 41. Proton resonance enhancement in aqueous MnCIz solutions as a function of RF saturating power. Reprinted with permission from ref. 10. Positive 1H enhancements were also observed in organic solutions by Dwek et al. 110 for the t-butyl groups of tri-t-butyl phenol in TTBP. Many solvents similar to tri-t-butyl phenol were used, but these did not.give positive enhancements (Table 8). As a result, it was concluded that both TTBP and its precursor were
Advan. MoL RelaxationProcesses, 4 (1972) 229-354
DYNAMIC
TABLE
NUCLEAR
303
POLARIZATION
8
PROTON DNP MEASUREMENTS WITH T T B P Reprinted
AT 3 3 0 0 GAUSS
w i t h p e r m i s s i o n f r o m ref. 110.
Compound
Mono-t-butyl
Si#n o f enhancement
benzene
1,3,5-Trimethyl benzene Hexamethyl
CHa
Aromatic
Other
--
--
--
--
--
--
OMe
--
--
OMe
--
--
OMe
--
--
OMe
--
--
benzene
1- M e t h o x y - 2 , 4 , 6 - t r i m e t h y l 1-Methoxy-4-t-butyl
benzene
benzene
1-Methoxy-2,6-t-butyl
benzene
1-Methoxy-3,5-t-butyl
benzene
Di-t-butyl benzene 1,3,5-Triphenyl benzene Tri-2-butoxylethyl
phosphate
Tri-t-butyl phosphate 1-Methoxy-2,4,6-t-butyl
benzene
Tri-t-butyl phenol
--
CH2
--
--
--
--
q-
--
OMe
required to give the positive enhancement, and that this arose as a result of proton exchange between TTBP and tri-t-butyl phenol, viz. ROH+RO. = RO.+ROH
(112)
In the radical, all protons are subjected to strong scalar coupling. When proton exchange occurs to form the diamagnetic phenol whose NMR spectrum is being recorded, the positive polarization will remain and will start to decay to the expected negative value for intermolecular coupling. That the ring protons exhibit no scalar coupling is attributed to the lack of a suitable modulating mechanism (motion). For the t-butyl protons, modulation by rotation of the t-butyl groups was postulated. However, this interpretation was questioned by Hausser and Stehlik 73. For the aqueous MnC12 solutions considered above, a similar interpretation is possible. While in the solvation sphere of Mn + +, the protons of water are subjected to strong scalar coupling. If they exchange rapidly with the solution, a net positive enhancement can be observed. The examples above serve to illustrate the type of information obtainable from 1H DNP measurements. In addition to protons, X 9 F and 3 1 p nuclei have been studied in some detail, and these have the added characteristic of showing scalar coupling. We turn now to 1 9 F . Advan. Mol. Relaxation Processes,
4 (1972) 229-354
304
s. POTENZA
C. Experimental results f o r fluorine nuclei 1. Low-field measurements
In contrast to hydrogen, the dynamic polarization of 19 F nuclei is extremely sensitive to the detailed chemical environment of the resonating nucleus. Observed enhancements are governed both by the type of free radical and fluorocarbon present. The effect of varying the free radical 74 is vividly demonstrated in Table 6 which lists DNP results at 74 gauss for C 6 F 6 with a variety of free radicals. Extrapolated 19 F enhancements vary from - 2 0 0 , which is far removed from the dipolar limit ( - 3 5 0 for fluorine) to +450, which is approximately 65 ~ of the scalar limit. Fluorine contact components, cv, derived from the observed enhancements using eqn. (47) with q/3.0 = r/1.7 = s/10.1, vary from c F = 2.6 for PODS and G A L V to 56 for naphthalene negative ion. Hence, for systems with large negative enhancements, dipolar coupling dominates the spin-spin interaction, while for systems with large positive enhancements, the reverse is true. For example, with WBPC, we may calculate the ratio of scalar to dipolar coupling as: c
22.1 -
2q+r+s
1.24
17.8
It is interesting to note that sterically well shielded radicals such as TTBP and GALV, which contain bulky t-butyl groups, lead to more negative enhancements than relatively planar radicals such as TCSQ and TPPY. It may be, then, that 19F scalar coupling is related to the availability of the odd electron at the radical edge. A second example of the sensitivity of 19 F NMR enhancements to radical type is given in Table 9 which shows values 74 of U~ovfor CFaCCI 3. Again, some fluorine scalar coupling is observed in all cases. Further, comparison with the C 6 F 6 TABLE 9 DYNAMIC POLARIZATIONIN 1, I, I-TRIFLUORO-2,2)2-TRICHLOROETHANE Reprinted with permission from ref. 74.
Radical
Additional solvent
Relaxation Maximumobserved Extrapolated time (sec) enhancement enhancement TH
GALV TTBP DPPH TCSQ WPBC
Acetone None Acetone Acetone Acetone
(50 ~) (50 ~o) (90~) (75 ~)
TF
1.4 1.1 0.3 0.6 0.6 2.5 2.8 5.1 3.6
GH
--245
GF
--210 --220 --89 --68 --265 --115 --70 +9
Advan. MoL Relaxation Processes, 4 (1972) 229-354
U~H
U~F
--320 --270 --280 --310
--240
--325
--160
--310
+40
Contact
relaxation component cF
1.1 1.0 1.7 3.6 10.0
DYNAMIC
NUCLEAR
305
POLARIZATION
results shows that for any given radical, CFaCC13, which contains aliphatic fluorine, shows less scalar coupling than C6F6. Fluorine scalar rates for a larger selection of aromatic and aliphatic fluorocarbons 56 are shown in Table l0 and in Figs. 42 and 43. For Table 10, the free radical DPPH was used exclusively. Relatively small values of cF for aliphatic fluorocarbons are again reported, and it is interesting to note that the largest scalar rate for aliphatics comes from 1,2,4-trifluorobromobutene which has one F adjacent to a double bond. Figure 42, which shows cF for a variety of fluorobenzenes, is interesting in several respects. First, with DPPH, CF increases with T A B L E 10 EXTRAPOLATED
~gF ENHANCEMENTS
DPPH
WITH
AT
74 GAUSS
R e p r i n t e d with permission f r o m ref. 56.
Fluorocarbon
Additional solvent
Uoo
c~
1,1,1-Trifluoro-2,2,2-trichloroethane 1,2-Dichloro- 1,2-difluoroethane
50 % acetone None 50 ~ acetone 50 % acetone 50 ~ acetone None 5 ~ a c e t o n e - 9 0 % CCI, None 5 % a c e t o n e - 9 0 % CC14 5 % acetone-90 % CCI, None 50 ~ acetone 50 % acetone 50 % acetone 50 % acetone 50 % acetone 50 % acetone
-- 235 -- 170 -- 180 --230 --205 -- 185 --205 -- t90 --240 --200 -- 170 -- 15 --40 --55 --25 --35 -- 50
1.8 3.1 2.8 1.8 2.3 2.7 2.3 2.6 1.6 2.4 3.0 7.5 6.6 6.2 7.1 6.8 6.4
!,2-Difluoro-l,l,2,2-tetrachloroethane 1,1,2,2-Tetrafluoro- 1,2-dibromoethane 0q~,0t-Trifluorotoluene Perfluoro-n-hexane 1-Fluoro-n-octane Perfluorocyclohexane Perfluorodecalin 1,2,4-Trifluorobromobutene Hexafluorobenzene
1,2-Dibromotetrafluorobenzene 1,2-Diiodotetrafluorobenzene Chloropentafluorobenzene Bromopentafluorobenzene Iodopentafluorobenzene
*20 • DPPH a Golvinoxyl
•
0
-50
~ "U u
(J
~5
n
E
-~oo
~
-200
~
4
o 3 o
2
ee D o O D o D
~,
81 0
1
2
3
4
5
6
-350
Number of fluorines on benzene ring
Fig. 42. Fluorine contact coupling in substituted fluorobenzenes with G A L V a n d D P P H . Reprinted with permission f r o m ref. 56.
Advan. MoL Relaxation Processes, 4 (1972) 229-354
306
J. POT~NZh
4.4
4.2
,~ •"
/ l > " ~ " - - m NOz i,,¢,-- . . . . . . -a I
4.0
3.6
./
.2 u 3,2 2.8 P-6
/
x
g '. . . . ORTHO META
' PARA
Substituent p o s i t i o n r e l a t i v e to fluoPine
Fig, 43. Fluorine contact coupling in substituted fluorobenzenes with DPPH. Reprinted with permission from ref. 56.
the number of fluorines on the ring, in contrast to GALV. Secondly, values for these aromatic fluorines are all larger than the aliphatic values in Table 9. Lastly, DNP measurements for several disubstituted benzenes (Fig. 43), show that fluorine meta to any substituent shows a higher scalar rate than when it is ortho or para. Apparently, DNP measurements are sensitive to ~-orbital effects. In sum, these low-field results indicate a sensitivity of fluorine DNP to chemical environment at least as great as that of the chemical shift.
2. Possible interpretations for scalar coupling Physically, variations in cv could arise from changes in either A or zs (eqn. (52)). An increase in A upon change of radical would indicate greater unpaired electron density at the fluorine nucleus (eqn. (39)), while an increase in zs would indicate either greater microviscosity or a tendency for the colliding species to stick together. Values for A and Ts may be obtained from multifield measurements, and these will be presented later. Chemically, two mechanisms for scalar coupling are plausible: exchange polarization 111, after the manner of coupling on free radicals, and complex formation. Exchange polarization may be understood as follows. Consider a radical such as benzene negative ion which has an unpaired electron in arc orbital formed from the atomic 2p= orbitals of carbon. Since the n orbital contains a node in the plane of the ring, we expect no spin density at hydrogen. However, EPR results for this and other hydrocarbon radicals 3~ show beyond doubt that the protons of aromatic free radicals contain some spin density which originates via exchange polarization of the C - H sigma bond. For example, the EPR spectrum 112 of C6Iq 6 - consists of 7 equally spaced lines because of hyperfine coupling of the electron with six equivalent protons. Adman. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
307
POLARIZATION
In Fig. 44(a), one of the C - H bonds of C6H6- with two paired electrons is shown, along with a C2pz orbital which has some spin density. The question is" does this electronic configuration give a valid description of C r H 6 - ? The answer is no, because the odd electron will tend to unpair the electrons in the C - H bond. A more realistic description of the bonding is shown in Fig. 44(b). There, the electrons in the C - H bond are correlated with the odd electron. This slight unpairing of electrons in the C - H bond gives rise to spin density at H of the opposite sign from that of the unpaired electron if it is assumed that the partial triplet formed is lower in energy than the corresponding singlet; in this case the hyperfine coupling constant would be negative. For protons on aromatic radicals, one electron in a 2p orbital at C produces 35, 113 a hyperfine splitting A of approximately 25 gauss. Smaller values of spin density give proportionally smaller splittings. 1 e - ~ 25 G
(a)
(b)
1e-~ 100 G
66
1 e-tu 700 O
(c)
Fig. 44. Intrarnolecular exchange polarization. (a) T h e n a n d a orbitals o f C r H r - are regarded as distinct. (b) A zt-cr interaction unpairs slightly the electrons o f the C - H b o n d leading to spin density at H. (c) F o r C r H s F - , two polarizations are possible, each o f different sign, a n d a net spin density is observed.
For fluorine, the situation is more complicated in that fluorine may participate in the n system, Two types of polarization, shown schematically in Fig. 44(c), are possible. The first is equivalent to that with protons except that 1 e at C gives114 a splitting of approximately 100 gauss. At fluorine, one electron in a 2p orbital gives 114 a splitting of approximately 700 gauss. Further, the sign of the spin density will be opposite to that for polarization at carbon and one should observe a hyperfine splitting A which depends upon the n e t spin density at F. This in turn should depend on the fraction of the odd electron located at C and at F. For intermolecular coupling, similar arguments apply except that the unpaired electron and the magnetic nucleus are on different compounds. Figure 45 shows one possibility for fluorobenzene colliding with p-benzosemiquinone. During the collision, the odd electron may slightly unpair the electrons at fluorine, or it may interact with the vacant n orbitals of fluorobenzene if one is available. Advan. MoL Relaxation Processes, 4 (1972) 229-354
308
J. POTENZA
Fig. 45. Interrnolecular exchange polarization. The unpaired n electron of benzoserniquinone delocalizes into vacant z~orbitals on fluorobenzene. By a n-a polarization of the C-F bond, spin density arises at F. In either case, some spin density can result at the F nucleus by the above mechanism, but here the degree of polarization depends upon the relative orientation and time of contact of the colliding species. Complex formation, the second mechanism, occurs when the electrons of both molecules become delocalized or redistributed upon association. Complexes have been found responsible for solvent effects in EPR spectra lj5' 116. There, the solvent perturbs the unpaired electron causing a change of electron density and consequent changes in A. With one, we are looking at the reverse effect, that of the radical on the solvent. Qualitatively, exchange polarization and complex formation can account for low-field 19F enhancements 19. For example, since a-orbitals do not lead to complex formation in general, aliphatics should have lower scalar rates than aromatics if this mechanism is dominant. Further, well-shielded radicals such as TTBP and GALV which contain very little spin density in exposed positions should neither complex well nor lead to large degrees of exchange polarization. They should then give large negative enhancements, as is observed. On the other hand, poorly shielded planar radicals colliding with aromatic fluorocarbons should complex readily, polarize strongly and give large positive enhancements. The absence of scalar coupling for protons in C - H bonds may be understood in terms of the relatively small coupling parameter of hydrogen (25 gauss/electron) as compared with fluorine. These ideas received further support from molecular orbital calculations involving benzosemiquinone and various fluorocarbons 19. Induced spin densities at fluorine for comparable collision attitudes were shown to increase in the order CF 4 < C6HsF < C6H 6 < C10F8 (Fig. 46). The behavior of the fluorobenzenes with D P P H in Fig. 42 may be understood on this basis. Further, plane-plane collisions between aromatics were shown to be much more effective in leading to Advan. MoL Relaxation Processes,
4 (1972) 229-354
309
DYNAMIC NUCLEAR POLARIZATION
Q
0
2"2~5A~-1.70
~
3.75
O.
0.85
Q05
~'I"~F0.00
105 F
0.60 Q 0.15 Q30 O.I
OO5
0.30
F4.35
5~~.~F
Q95
o~o.L ~""~/~,/ ~Fa05 F 035
F 1.10
0.95 3.80.'"
ODO F
O35
F F
Q10
.Q
F010
005
Fig. 46. Induced spin densities ( × 104) for several fluorocarbons in collision with benzosemiquinone. The radical is located 2.25 A from F with its plane in the plane of the paper.
spin density at F than edge-on collisions. This raises the question of possibly detecting stereospecific collisions in liquids. The results in Fig. 46 also indicate that collisions far removed from F can effectively produce spin density at F; e.g. spin information is transmitted over a relatively long distance. Last, we observe that only a small fraction of the electron (about 0.001) need be transferred to the solvent to produce appreciable polarization. 3. MultifieM measurements M u l t i f i e l d 19F DNP results have been reported by several groups (refs. 20, 55, 105, 106, 108, 109, 117, 118). Except for the results presented below, these have been restricted in nature, either with regard to the number of fields examined or to the chemical compounds used. Below, we shall consider a variegated array of radicals and fluorocarbons at widely separated field strengths. This has the advantage of allowing broad chemical trends in the data to be examined. U l t i m a t e 19F NMR enhancements at four field strengths 118 are shown in Table 11. Sixteen radical-solvent pairs were studied. These included all combinations of the fluorocarbons C F 3 C C 1 3 (TCF); ~,a,~-trifluorotoluene (TFT), hexafluorobenzene (HFB) and octafluoronaphthalene (OFN) with the radicals TTBP, GALV, TCSQ and TPPY. Both radicals and fluorocarbons span a wide Advan. Mol. Relaxation Processes, 4 (1972) 229-354
310
J. P O T E N Z A
T A B L E 11 ULTIMATE 1 9 F NMR ENHANCEMENTS AS A FUNCTION OF MAGNETIC FIELD STRENGTH
Reprinted with permission f r o m ref. 118.
Field TCF strength (gauss) U~H
Uoov
U~on
UooF
U~H
UooF
U~H
U~v
TTBP
74 3050 3650 8900
--310 --250 --260 --82
--235 --55 --40 +5
--310 --190 --165 --81
--240 -- 27 --22 --7
--315 --260 --275 --83
--135 --21 +11 +48
--310 --260 --240 --66
--180 --22 --20 +39
GALV
74 3050 3650 8900
--320 --175 --170 --28
--225 --19 --6 +12
--310 --185 --155 --33
--230 --25 --7 +3.5
--315 --210 --185 --34
--145 +7 +13 +29
--320 --145 --155 --32
+135 +25 +49 +44
TCSQ
74 3050 3650 8900
--325 --145 --140 --66
--240 --26 --7 --23
--315 --140 --140 --45
--150 --13 --7 --3
--280 --110 --97 --38
+195 --20 --11 -- 15
--280 --105 --120 --40
+375 --35 --29 --23
TPPY
74 3050 3650 8900
--310 --175 --170 --37
--80 --12 --6 +6
--310 --175 --150 --76
--30 --7 --2 +3
--270 --165 --160 --63
+300 +31 +22 +60
--300 --185 --185 --45
+445 --31 --17 +21
Radical
TFT
HFB
OFN
range of chemical types. Examination of the results reveal that the enhancements fall into two distinct categories: systems which give large negative low-field enhancements tend to cross the axis and become positive at high field, while systems with positive low-field enhancements become negative at high field. Curiously, TPPY with OFN, the most positive low-field system studied, crosses the axis twice. A single crossing of the axis is consistent with the spectral density curves in Fig. 39, and indicates that systems with large positive low-field enhancements have zs > zaHowever, the simple spectra in Fig. 39 do not predict two crossings, and this could be due to two scalar correlation times or to a more complicated frequency spectrum of molecular motions '°7. Analysis of the results in Table 11 gave the values of A, zs and za shown in Table 12. Dipolar correlation times show no apparent trends, while both zs and A increase with increasing low-field enhancement. Hence, systems with small values for cv show weak hyperfine coupling and short scalar correlation times. In contrast, systems with large values for CF have both strong hyperfine coupling and long scalar correlation times. Overall, this is precisely the behavior expected chemically if increases in A correspond to increases in exchange polarization and increases in zs to sticky collisions and increased complexation. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR P O L A R I Z A T I O N
311
TABLE 12 CORRELATION TIMES a AND RELATIVE SCALAR HYPERF1NE COUPLING ENERGIES FOR FLUORINE NUCLEI IN FREE-RADICAL SOLUTIONS
Reprinted with permission from ref. 118. Radical
TCF
TFT
HFB
OFN
Td
Ts
Arel
Td
Ts
Arel
Td
Ts
Arel
Td
Ts
-~rel
TTBP
1,6 (S)
0.7
2.3
2.4 (S)
0.9
2.4
1.6 (S)
0.8
3.0
1.8 (S)
0.7
2.9
GALV
3.2 (S)
0.9
2.6
2.9 (S)
1.0
2.4
2.6 (t)
1.4
2.9
3.5 (D)
4.0
4.1
TCSQ
2.3 (S)
1.0
1.8
3.3 (1)
2.2
2.7
2.4 (O)
6.0
3.1
2.0 (O)
11.0 3.5
PPY
3.0 (1)
2.5
2.7
2.0 (D)
1,8
3.2
2.1 (D)
5.5
3.9
2.4 (D)
11.5 4.5
a Times are in units 10-11 sec. A l t h o u g h it is n o t i m m e d i a t e l y a p p a r e n t , several a d d i t i o n a l interesting conclusions m a y be d r a w n f r o m the analysis o f the d a t a in Tables 11 a n d 12 when s u p p l e m e n t e d b y results o f L C A O - M O calculations, W e assume that the three generalized r a d i c a l - s o l v e n t collision attitudes shown in Fig. 47 are representative o f the collision process between a r o m a t i c molecules 19. F o r p l a n e - p l a n e a n d at y p e collisions, o v e r l a p o f the 2p electrons c o m p r i s i n g the radical ~ system with the F2p o r b i t a l is o f the ( 2 p - 2 p ) a-type, whereas for n collisions, it is ( 2 p - 2 p ) re. T h e relative effectiveness o f these collisions for the t r a n s m i s s i o n o f spin inform a t i o n to fluorine nuclei m a y be crudely assessed by c o m p a r i n g ( 2 p - 2 p ) a a n d (a) ~
(b)
CONTACT
ff CONTACT
f~ jJ
(c~ PLaNE-PLANECONTACT i I
'/ ~J
Fig. 47. Generalized collision attitudes for fluorobenzene and benzosemiquinone. Reprinted with permission from ref. 19. Advan. MoL Relaxation Processes, 4 (1972) 229-354
312
J. P O T E N Z A
TABLE 13 O V E R L A P I N T E G R A L S S FOR F " ' " O SYSTEM
Reprinted with permission from ref. 19. ru
S,
S,
SdS,
2.00
0.05615
0.00980
5.74
2.25 2,50
0.02839 0.01367
0.00417 0.00173
6.81 7.90
2.75
0.00633
0.00070
9.08
3.00
0.00284
0.00028
10.2
3.25
0.00124
0.00011
11.3
(2p-2p) n overlap integrals for a F atom separated by a distance r o. f r o m an oxygen a t o m (if the collision is with G A L V or TTBP). These integrals are given in Table 13, f r o m which it is apparent that a overlap is much greater than n overlap, the ratio increasing with increasing distance between the nuclei. Somewhat more refined calculations confirmed these results and led to estimates o f intermolecular potentials for the various collision attitudes between benzosemiquinone and several fluorocarbons. A screened c o u l o m b potential of approximate form exp [ - 2 ( r ~ - d ) ] was assumed. Here r u is the distance between F and O nuclei, d is the distance o f closest approach, and 2 describes h o w rapidly the interaction energy increases as the molecules move closer together. Values 19 for 2 are shown in Table 14. F o r both n and plane-plane collisions, 2 is nearly independent o f the fluorocarbon chosen, while for tr collisions this is not true. M o r e important, 2 for plane-plane collisions is considerably smaller than for either rc or a collisions. A small value of ), indicates a gently rising potential and therefore for plane-plane collisions, we expect buildup and decay of spin density
Spin density
¢ T~me
(a)
~
Time
P
(b)
T~me ~
(c)
Time
(d)
Fig. 48. Schematic comparison of collisional pulse shapes for (a) plane-plane, (b) a, (c) ~ collisions. The height of the pulse will depend on the spin density at F, while its width is governed by 2 or r~. Part (d) shows the pulse that best fits ONP data for C 6 F 6 with GALV and TTBP (ref. 106). Advan. Moi. Relaxation Processes, 4 (1972) 229-354
313
DYNAMIC NUCLEAR POLARIZATION TABLE 14 AVERAGE VALUES OF /~ FOR V A R I O U S F L U O R O C A R B O N S A N D C O L L I S I O N T Y P E S
Reprinted with permission from ref. 19.
a Plane-plane
CH4
CF4
C6H~F
~
6.2 9.8
6.4 6.6 3.2
6.6
2.8
3.4
at fluorine over a relatively long period of time. In contrast, for n and a collisions, the interaction time should be smaller. This is shown schematically in Fig. 48. The half width of each pulse is roughly equal to the scalar correlation time. We are now in a position to interpret multifield fluorocarbon DNP results in terms of probable collision pulses 106, 1a8, 119. For systems with predominantly n interactions, we expect short scalar correlation times, while when plane-plane collisions become important, zs should increase. Qualitatively, this is in agreement with the enhancement data, since aromatic radicals and aromatic fluorocarbons give the largest correlation times. A more detailed analysis of these collision pulses (ref. 119) also accounts for the rate of enhancement decline with increasing feld strength. An example of stereospecific collision pulses was given by Mi.iller-Warmuth et al. 106 who studied the DNP field dependence of several fluorocarbons with GALV and TTBP. For aliphatic fluorocarbons, the enhancement spectra could be interpreted in terms of simple pulses such as those in Fig. 48(a)-(c). However, with C6F 6 , the only aromatic fluorocarbon used, a simple pulse shape could not be used. Rather, the complex pulse shown in Fig. 48(d) was used. This pulse probably arises from a combination of n and tr collisions. The above results show that the type of information available from 19F DNP, because of scalar coupling, is quite different from that obtained from ~H spectra. Because they are sensitive to chemical effects, 19F enhancements may be used to probe molecular collisions more from a chemical viewpoint.
D. Experimental results for phosphorus nuclei 1. Low-field results Phosphorus DNP results are not as extensive as those for either 19F o r tH. This is because phosphorus NMR signals are relatively difficult to detect experimentally, and because many free radicals decompose rapidly in the presence of phosphorus-containing compounds. Fortunately, BDPA is stable for weeks with almost any phosphorus-containing compound 12°, and with this radical, many systems Advan. Mol. Relaxation Processes, 4 (1972) 229-354
314
J.
POTENZA
T A B L E 15 3 I p DNP PARAMETERS FOR PENTAVALENT PHOSPHORUS WITH B D P A AT 74 GAUSS R e p r i n t e d with permission f r o m ref. 120.
Solvent
Gloon
G~n
Gloop
G~p
Uoop
ce
--160 --115 --195 -- 285 --280
--270 --70 --2 + 550 +430
--300 --90 --5 + 825 +600
--590 --240 --8 + 895 +670
1.3 4.8 7.9 39.1 25.6
--220 --320 --230 --310
--350 --480 +245 +550
--420 --550 +370 +705
--600 --550 +500 +705
1.2 1.6 19.2 27.2
--165 --210 -- 180 -- 160 --170 -- 330 --275
--310 --190 -- 195 -- 270 --80 -- 445 --60
--350 --280 -- 350 -- 300 --150 -- 580 --90
--650 --415 -- 595 -- 590 --280 -- 580 -- 100
0.8 2.8 1.2 1.2 4.3 1.4 6.5
--155 --330 --155 --155
+40 +30 +30 +95
+60 +40 +45 +130
+125 +40 +90 +260
10.1 8.6 9.4 12.8
Phenylphosphonic halides (C6Hs)aPO/C6H6 (C6Hs)2P(O)C1 C6HsP(O)C12 P( O) CI a/C6H6 P(O)Bra/C6H6
--140 --100 --115 -- 185 --165
Phenylthiophosphonic halides ( C6Hs)aPS/C6 H6 (C6Hs)aPS/CHC13 (C6Hs)PSC12 P(S)CIa/C6H6
--190 --270 -- 145 --220
Alkyl and thioalkyl phosphates (MeO)aPO (EtO)sPO (n-BuO) 3PO (C6HsO)zPO/C6H6 (EtO)2P(O)C1 (EtO) 3PS (EtO)2P(S)C1
--135 --160 -- 105 -- 140 --75 -- 225 --95
Dialkyl and diaryl phosphites (MeO)zP(H)O (EtO)2P(H)O (n-BuO)zP(H)O (C6HsO)2P(H)O
--110 --190 --115 --95
were examined at 74 gauss. Experimental results are listed in Table 15 for pentavalent phosphorus compounds and in Table 16 for trivalent compounds. Similar results for many of these compounds were also obtained 121 with TTBP, although there only the sign of the enhancement could be measured because of rapid radical decomposition. In Tables 15 and 16, Gloou is the largest observed proton enhancement, Go~n is the proton enhancement extrapolated to infinite RF power, while Gloov and Go~p are corresponding values for phosphorus in the same solutions. Values for G~H fall short of the dipolar limit primarily because the EaR line of BDPA was too broad to saturate completely and not because of proton scalar coupling. For this reason, values of the ultimate 3 t p enhancement were obtained by the ratio method mentioned above 74. Values for cp, the 31p contact component, were obtained using q/3.0 = r/1.6 = s/9.6. A cursory glance at Tables 15 and 16 shows that phosphorus enhancements, like those for fluorine, are extremely sensitive to chemical environment. ExtraAdvan. Mol. Relaxation Processes, 4 (1972) 229-354
315
DYNAMIC NUCLEAR POLARIZATION TABLE 16 3tp DNP PARAMETERSFOR TRIVALENTPHOSPHORUSWITH BDPA AT 74 GAUSS Reprinted with permission from ref. 120. GlooH
GooH
Gloop
Goop
UQcI,
cp
Phenylphosphine halides (C6Hs) aP/C6H6 --110 (C6Hs)aP/CS 2 --155 (C6Hs)2PC1 -- 125 CnHsPCI2 --200 PCla/C6H6 -- 190 C6HsPBr2 -- 135 PBr3/C6H6 --200
--150 --255 --200 --320 --205 --250 --250
+290 +555 +480 +665 +870 +460 +870
+415 +800 +670 +1090 + 1070 +600 +1050
+860 +970 + 1040 +1090 + 1610 +745 +1300
36.4 45.4 52.8 59.4 oo 29.3 109
Trialkyl phosphites (MeO)3P (EtO)aP (i-PrO)3P (n-BuO)3P (C6HsO)aP/C6H6
--200 --210 --200 --130 --240
--310 --330 --290 --230 --285
+660 +675 +565 +380 +795
+1000 +950 +775 +605 +1000
+1000 +950 +835 +825 +1050
48.3 43.5 34.7 33.8 54.1
Miscellaneous (EtO)2PCI (C6Hs)2PH
--200 -- 140
--310 -- 155
+540 +460
+790 + 525
+790 + 1060
32.4 55.4
Polyhedral phosphorus Pa/CS2/C6H6 --235 P4S3/CS2/C6H6 --280
--285 --325
+915 + 1180
+970 + 1420
+1050 + 1420
54.1 182
Solvent
p o l a t e d e n h a n c e m e n t s v a r y f r o m - 6 5 0 for t r i m e t h y l p h o s p h a t e to + 1610 for p h o s p h o r u s trichloride. This covers a l m o s t the entire theoretical range o f enh a n c e m e n t expected (Table 4). I n addition, the large observed e n h a n c e m e n t s indicate t h a t DNP m a y be a v a l u a b l e tool for investigating 31p N~R at low concentrations. Chemically, several effects are significant. F o r example, where c o m p a r i s o n s are possible, trivalent p h o s p h o r u s always shows m o r e scalar c o u p l i n g t h a n p e n t a v a l e n t p h o s p h o r u s ( c o m p a r e ( M e O ) 3 P with ( M e O ) 3 P O , PC13 with POC13, etc.). This is a general o b s e r v a t i o n first n o t e d by D w e k a n d R i c h a r d s 122. In a d d i t i o n to the large differences in e n h a n c e m e n t between t ¢~I a n d pV, several smaller substituent effects m a y be noted. Thus, for the p h e n y l p h o s p h o n i c halides, enh a n c e m e n t s increase as 4~ is replaced by CI, indicating t h a t CI t r a n s m i t s spin density to P better t h a n q~. W h e n Br is substituted for CI, the e n h a n c e m e n t decreases ( c o m p a r e P O B r 3 , POCI 3 a n d PBr3, PCI3). W h e n R O is replaced by H, the e n h a n c e m e n t increases ( c o m p a r e ( M e O ) 3 P O with ( M e O ) z P ( O ) H , etc). Finally, the effect o f substituting S for O is n o t clear since ( E t O ) 3 P S shows less scalar coupling t h a t ( E t O ) a P O , the reverse o f ( E t O ) 2 P ( S ) C I a n d (EtO)2P(O)CI. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
316
J. POTENZA
A detailed examination of the data shows that scalar coupling decreases in the order: lone pair > H > C1 > Br > C6Hs > RO. Such large substituent effects undoubtedly arise from the central location of P atoms in phosphorus compounds with consequent possibilities for substitution. In contrast, fluorine and hydrogen are always located at molecular peripheries and are therefore always available for interaction with the free radical. Thus, for phosphorus, we may make an additional distinction between intermolecular coupling mechanisms. Coupling may be either direct or indirect, depending on whether the radical acts directly upon electrons situated at phosphorus or indirectly via long-range conjugation. The fact that enhancements increase with increasing substituent size strongly suggests the presence of direct coupling, while the large positive enhancements obtained with compounds such as C13PO , in which phosphorus is well shielded sterically, suggests spin transmission through delocalized bonding orbitals. As an example of direct coupling, the large positive enhancements of trivalent phosphorus may be regarded as due primarily to radical collisions with the lone pair electrons. Since these contain some s-orbital character, any unpairing of these electrons will result directly in spin density at P and resultant large scalar coupling. Several chemical applications of 31p DNP have been reported. In an attempt to determine the extent of electron delocalization in phosphonitrilic ring compounds of formula (PNCI2)~, x = 3-7, ~ P enhancements were measured with several radicals 22. The degree of aromaticity in these compounds has been of concern for several years 123' 124. The detailed order of enhancements, shown in Fig. 49, was found to be nerarly independent of the radical used, indicating that cp depends primarily on the chemical properties of the (PNCI2)x rings and less on the nature of the radical. Interpretation of the enhancement data led to the -300
• ,.,.200 8 E 0 u
e- ~100 o ¢0
~
0
E
~
BDPA
TTBP GALV DPPH
-100
I
3
i
i
I
}
4
5
6
7
n in (PNCla) n
Fig. 49. Extrapolated alp NMR enhancements for (PNC12)~ compounds with the four free radicals indicated. Reprinted with permission from ref. 22. Advan, MoL Relaxation Processes, 4 (1972)229-354
DYNAMIC
NUCLEAR
317
POLARIZATION
suggestion of delocalized orbitals in the rings. It was suggested that the question of aromaticity in P N ring systems could be resolved further by comparing polarizations for compounds such as PsNs(NMe2)9C1 and PsNs(NMe2)lO. The latter gives negative 31p enhancements, while the former, because of the positive substituent CI, should give a positive enhancement. I f positive enhancements were observed at all phosphorus atoms in the chloride, delocalized orbitals would be present. Unfortunately, monochlorinated phosphonitrilics are difficult to prepare. A second chemical application of 31p DNP involves the detection of stereospecific collision attitudes and hyperfine interactions zl. Ultimate 31p enhancements were measured at 74 gauss for eight phosphorus compounds with three free radicals. Values for U~p and cp are shown in Table 17. Overall, these results substantiate the conclusions presented above. Well shielded pV compounds show highly negative Uoo values independent of the radical chosen, whereas stericaUy exposed pli! compounds give large positive enhancements. And, variations in enhancement due to differences in phosphorus chemical environment far outweigh variations due to radical type. T A B L E 17 31p DNP ENHANCEMENTS AT 74 GAUSS FOR SEVERAL FREE RADICALS
Reprinted with permission from ref. 21. Compound
q~aP
BDPA
TTBP
cp
U~op
100
DPPH
Cp
Uoop
cp
U~op
+1270
70
+1160
27
+700
(MeO)aP
29
+
740
21
+
550
19
+500
(PNCI2)3
14
+
300
12
+
225
10
10
+
110
6.8
-- 75
-----
300 600 700 500
4.0 0.6 1.6 7.5
--300 --680 --560 -- 35
(MeO)2P(O)H
9.5
+
85
(EtO)2P(S)CI (MeO)aPO (EtO)aPS (Me2N)aPO
5.2 2.1 1.8 0.4
-----
200 500 530 750
4.0 1.2 0.4 2.1
+
50
It is interesting to note the radical order for decreasing scalar coupling. With six of the eight compounds tested, scalar coupling decreases with free radical in the order B D P A > TTBP > D P P H . This behavior is different from that for fluorocarbons where in general B D P A > D P P H > TTBP. With (MeaN)3PO, the radical order is D P P H > TTBP > BDPA, while for (MeO)2P(O)H, it is TTBP > B D P A > DPPH. For fluorocarbons, differences in scalar rate with different radicals were related to spin exposure at the radical edge. Here, a different interpretation must apply, and it was suggested that the observed radical order arose partially from stereospecific hyperfine interactions. Adoan. Mol. Relaxation Processes, 4 (1972) 229-354
318
J. POTENZA
This may be understood as follows. In addition to peripheral electron distribution, the radicals differ further in one significant way - the atomic species which has maximum spin density. The O atom of TTBP, the N atoms of D P P H and the allyl C atoms of BDPA are each expected to share some 30-50 9/00of the unpaired electron. Thus, observed scalar rates for, say, TTBP could arise from a combination of peripheral electron exposure and primary collisions with oxygen. Evidence for such collisions comes from (Me2N)3PO which shows an unusually large scalar coupling with DPPH. It was suggested that this indicates a significant amount of transient bonding, perhaps between the radical and solvent lone-pair electrons. The large scalar rate observed for (MeO)2P(O)H with TTBP may similarly be interpreted in terms of transient hydrogen bonding between the TTBP oxygen atom and the solvent proton bonded to phosphorus:
.•
~/OMe & . . . . H--P~oMe
Additional evidence for the microscopic detection of hydrogen bonding came from a study of phosphorus DNP with nitroxide radicals ~25 which have almost all of the unpaired electron at the N - O sites. There, (MeO)2P(O)H gave an exceptionally large positive enhancement. Hydrogen bonding has also been detected by DNP in proton solutions at high field 126. Considering these results, it is interesting to speculate about the possibility of examining motion along a reaction coordinate. That is, for reacting systems, do those collisions which give large scalar coupling ultimately lead to chemical reactions? Many of the ideas presented above could be examined further by calculating correlation times and hyperfine coupling constants from multifield measurements. 2. Hiyh-fieM measurements Few 31p high-field DNP results have been reported, and none has been interpreted in detail in conjunction with low-field results. The available data are listed in Table 18. All measurements were made at room temperature with the free radical TTBP. For the data at 74 gauss, extrapolated enhancements are reported127, while at 12,500 gauss, maximum observed enhancements are given 128. At 3300 gauss, only the sign of the enhancement could be observed 12a, and this precludes accurate calculations of %. Nonetheless, we note that of the eight samples investigated, only two enhancements change sign, and these do so at 12,500 gauss. For the remainder of the systems, and for all pm systems, the sign of the enhancement does not change. This contrasts sharply with aromatic fluorine data, where axial crossings were observed below 3300 gauss, and indicates that scalar correlation times in 31p solutions containing well-shielded radicals do not depend Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
319
TABLE 18 MULTIFIELD 31p ENHANCEMENTS WITH
TTBP
Compound
74 yauss
3300 oauss
12,500 oauss
~aP (EtO)3P (MeO)aP (MeO)2P(O)H (Me2N) 3PO
+ 1160 + 660 + 550 + 110 -- 500 - - 600 -- 700 -- 750 Not studied
+ + + + ------
+20 +30 +50 Not studied 0 0 + 3 0 + 3
(MeOa)PO
(EtO)3PS (EtO)3PO (EtO)2P(O)CI
critically u p o n the n a t u r e of the solvent. Further, the scalar spectrum is seen to extend t o very high frequencies, especially for trivalent phosphorus. It has been suggested x6 that DNP, because of the possibility of observing large NMR e n h a n c e m e n t s , could be used to o b t a i n high-resolution NMR spectra of nuclei with low NMR sensitivity. A n example of a 31p high resolution spectrum is s h o w n in Fig. 50 for trimethyl phosphite with 10-3 M T T B P at 12,500 gauss (ref. 122). The multiplet resolution is good, b u t this is a favorable case since pin comp o u n d s give large e n h a n c e m e n t s at high field. F o r pV c o m p o u n d s , observed enh a n c e m e n t s at 12,500 gauss seem too small with T T B P to be o f m u c h value for e n h a n c i n g spectra. However, other radicals m a y give larger e n h a n c e m e n t s at high field.
Fig. 50. 31p spectrum of P(OMe)3 containing 10- 3 M TTBP. The arrow indicates the unenhanced signal. The enhancement shown is +35. Reprinted with permission from ref. 122. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
320
J. POTENZA
Recently, Dwek et al. 23 applied DNP to enhance the a l p NMR spectra of relatively insoluble phosphorus chalcogenides. Accurate chemical shifts and coupling constants were reported for several compounds, as shown in Table 19. In the case of P4Se3, which has the polyhedral structure
the resolution was good enough to obtain 31p-77Se coupling constants, the first to be reported. Since all results were obtained with non-spinning samples, increased signal-to-noise ratios could be obtained by spinning. Greater sensitivity could also be obtained by using a CAT. Although the enhancement of aXp NMR spectra by D ~ is not likely to find wide applicability over routine high-field methods, applications akin to that above are likely to be forthcoming, especially with dilute samples. TABLE 19 a l p DNP RSULTS FOR PHOSPHORUS CHALCOGENIDES Reprinted with permission f r o m ref. 23.
Compound
Enhancement 3300 y
P4 P406 P4Sa
P4S5 P4S7 P4Slo P4SaI2 P4Sea
P459
12,500 g
~-{~- 600 a -[- 60 P+ P+76 P'+ P'-}-69 P: P ' I . 0 P: P' 1.1 N o t observed N o t observed + ca. + 2 0 + + P+ P+80 P'+ P'+80 P : P ' 1.0 P : P ' 1.0
-F
Chemical shift b (p.p.m. from ext.
Coupling constant
(Hz)
P406)
d- 45.5 zL0.2 +233.6i0.2
+ 55.9j 0.4 -- 14.3=1=0.6 + 75.3±0.2 +217.7±0.2
2j(p...
p,) = 71=[:1
2j(p...p,) = 72+1 1J(P-Se) = 263 ~_ 10 I J ( P ' - S e ) = -r-563:k20 2 j ( p . . . . Se) = - - 5 7 i 1 0 1j(p, p,) = 157:k10
~-
a M a x i m u m value observed. Extrapolation to infinite microwave p o w e r gives + 11004-200. b Uncorrected for susceptibility; estimated correction is i 0 . 2 p.p.m.
In addition, some use with systems of biological importance 129 may develop, particularly if radicals are found which give large enhancements for pV compounds. Here, one can envisage a radical colliding with a phosphorus-containing macroAdvan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
POLARIZATION
321
molecule, and via the magnitude and field dependence of the enhancement, giving information on the chemical environment of phosphorus. In some ways, this is analogous to the well known spin-labeling techniques ~3°-~35 developed by McConnell and co-workers where an unpaired electron is bound to a macromolecule and its environment monitored by EPR. With DNP, additional information concerning the nature of collisions near phosphorus may be obtained and the two techniques could supplement each other.
E. Experimental results for carbon nuclei Because of its small magnetic moment and low natural abundance (1.1 ~), 13C is extremely difficult to detect using NMR techniques. However, 13C NMR spectra can be observed using a CAT and such spectra are finding increasing importance in organic chemistry136' ~37. Precisely because of the small value of/~ for 13C, we expect 13C NMR enhancements to be extremely large (Table 4), and zero signals extremely small. This makes quantitative enhancement measurements difficult to obtain, and, as a result, few DNP experiments have been performed. The first mention of ~3C ONe was by Hausser and Reinbold ~3s. At 3300 gauss, they measured 13C enhancements of 0.5 cm 3 samples of C6H6 and C 6 D 6 with the free radical BDPA. Their results are shown in Fig. 51. Unenhanced spectra
~H o
°
:~ H0
p
e
T ~ ~H0 Fig. 51. N a t u r a l a b u n d a n c e e n h a n c e d l s C NMR signals f r o m (a) benzene, (c) C6D6 ; (b) is a triple resonance experiment. Reprinted with permission f r o m ref. 138.
could not be observed, but by comparison of signal strengths with protons at the same frequency, they concluded that C6H6 was enhanced - 300 times, C6D 6 - 350 times. In addition, by simultaneously saturating the electrons of BDPA and the protons of C 6 H 6 (Fig. 51(b)), they obtained an enhancement of -1200. The Advan. MoL Relaxation Processes, 4 (1972) 229-354
322
J. P O T E N Z A
latter is a triple resonance experiment t a9, 14o which we have not discussed. Basically, it corresponds to a nuclear-nuclear Overhauser effect coupled with the electron-nuclear Overhauser effect. When the protons are saturated, the multiplet structure of carbon collapses as expected for heteronuclear decoupling and the signal is enhanced slightly. Small enhancements of this type have been observed in nuclear decoupling experiments without free radicals 141. Overall, Fig. 51 shows that 13C spectra may be recorded with one sweep at 3300 gauss. With a CAT, it should be possible to detect 13 C zero signals and obtain quantitative enhancements. In 1965, Imbaud 142 reported enhanced 13 C spectra for several hydrocarbons and fluorocarbons. Well resolved spectra were obtained, although enhancement magnitudes were not given because zero signals could not be measured. The most complete experimental treatment of I~C DNP to date has been that of Natusch and Richards 14a. At 3300 gauss, using the free radical TTBP, they measured ~aC enhancements for a variety of compounds, with the results shown in Table 20. TABLE 20 13C
DNP RESULTSAT 3300 GAUSSWITH TTBP
Reprinted with permission from ref. 143. Solvent
Sign of
Notes
enhancement
Very strong Very strong
c6n 6
CGF6 C6D 6 C6HsF
C~Hs-CHs C6Hs-CFs C6H4-(CH s)z C6Htz Fe(CO)s CHCIs CHBrs CH~CI2 CH2Brz CH2I~ CHsl CCI~ CFCIs CFaCCIs CH3OH CHaCN H'CO2"CH3 CHs'CH2"OH (C2Hs)2CO CS2 2,4,6-Tri- t-butylphenol
Enriched sample + + + + + +
N o resonance observed --
SCN resonance very strong --
-+(t-Butyl) Conc. solution in benzene -- (Aromatic)
Advan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR
POLARIZATION
323
In general, negative enhancements, indicative of dipolar coupling, were obtained except for all but one of the halo-substituted methanes, which showed positive enhancements. Tri-t-butyl phenol in benzene also gave a positive enhancement, but because of the possibility of chemical exchange, this should be regarded as a special case (see above). The 13C spectrum of tri-t-butyl phenol (Fig. 52) shows clearly a positively enhanced quartet from the t-butyl protons and negative enhancements for the ring protons in accord with the 1H results presented above. That large halogen atoms lead to positive enhancements is in accord with the lowfield phosphorus data presented above. a
a - 13CH3 q u a r t e t b - '3C(CH3)3 s i n g l e t c - A r o m a t i c 13C of s o l v e n t b e n z e n e + phenol
a
Fig. 52. Natural abundance ~aC spectrum of tri-t-butyl phenol in benzene with TTBP. Reprinted with permission from ref. 143.
Some idea of the magnitude of the enhancement at 3300 gauss was obtained by studying a 62.5 ~ ~3C enriched sample of Fe(CO)5. The zero signal was seen easily and an enhancement of - 3 5 was observed. Attempts were made to observe enhanced 13C spectra at 12,500 gauss, but none could be observed with natural abundance samples. Since the enriched Fe(CO)5 sample gave an enhancement of 4 at 12,500 gauss, it was concluded that the frequency spectrum is near zero at that field. In terms of magnitude of the enhancement, then, these preliminary results indicate that 1a C behaves like a~p, which suggests that fields of 3300 gauss or lower may be used to obtain relatively large enhancements and high resolution. The most dramatic example of the possibilities which exist with a3C in natural abundance was given by Gr~tzedick and Miiller-Warmuth 144. They reported observing both enhanced and unenhanced ~3C NMR spectra of benzene with TTBP at 176 gauss. At this low field, all signals were accumulated on a CAT; the enhanced signal required 40 min and the unenhanced signal a week to observe. Relaxation times were measured and the a3C NMR signal was extrapolated to infinite RF power in the usual way. In this manner, the quantitative enhancements shown in Table 21 were obtained. (The values for CHaI were obtained using an enriched sample and BDPA.) Analysis of the data indicates that the scalar relaxation component in both cases is less than 30 ~ . Qualitatively, this agrees with the fluorine data presented above, which showed large negative enhancements for Advan. MoL Relaxation Processes, 4 (1972) 229-354
324
J. POTENZA
TTBP. Significantly, the benzene spectrum was a resolved doublet, as expected, which demonstrates the possibility of obtaining high resolution ~aC spectra at relatively low fields where enhancements are large. TABLE
21
Uoo C AT 176 GAUSS FOR C 6 a 6 IN T T B P AND C H a l I N
BDPA
R e p r i n t e d w i t h p e r m i s s i o n f r o m reE 144.
Temp. 333 294 270 250 232 218
°K
(C6H6/TTBP)
(CHal/BDPA)
--210 --450 --540
--- 20 - - 55 --100 --130 --140
If DNP is to find application as a tool for observing weak NMR signals, it will probably be for 1aC where chemical shifts and coupling constants are large enough and natural sensitivity low enough to warrant the additional effort required to construct and maintain the double resonance spectrometer. Regardless of applications to high resolution NMR spectroscopy, 13C enhancements, because they seem sensitive to chemical environment, are likely to be measured with increasing frequency in the future. With time averaging computers, stable systems and large sample volumes, zero signals can probably be measured conveniently at fields as low as 500 gauss, and this may be close enough to the zero-field limit to permit scalar parameters to be obtained. Values so obtained could be compared with proton, fluorine or phosphorus data taken on the same compound and this would give a better understanding of molecular collisions in liquids.
V. E X P E R I M E N T A L RESULTS - C I D N P
A. Alkyl and aryl radicals Alkyl and aryl radicals generated by the thermal decomposition of peroxides or azo compounds were studied by Kaptein 59 (alkyl) and by Bargon and Fischer (refs. 24, 145) (both). In the simplest case, phenyl, chlorophenyl and o,p-dichlorophenyl radicals were produced 145 by thermally decomposing dibenzoyl-, p-chlorodibenzCyl- and o,p-dichlorodibenzoyl peroxides respectively. Here, the reaction scheme given by eqn. (55) applies and the products showing ODNP were benzene, chlorobenzene and m-dichlorobenzene. Observed enhancements increased in the order Advan. Mol. Relaxation Processes, 4 ( 1 9 7 2 ) 2 2 9 - 3 5 4
DYNAMIC
NUCLEAR
325
POLARIZATION
T A B L E 22 OBSERVED AND CALCULATED ENHANCEMENTS (40 MHz) OF C6HsCI AND C6H 6 Reprinted with permission f r o m ref. 145.
Temp.
C6Hs CI
IIO°C 120 ° C
C6H6
Gobs
Gcalc
Gobs
Gcalc
- - 6.3 - - 16
--6.2
--20
--20
[m-C6H4CI2I < 1C6H5Cll < IC6H61. Experimental enhancements, shown in Table 22, were obtained for C6H5C1 and C 6 H 6 ; m-C6H4CI2 gave a complicated spectrum and could not be compared with benzene and chlorobenzene. Calculated enhancements, also shown in Table 22, were obtained from eqn. (59) assuming pure dipolar coupling. ]?he various parameters required to calculate G from eqn. (59) were approximated either from values taken from the chemical literature on other systems or they were estimated. For example, T1M, the spin-lattice relaxation time of the product, was taken to be that of the pure solvent 146, while the correlation time • for chlorobenzene was estimated from that of benzene 146. Values for p, p' and a, the relaxation transition probabilities, were obtained by using the abovementioned correlation time. On the basis of enhancements calculated using these parameters, it was concluded that the Fischer cross-relaxation model described above adequately described the polarization process and that chlorobenzene gave smaller enhancements than benzene, as a result of different parameters. Presumably the even smaller enhancement for m-dichlorobenzene would arise for the same reason. The results are probably better interpreted in terms of the KapteinCloss theory of CIDNP. The reaction intermediates are regarded as radical pairs during the bond-breaking step and the observed enhancements are accounted for if it is assumed that Ay varies regularly as C1 substitutes for H on the phenyl radical. This is a reasonable assumption since CI has a much larger a5 spin-orbit coupling parameter than H. A similar quantitative treatment based on eqn. (59) was offered for methane produced via decomposition of diacetyl peroxide in dimethylphthalate, viz. O
II
O
JJ
O
fl
CH3COOCCH 3 ~ 2 CHACO" ~ 2 CH3"+2 CO2 C H 3 • q- solvent
(113)
~ CH4 + solvent.
Again, the intermediates are more properly characterized as radical pairs. During the reaction, a transient emission signal at 6 = 0.79 p.p.m, was observed and attributed to dissolved methane. The coupling was assumed to be purely dipolar Advan. Mol. Relaxation Processes, 4
(.1972) 2 2 9 - 3 5 4
326
J. POTENZA
and quantitative agreement was reported. Lists of the parameters used to calculate enhancements may be found in the original literature 1¢5. The results here can also be interpreted with the Kaptein-Closs theory, assuming only scalar coupling terms in the Hamiltonian. Overall, these relatively simple systems demonstrate the possibility of detecting and determining the properties of short-lived radicals and reaction intermediates. Because their NMR spectra are simple, they should probably be studied in more detail to determine exactly what information can be obtained. A thorough experimental treatment of alkyl radicals was given by Kaptein 59. Methyl, ethyl, propyl, isopropyl and t-butyl radicals were studied at 3500, 14,000 and 23,000 gauss in two reactive solvents: thiophenol and hexachloroacetone. Except for t-butyl, all radicals were generated by thermal decomposition of the appropriate diacyl peroxide (RCOO)2. The following reactions apply. O
O
II
I1
(RCO)2 ~ 2 RCO"
(114)
O II RCO.
(115)
-o R-+CO
O
2
O
R" + RCO. --', RCOR
(116)
2 R. -~ R-R
(117)
2 R. ~ Disproportionation products
(118)
In addition to the above products, the radical intermediates may react with the solvent as follows. In thiophenol, we obtain O
O
RCO-+t~SH -o RCOH+qSS.
(119)
R- +~bSH
--* RH +q~S.
(120)
R- +~bS-
--, ~bSR
(121)
R" +thS-
~ Disproportionation products
(122)
In perchloroacetone, the possibilities are 0
0
II
II
R" + CI3CCCC13 --* R-CI+ CCIaCCC12, Advan. Mol. Relaxation Processes, 4 (1972) 229-354
(123)
327
DYNAMIC NUCLEAR POLARIZATION O
G
II
II
R - + CC13CCC12" ---, CCI3CCCI2R
(124)
o R.+CCIaCCC12" ~ Disproportionation products
(125)
Thus a host of products are possible, and for many, enhanced spectra were observed. For example, the results of thermal diacetyl peroxide decomposition are shown in Table 23. Appended to the chemical shift is the letter A, E or N, depending upon whether the signal was observed in enhanced absorption, in emission, or was normal (unenhanced). TABLE 23 CIDNPRESULTSFROMTHERMALDECOMPOSITIONOF DIACETYL PEROXIDE Reprinted with permission from ref. 59. 6 (p.p.m.)
Assignment
Product o f reaction
Methane Acetic acid CH3 Thioanisole CH3
120 119 121
Ethane 1,1,1,3,3-Pentachloroacetone Methyl acetate (acetate CH3) Methyl acetate (OCH3) Methyl chloride
117 125 116 116 123
From thiophenol
0.13 A 1.84 N 2.24 E In perchloroacetone
0.83 E 1,69 1,96
E N
3.54 E 2.94 A
In thiophenol, three products were observed: methane, acetic acid and thioanisole. Methane, which is formed via the abstraction reaction (120) shows a positive enhancement, while the methyl protons of acetic acid formed from reaction (119) show no enhancement. The results with perchloroacetone may be analyzed similarly. Overall, for methyl radicals involved in these reactions, products from radical coupling reactions show negative enhancements while those from abstraction reactions give positive enhancements. The positive enhancement observed for methane here is exactly the opposite of that reported above ~4s for a different solvent. That the acetate protons of both methyl acetate and acetic acid are unenhanced was attributed to a short radical lifetime for the acetate radical 14~ which would cause polarization to decay in the radical before products formed and would be the determining factor if polarization is effected when the radicals form. Advan. MoL Relaxation Processes, 4 (1972) 229-354
328
J. POTENZA
However, if radical pairs are required for polarization, a modified interpretation will be required. The information contained in these spectra is almost unbelievably detailed. In principle, they contain information for the several product species similar to that presented above for non-reacting samples. Results for the decomposition of dipropionyl peroxide, which gives ethyl radicals as intermediates, are shown in Table 24. The major difference between these results and those for methyl radicals is the appearance of emission and absorption within enhanced multiplets. In thiophenol, only emission or enhanced absorption is observed within a given multiplet, while in perchloroacetone, all enhanced multiplets show simultaneous emission and absorption. For the product butane formed in a radical combination reaction, low field multiplet lines are negative, high field lines positive, while for ethyl chloride formed by C1. abstraction from the solvent the reverse is true. This is in accord with the recent theory developed by Fischer67. TABLE 24 CIDNP
RESULTS FOR
THE
THERMAL
DECOMPOSITION O1~ D I P R O P I O N Y L
PEROXIDE
Reprinted with permission from ref. 59.
Assignment
Product of" reaction
From thiophenol 0.75 E 0.93 triplet N 2.09 quartet N 0.95 triplet N 2.12 quartet N 1.12 triplet A 2.68 quartet E 2.45
Ethane Propionic acid CH3 Propionic acid CH2 DiproDionyl peroxide CH3 DiproDionyl peroxide CH2 Thiophenetole CH3 Thiophenetole CH2 Spinning sideband of solvent SH peak
120 119 119
From perchloroacetone 0.90 triplet E/A 1.30 E/A 1.21 triplet N 2.40 quartet N 1.47 triplet A/E 3.52 quartet A/E
Butane CH a Butane CH2 Dipropionyl peroxide CH3 Dipropionyl peroxide CH2 Ethyl chloride CHa Ethyl chloride CH2
117 117
(p.p.m.)
121 121
123 123
Enhancements for thiophenetole are more difficult to treat. It was suggested that the positive enhancement of the methyl protons might indicate modulation of the scalar field by rotation of the methyl group in the ethyl radical. The methylene protons are not free to rotate with respect to the unpaired electron, and for them a dipolar mechanism might be dominant. However, other interpretations Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
329
based entirely on scalar coupling with radical pairs seem possible. For example, different signs could arise because the signs of the hyperfine coupling constants for the CH2 and CH 3 groups in the ethyl radical are opposite. Systems with propyl, isopropyl and t-butyl radical intermediates gave spectra similar to those above and will not be considered in detail here. However, two points should be mentioned. First, in the decomposition of dibutyl peroxide, no 7 proton enhancements could be observed. This indicates that spin information in alkyl chains is rapidly attenuated, encompassing no more than 2 or 3 carbon atoms. The second point concerns the reaction of t-butyl radicals produced by the following reaction scheme.
In thiophenol, isobutane is formed via reaction (120) and the methyl protons give a negatively enhanced doublet. In perchloroacetone, isobutane is also formed, but this time by disproportionation (reaction (118)). Here, the CI-[3 doublet shows emission at low field and absorption at high field. That the abstraction product in thiophenol shows net enhancement is in accord with the theory of Closs if polarization is produced in a radical pair with A# # 0, such as might occur in the initial bond-breaking step or in a non-reactive encounter between ~bS" and t-Bu.. For isobutane produced by disproportionation, A# ~ 0, and only transverse polarization is expected. Results of this type, when interpreted completely, may lead to a detailed description of individual steps in a reaction sequence. Bargon et al.24 also examined the thermal decomposition of diacyl peroxides. O II They decomposed (CH3(CHz),CO)2, n = 1, 6, 7, 8 and 10 in hexachlorobutadiene. During the course of the reaction, transient emission and enhanced absorption lines were observed in the region 6 = 4-5.5 p.p.m. These lines, which were not present after the reaction was over, were attributed to intermediate unsaturated compounds produced by disproportionation reactions. Reaction (118) gives an n-alkane and a 1-alkene, the latter may give the transient signals, then react further to give branched alkane products whose N~R spectra appear at the end of the reaction. CIDNP, then, may be used to detect and determine the nature of transient diamagnetic intermediates in rapid radical reactions. B. Photochemical appfications - tests o f the Kaptein-Closs theory
As indicated above (eqns. (61) and (62)), DNP can also be produced by optical transitions which lead to radical pair intermediates. The first mention of such optically induced DNP was by Cocivera 14s, who studied anthraquinone. A Advan. MoL Relaxation Processes, 4 (1972) 229-354
330
J. POTENZA
0.005 M solution in C 6 F 6 w a s irradiated at 3000-4000/~ using a 3500 watt mercury lamp. Under these conditions a steady triplet state concentration of anthraquinone is obtained which then reverts to the ground state (eqn. (127)). o
o
(127) o
o
Here, no net reaction is occurring; however, DNP may arise by triplet-singlet crossover according to the mechanisms presented above.
R A f,
li
R
b
I
i
I
I
It
d
Fig. 53 (a) 1H NMR spectrum of 0.005 M anthraquinone in C6F6 prior to irradiation (47 scans with CAW);(b) the same spectrum during irradiation (12 scans); (c) slow passage IH NMR spectrum without irradiation (65 scans); (d) slow passage spectrum during irradiation (16 scans), and (e) slow passage spectrum after 30 min irradiation (65 scans). Reprinted with permission from ref. 148.
The results are shown in Fig. 53. Note that all spectra required several passes with a CAT to be observed because of the low concentration of anthraquinone. Two points should be mentioned. First, all signals in the enhanced spectra are negative; however, all proton enhancements do not have the same magnitude. Second, the emission signals are broader than the normal absorption signals. Presumably the broadening arises from a triplet energy transfer process while the enhancements Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
331
arise from different mixing coefficients for the various nuclear states. The important point is that studies of this sort may prove valuable for investigating the excited states of organic molecules. Photochemically induced DNP has also been employed by Cocivera et al. (refs. 149, 150) to examine photochemical mechanisms, including those proceeding via chain reactions (to be discussed below). In one experiment, benzaldehyde was irradiated with 2000-4000 A light; the resulting 60 M H z proton NMR spectra are shown in Fig. 54. With C 6 D 6 as the solvent (spectra (a), (b)), a positive enhancement (A) for the low-field aldehyde proton was observed in addition to some emission in the ring proton region. A negatively enhanced high-field peak not belonging to benzaldehyde was also observed. Similar experiments with CC14 gave spectra (c) and (d). The spectra are similar to those for C6 D 6 except that the highfield region shows additional peaks.
I
c._~
I
,
I
I
I
#'~_
't "-
Fig. 54. (a) 60 MHz 1H spectrum of ~CHO in C6D6 before irradiation (12 scans); (b) the equivalent spectrum during irradiation (2 scans); (c) 1H spectrum of ~CHO in CC14 before irradiation (3 scans); (d) 1H spectrum of ~CHO in CC14 during irradiation (3 scans), 1H spectrum of benzoin in C6D6; (e) before irradiation; (f) during irradiation, and (g) after irradiation (all 2 scans). Reprinted with permission from ref. 149.
On the basis of this evidence, it was suggested that the reactions proceed via a radical pair mechanism and that the high-field peak in spectrum (b) results from the C - H proton of benzoin, ~bC(O)CH(OH)@. This assumption was tested by photolysing benzoin, which gave spectrum (f), equivalent to spectrum (b). Hence radical pair formation is a reversible process. Overall, the CIDNP results support the following mechanism for the photolysis of benzaldehyde. Advan. MoL Relaxation Processes,
4 (1972) 229-354
332
J. POTENZA
4,CH
•
4, H
E I" oII 4, H
?"1
+4,CH
OOH LII
• 4,CC-~ I
(128)
H 'l
O II > 2 4,CH •
polarized
polarized
O OH
I[ I 4,c-c-4 1
> 4 H
H
""
>2~CH'~
polarized
J
The scheme accounts for polarization of both the aldehyde proton of benzaldehyde and the C - H proton of benzoin. Photochemical reactions proceeding via triplet state intermediates were studied by Closs and co-workers. In one series of experiments 6°, the photo-decomposition of 4,2CN2 was studied in several solvents containing benzylic H atoms. Focused light from a 500 watt super high pressure Hg lamp was used for irradiation and reaction times were approximately 8 min. The reactions are hv
4,2CN2 ~
4,2C:
[
(129)
I1 X
1 4,2C: + ArCH2X ~ III
X X
I
I
4,zCHCHAr + A r C H C H A r + 4,2CHCH4,2 IV
V
VI
where (a) Ar = 4,, X = H (III = toluene) (b) Ar = 3,5-(CH3)2C6H3, X = H (1II = mesitylene) (c) Ar = ~b, X = COOCH3 ( I I I = methyl phenylacetate) (d) Ar = 4,, X = CN (III = benzyl cyanide) A typical spectrum is shown in Fig. 16(a). All systems showed multiplet effects and some had net polarization superimposed, reproducing many of the expectaAdvan. Mol. Relaxation Processes, 4 (1972)229-354
333
DYNAMIC NUCLEAR POLARIZATION
tions noted in the theory section. In particular, the products t~2CHCHt ~
and
I COOCH3 q52CHCH~b, obtained with substituents (c) and (d) respectively, both showed AB
I CN quartets (Fig. 18) with lines 2-1 and 3-1 positively enhanced and lines 4-3 and 4-2 negatively enhanced. Lastly, an interesting comparison between photochemically and thermally induced spectra was offered. Polarized spectra of t~2CHCH2C6H 3(CHa)2, q52CHCHtk and qSCHCH(CN)q5 were obtained both by thermolysis
I
COOCH 3 and photolysis of t~2CN 2 in the appropriate solvent. In all cases the spectra
obtained were identical, indicating that the same processes produce polarization. Several additional systems which do not lend themselves to thermal decomposition were also studied photochemically. Thus, 0.1 M benzophenone was photoreduced T M by toluene and ethylbenzene to give the products shown in eqn. (130). OH q52CO+ RCH2q5
• tkEC-CHth + qSCH-CH~b+ (qSCH)2
I
I
l
OH OH VIII
R
VII
(130)
I R
IX
With toluene (R = H), the methylene protons of VII showed A with an enhancement of approximately 250. The steady state concentration of polarized VII was estimated to be 2 × 10-* M, indicating the sensitivity of detection. With ethylbenzene (R = CH3) , the methyne quartet of ~b2C(OH)CH(q~)CH3 showed A/E and the outermost lines were enhanced the least. Analysis of the central lines of the quartet gave G = 1300_ 200 for the magnitude of polarization. This is the largest proton polarization reported to date. Overall, C1DNP seems well suited for the qualitative detection of radical pairs in photochemical reactions. We turn now to a more detailed examination of the spectra in terms of the Kaptein-Closs theory. A thorough test of the Kaptein-Closs model incorporating variations in both g and A was given by Closs et al. 68. To show that variation of Ag within a radical pair can produce net enhancement, radical coupling products derived from the photochemical reactions of substituted benzophenones with substituted toluenes were studied. p - X C 6 H 4 C H 3 + [O = C(C6H4-p-Y)2]
hv •
OH [p-XC6H4CH2" X
"C(C6H,-p-Y)2] XI
~
(131)
p - X C 6 H 4 C H 2C(C6H4-p-Y)2OI-[ Advan. Mol. Relaxation Processes, 4 (1972) 229-354
334
J. POTENZA
where (a) X = H ,
Y=C1
(b) X = H,
Y=H v=H
(d) X = B r ,
Y=H
For these systems, the methylene protons are equivalent and are coupled to component X. The OH proton is rapidly exchanged68; hence all methylene NMR transitions are equivalent and no enhancement should be observed if Ag = gx -#x~ = 0. This is verified by the mixing coefficients M i for this system, which are shown in Table 25. With Ag = 0, oniy hyperfine mixing terms are present. But since g of a radical depends on the spin-orbit coupling parameter, which increases with atomic TABLE 25 MIXING COEFFICIENTS
Ms
FOR SYSTEMS WITH TWO NUCLEAR SPINS
Reprinted with permission from ref. 68.
Nuclear state
Both spins on component 1 M1
One spin on each component Mj
tiff ~xfl flc~ ~
flHoA,q/2--A~/4-- A2/4 flHoAg/2 + A~/4-- A2/4 flHoAg/2-- Ax/4 + A2/4 flHoAg/2 + A~/4 + A2/4
flHoAO]2-- Ax/4 + A2/4 flHoAg/2 + A x/4 + A2/4 flHoAg/2-- A~/4-- A2/4 flHoAg/2 + A~/4--A2/4
number, we expect Ag to increase from reaction (a) to reaction (d). If the hyperfine coupling constants are such that A~ = A2 and both are negative, methylene spectra from reactions (a) and (b) should show absorption while spectra (c) and (d) should give emission. The observations (Fig. 55) are in excellent agreement with the predictions of the theory.
(a)
(b)
(¢)
I (d)
I
Fig. 55.1H spectra of methylene protons for the products (a)-(d) of eqn. (13 l). S is a 1aC solvent satellite. Reprinted with permission from ref. 68.
Advan. MoL Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
335
A second series of experiments designed to allow theoretical reproduction of spectra showing multiplets was also reported 68. Photoexcited substituted benzaldehydes were reacted with substituted diphenylmethanes according to p - X C o H 4 C H O + CHz (C6H4-p-Y)2 OH [p-XC6H4CH"
"CH(C6H4-p-Y)2 ]
XII
XIII
032)
OH
I ~"p - X C 6 H 4 C H C H ( C 6 H 4 - p - y ) z
where (a) X = B r ,
Y =H
(b) X = C l ,
¥=H
(e) X = H,
Y=H
(d) X = H,
Y =C1
(e) X = H,
Y=Br
Again, Ag = g x u - gxtH is expected to decrease in going from (a) to (e); however, here the protons in the radical pair are not equivalent and AB doublets should be observed (Fig. 56). The mixing coefficients for these systems with one spin on each component of the radical pair are shown in Table 25 where A~ refers to the hyperfine coupling constant of the benzylic proton in p-XC6H4CH(OH)" and A2 to that of (p-Y-C6H4)2CH'. Enhancement magnitudes can now be calculated from the mixing coefficients and eqn. (87) if values for A1, A2, Jee, ~, we and Ag are
Fig. 56. Observed and calculated spectra for the products (a)-(e) of eqn. (132). S is a 1aC satellite. Reprinted with permission from ref. 68. Advan. )Viol. Relaxation Processes, 4 (1972) 229-354
336
J. POTENZA
known. Values for A1 and A 2 were taken from the literature; J~e was assumed to be 108 rad./sec, z 10-9 sec, and it was further assumed that we > 50 w~. With these assumptions, Ag was varied to produce the best fit for the spectra in Fig. 56. As expected, A# decreased in going from reaction (a) to reaction (e), Further, the magnitude of Ag was approximately 10-3-10-4, in accord with what might be expected for radicals of this type. The calculated spectra shown in Fig. 56 agree remarkably well with experiment, demonstrating the validity of the approach. As stated above, reaction products produced from singlet precursors should show multiplet polarization opposite to that produced from triplet radical pair precursors 33, 64. This was demonstrated semiquantitatively for the production of 1,1,2-triphenylethane by singlet and triplet paths. The polarization shown in Fig. 16 can be understood with the aid of Fig. 21, which shows singlet and triplet manifolds for a radical pair containing two protons. If transitions labeled w0 are those of highest probability and if triplet radical pairs are produced first, states 14 and 15 will populate at the expense of 6 and 7. Since only the singlet radical pair can form product, product states with m z near zero will be overpopulated. With a singlet precursor, wo transitions will cause states 6 and 7 in the triplet manifold to populate at the expense of singlet states 14 and 15; thus the singlet radical pair will have nuclear states with mz furthest from zero overpopulated. For the same reaction product, then, singlet and triplet precursors should lead to opposite multiplet enhancements. The above considerations were made more quantitative with the KapteinCloss theory. Spectra of the reactions indicated in eqn. (133) were studied 1°~ and the results are shown in Fig. 57.
[(p-XC6H4)2C: ] + CH 3C6H4-p-Y
(a) X = C l ,
Y=H
(b) X = Y = H (c) X = H , Y = CI
] ]hv > [(p-XC6H4)2 CH" "CH2C6H4-P'Y] [
(p-XC6 H4)2 CHN=NCH2C 6H4-p-Y -1
(d) X = C 1 ,
1v
(l 33)
(p-XC6 H4)2 CHCH2C6 H4-p-Y
Y=H
(e) X = Y = H (f) X = H , Y
=C1
Reactions (a)-(c) differ from (d)-(f) in the multiplicity of the precursor. Mixing coefficients M j were evaluated for the benzylic protons of the product and eqn. (87) was used to reproduce the spectra. Agreement between theory and experiment is good, as shown in Fig. 57. Further, reactions (a)-(c) and (d)-(f) do indeed show opposite polarization as expected. Thus CIDNP may prove useful for determining radical pair spin multiplicities. Adoan. Mol. Relaxation Processes,
4 (1972) 229-354
DYNAMIC
(a)
NUCLEAR
POLARIZATION
337
(b)
'" '-, [l", _# (d)
(e)
Cf)
II
I
Fig. 57. Observed a n d calculated spectra for the products (a)-(f) o f eqn. (133), S is a ~aC solvent satellite. Reprinted with permission f r o m ref. 104.
It is important to note that the treatment here in terms of mixing coefficients does not differ in principle from that involving transition probabilities. These are merely different ways of describing the same physical situation. With Fig. 21, the nucleus-electron states are regarded as fixed and different transition probabilities between the states give rise to enhanced spectra. With the time-dependent theory, different states in one manifold change multiplicity more quickly than other states; this is equivalent to saying that there is a large transition probability between the states. Physically, both theories require that the components of the radical pair diffuse to a point where Aii ~ Jee, at which point singlet and triplet states can interconvert. In sum, the combined hyperfine, isotrooic g shift theory accounts semiquantitatively for all aspects of CIDNV spectra produced from radical coupling reactions. Only scalar coupling is assumed and only ~ and fl protons were considered. Many questions still remain to be answered before a complete theory of CIDNP applicable to all reactions at all field strengths can be said to exist. First, Advan. Mol. Relaxation Processes, 4 (1972) 229-354
338
J. POTENZA
there is the question of scalar vs. dipolar coupling. Closs interpreted his results in terms of scalar coupling, while Kaptein and Oosterhoff 64 used mixed scalar and dipolar coupling to generate expressions for the enhancement of products obtained from alkyl radicals. Protons ~ to the unpaired electrons were assumed to be dipolar coupled, protons fl scalar coupled. Second, there is some question as to how polarization arises in radical transfer reactions. Gerhart and Ostermann 7° assumed that polarization was produced when a free radical collided with a solvent molecule, while both Kaptein 64 and Fischer 6v assumed that polarization is produced as radical pairs form in the primary dissociation step. Nuclear polarization is then transferred to the product of the transfer reaction. Lastly, the field dependence of CIDNP requires elucidation. However, considering the results obtained to date, it seems only a matter of time before a unified theory is developed. C. Chain reactions Bargon and Fischer 14~ examined CIDNP spectra obtained from the addition of phenyl radicals to double bonds. In one experiment, benzoyl peroxide was used as a typical initiator in a solution of methyl methacrylate. Instead of the expected emission line from phenyl radicals, an enhanced absorption signal at 6 = 7.32 p.p.m, was observed. The positive polarization was attributed to phenyl protons of radicals such as O ~bCH2-(~COCH3
I CHa which form when th" reacts with the solvent. Multiplet effects were also observed for the aliphatic protons, indicating that methyl methacrylate is involved in the polarization-producing process. The positive enhancement was assumed to arise from long range coupling of the radical electron with the phenyl protons in analogy with EPR results from similar systems 62 where long range coupling is observed. The scalar field would then be modulated by rotation about C-C single bonds, a possibility which does not exist for ~b" (but which does exist for 4~C(O)O'). To examine chain proton enhancements further, benzoyl peroxide was decomposed in styrene and CBr 4. Reactive CBr 4 was used to terminate the chain quickly in order to avoid complicated spectra. The NMR spectrum of the product ~CHBrCH2CBr 3 showed E/A multiplets for both the ~ and fl protons. By unraveling the details of these spectra, information bearing on the first steps in polymerization reactions may be obtained. Cocivera and Roth 15° applied optically induced DNP tO detect a chain mechanism. Methyl diazotate, XIV, was irradiated in both CC14 and CDC13. The C - H protons of the products XVI and XVII both showed E, as indicated. Advan. Mol. Relaxation Processes, 4 (1972)229-354
DYNAMIC
NUCLEAR
0 0 II k~ I[ N2CHCOCH3 ~ -'- :CHCOCH3 XIV
339
POLARIZATION
CI O CCI4
~" CC13C-COCH3
XV
H
XVI
t
E
C10 coc13 I 1I :" CI2C-C-COCH3 DH,
(134)
E
XVII A large longitudinal polarization might be expected since substituents on the components of the radical pair differ greatly in atomic number. What was not expected was the long time rate of decay of the emission signals. Typically, after irradiation stopped, emission was observed for approximately 3 min. This can be understood if Ta of the product protons showing enhancement is about 70 sec, a time which is much too long. Having ruled out a long T~, it was assumed that products form via a chain process after irradiation ceases. CIDNP, then, may prove to be a sensitive tool for investigating chain processes. D. Reactions involvin9 lithium alkyls - characterization of radical intermediates
Many of the early ODNP investigations by Ward et al. 26'31'152 and by Lepley and Landau 30. ~53- ~s6 involved reactions of lithium alkyls. These were investigated both to study the CIDNP process and to characterize reactive intermediates. Typically, ethyl or butyl lithium was reacted with an alkyl or aryl halide; the reaction between LiR' and RX may be considered to proceed as follows ~52 (R'Li)x R X + R ' L i ~- [R-, R'., XLi] ~ R L i + R ' X
(135)
Coupling and disproportionation products Here electron transfer gives a caged radical pair which can either react to form coupling and disproportionation products or to give exchanged halide and lithium alkyl, q~hese reactions are complicated further in some cases by the addition of various Lewis bases which are required to depolymerize the alkyl lithium. Since the base is presumably in the vicinity of the alkyl lithium, it can enter into the reaction. We shall consider this later. Experimental results from several systems are summarized in Table 26. Not all of the possible products were observed as enhanced spectra, although in some Advan. Mol. Relaxation Processes, 4 (1972) 229-354
340
J. P O T E N Z A
TABLE 26 C I D N P R E S U L T S F O R H A L O G E N - - M E T A L E X C H A N G E REACTIONS
Reaction mixture
NMR spectrum a
Comments
Ref.
26
~(p.p.m.)
Assignment
n-BuLi, n-BuBr diphenylacetylene, diethyl ether
4.8 5.8
Butene (=CH2) Butene (CH)
[E and A[ IobservedJ
n-BuLl, n-BuBr, np-entyne, diethyl ether
4.8 5.8
Butene (~CH2) 8utene (CH)
(A and E ]observed }inverse of [ kabove systemI
t-BuLi, n-BuBr
4.8 5.8
EtLi, EtI, benzene
n-BuLl, sec.-BuI, benzene
Butene (~CHz) Butene (CH) Isobutylene (vinyl)
E and A
1.0--1.6 1.85 3.2
Butane EtI (CH3) Etl (CH2)
E and A A/E A/E
3.2 4.2
CH3CHzCHICH3 (methyne) CHaCHzCHICH3 (methylene)
A/E E/A
152
Etl (CH2)
E/A
152
1.83 4.26 5.1-5.9
CH3CHICIi3 (CH3) CHaCHICH3 (CH) Vinyl
E/A E/A E and A
155
3.17
n-BuI
A/E
155
CH3CHzCH=CH2 (vinyl) Et2NCH=CHz (vinyl)
E/A A/E
153
EtLi, ~1 n-BuLi, 2-iodopropane
n-BuLi, 1-iodobutane, tetramethylene diamine
26
n-BuLi, 1-bromobutane, EtaN
26 E/A 152
a Some multiplets also have a longitudinal effect superimposed. A/E means low-field absorption, high-field emission.
cases all peaks were not characterized completely. These are not included in the Table. The observation of polarized products indicates the presence of radical pairs. In some cases, polarization of the halide initially present was also observed, indicating a reversal of the initial cage formation in eqn. (135). No polarization of lithium compounds was observed, presumably because the lithium alkyl polymer acts as a radical trap. R ' + (RLi)x = R(RLi)x"
(136)
If reaction (136) occurs appreciably, signals from lithium-containing compounds would be too broad to observe. 7Li NMR results might help clarify these observations. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC NUCLEAR POLARIZATION
341
The type of spectrum observed is extremely sensitive to the reaction mixture. An excellent example of this is provided by the first two entries in Table 26. There the systems differ only by an added unsaturated hydrocarbon which was found necessary to observe CIDNP. With diphenyl acetylene, the product butene showed both E and A; with 2-pentyne under the same conditions, the emission and absorption was reversed. According to current theories, this might indicate different radical pair multiplicities for the two systems or different signs for A. The system n-BuLi, 1-bromobutane and triethylamine is interesting because ClDNP is observed in 1-butene and in N,N-diethylvinyl amine. 1-Butene can form by disproportionation of two n-butyl radicals which is not unusual. However, the appearance o f enhanced N,N-diethylvinyl amine shows that the Lewis base is
5 = 2.61(A)
~
CI
b e n z e n e : e t hemrr ( 3 0 : 1 ) 40o/*
+EtLi
CI
(a) XVlll
3k"X-
CI 42*/.
~
2°I°
~M3
7°/°
6=4.45 (A'
/CI~C~CH
6 = 1 . 4 - - 1 . 9 (E)
~
C[
+
2 44~,o
3U3~-
EtLi
CI xviil
.
(b)
+
A
.
- reaction
EtCI
xxii
: LiC
EtLi ~
H+
~, 2 °to
xxIII
--
+
LiCl
.XIX . 4 4 " / *
Fig. 58. (a) Net reaction of l,l-dichloro-2,2-dimethylcyclopropane with ethyl lithium. (b) Reaction scheme for the system in (a). Reprinted with permission from ref. 31. Advan. 34ol. Relaxation Processes,
4 (1972) 229-354
342
J. POTENZA ¢
-~ . . . .
?,. . . . ~
;~
~ . . . . ~. . . . . . . . .
6
-i
" p.p.m.
Fig. 59. (a) IH Nr~ spectrum of ethyl lithium and 1,1-dichloro-2,2-dimethylcyclopropane in benzene; (b) the same system after addition of ether (composite); (c) the spectrum after completion of the reaction. Reprinted with permission from ref. 31. taking part in the reaction, presumably via the scheme ~53 Et2NCH2CH 3 + C 4 H 9 - --o Et2N(~HCH 3 + C4Ha0
(137)
Et2NI2HCH a + C4H9" ~ Et2NCH=CH2 + C4H 10 Detailed analysis of the multiplet structure here might further characterize the radical intermediate. Several reactive lithium alkyl systems have been studied with the aim of characterizing reactive intermediates. In one case, Ward et al. 31 examined the reaction of 1,1-dichloro-2,2-dimethyl cyclopropane, XVIII, with ethyl lithium in benzene-ether. Products of the reaction and yields are shown in Fig. 58(a). Proton YMR spectra taken before, during and after completion of the reaction are shown in Fig. 59. Dynamic polarization was observed for several protons as indicated in Fig. 58(a). The C H 3 protons of X I X showed E only, while the vinyl protons of the same product showed A. The only other clearly assignable portion of the spectrum was that for the proton e to C1 in XX, which showed a doublet of doublets positively enhanced at 6 = 2.61. S o m e of the intermediate absorption and emission in the region 6 = 0.25-0.6 was attributed to the remaining protons of XX, but additional transient lines were found in that region by comparison with pure XX. Lastly, it was noted that the methyl protons of X I X could not account for all emission in the region 6 = 1.4-1.9. The reaction sequence shown in Fig. 58(b) was advanced to account for these observations. As above, the reactants combine to form a caged radical pair in which polarization can occur. Disproportionation gives ethylene and XX, radical coupling gives XXI, while further electron transfer may result in lithium-halogen exchange to produce XXII, which can react further to produce XIX. Since X X I I is diamagnetic and is the product of a radical pair precursor, it may show CIDNI'. This may account for some of the unassigned peaks in the region 6 = 0.17-0.83. Advan. Mol. Relaxation
Processes,
4 (1972) 229-354
DYNAMIC
NUCLEAR
343
POLARIZATION
From the CIDNP data, we might expect to obtain some idea of the lifetime of the intermediate XX[I. Since polarization is observed in XIX, XXI[ should not live longer than the relaxation time of the protons in XIX if polarization is produced in the initial radical pair. However, polarization may also arise in the carbene XXllI and this would nullify the above argument. A second example of the use of CINDP to characterize reaction intermediates was given by Lepley 3°' 156. n-Butyl lithium was reacted with fluorobenzene and N,N-dimethyl benzylamine to give N-methyl-N(c¢-phenethyl)aniline as the major product (eqn. (138)). The Lewis base N,N,N',N'-tetramethyl ethylenediamine (TMEDA) was used as a catalyst and E/A was observed in the a-proton multiplet of XXIV.
(138)
n-BuLi +~bF+ (CH a)2NCH2~b 6 = 5.02(E/A) I
). C H 3 ]
hexane TMEDA
qSN-CHq5
I CH3 XXIV No other enhancements were reported; however, some spectral regions were obscured by solvent absorption. The reaction was assumed to follow the sequence outlined in Fig. 60. Butyl lithium reacts with q~F to produce benzyne which reacts further with (CH 3)2NCH2~b to produce the a ylide. The ylide rearranges via a radical path to give the product XXV. ÷1
I :
~ ylide
L~
CH3
t /,
I
+ :N--CH2
F"
~
F
~
+ n-C4HgL~ H
Fig. 60. Scheme for the reaction o f n-BuLi, fluorobenzene and N,N-dimethyl benzylamine. Reprinted with permission from ref. 30. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
344
J. P O T E N Z A
T A B L E 27 CIDNP RESULTS FOR n-BuLi-ARYNE-tert.-AM~NE REACTION PRODUCTS
Reprinted with permission from ref. 156. NR1R2 R a
Product chemical shifts 6 (p.p.m.)
Rl
R2
R3
~X
~bCH2
Me
Me
F, CI, P-Fz
5.02(quartet)E/A
ffCH2 ~6CH2 Me
F, CI
5.12(triplet)E/A;3.16(doublet)E/A
tfiCH2 Et
t~CH2 Et
Et Et
F F
4.95 (triplet)E/A; 4.44(singlet)N, 3.16(doublet)E/A 5.23 (singlet) N
n-Bu
n-Bu
n-Bu
F
5.78 N a, 4.82 N ~
a Vinyl p r o t o n s in 1-butene.
Additional evidence for caged radical pair precursors to products of the type described above is given in Table 27. Here eqn. (138) is followed but with different amines and halobenzenes. T M E D A was used as the catalyst and hexane as the solvent. The most interesting observation is that when two benzyl groups are present on the reacting amine, CIDNP is observed for more than one proton. With dibenzyl methyl amine, the triplet at 6 = 5.12 p.p.m, is assigned to the ~ proton of the product XXV[ while the doublet at 6 = 3.16 is assigned to the methylene protons of the migrating benzyl group. No polarization was reported for ~t5
= 5.12
l
q~N-CH~b CH2~b l XXVI
3 = 3.16
the methyl group. A similar effect was observed with dibenzyl ethyl amine. The observation of polarization in the migrating group was taken as further evidence for a caged radical pair intermediate. The possibility of a triplet carbenoid intermediate was eliminated since this might not be expected to produce Clr~NP at the fl protons. However, this interpretation might not be correct. If it is correct, it should be possible to use the Kaptein-Closs theory to determine the multiplicity of the radical pair and decide whether the reaction takes place by exciting the ylide to a triplet state or by homolytic bond cleavage. Advan. Mol. Relaxation Processes, 4 ( 1 9 7 2 ) 2 2 9 - 3 5 4
DYNAMIC
NUCLEAR
345
POLARIZATION
E. Radical pair intermediates in rearran#ement reactions
In several instances, CIDNP has been used routinely to test for the presence of radical pair intermediates in rearrangement reactions. An example was provided by Baldwin and Brown 32 who studied the thermal isomerization of XXVII. B,5 ~2.5-3.0__
/
[
~N/
(El?) ~ " " ~ ' i
A.5 =2.5-3.0
-~ ~"
(E/A) 140--170°C
xxvl[
"x x v.1
high yield
(139)
5%
Product XXIX was obtained in high yield along with 5 % of the dimer XXX. Proton NMR spectra at fi = 2.5-3.0 showed enhancements for both pairs of CH2 protons in XXIX. The low-field CH2 protons (labeled A in eqn. (139)) showed E/A; only one line of the CH2 fl protons could be observed and this showed E. These observations were taken as evidence for the intermediate XXVIII. No polarization of C methyl, N methyl or aryl protons was observed; only those protons nearest the migrating groups became polarized appreciably. Schollkopf et al. 1SAlSa studied lone pair rearrangements of sulfur and nitrogen ylides. With sulfur, the sulfonium ylide XXXI was decomposed thermally to give > 80 ~o of XXX[II as shown in eqn. (140). Small yields of XXXIV and XXXV were also reported.
o
[
H3C-S-C-HCq~
"
o
H3CS.--.C.-HCq5 ~ H3CS-CHCq5
I CH2q5
-CH2~b
XXXI
.CH20 _l
(140)
XXXIi
A--~ 0
0
II
II
•• H3CSCHC~b
I
+
CH2~b
~----A
H3CSCHC0
+ (~CH2):
I H3CSCHC~b
kl
t-E
o
XXXIII
XXXIV
XXXV
Advan. Mol. Relaxation Processes, 4 (1972) 229-354
346
J. POTENZA
_
_
.
_
_
_
CH2-
CH2-. ~
Fig. 61. CIDNV spectrum for the reaction shown in eqn. (140). Reprinted with permission from ref. 157.
The proton NMR spectrum, shown in Fig. 61 and obtained during the reaction, shows the methyne proton in XXXII[ positively enhanced, the methylene protons of XXXIII negatively enhanced and the CH2 protons of XXXV positively enhanced. This is further evidence for the intermediate XXXI[. Perhaps the most interesting observation here is the enhancement of dibenzyl, which must escape the solvent cage. A similar treatment of the ammonium ylide XXXVI showed emission and absorption peaks for the methylene protons of XXXVIII (eqn. (141)). This was taken as evidence for the radical pair intermediate XXXVII in contrast to a previously proposed ion-pair intermediate. ~bCH2
O
CHa-N+-(ZHC~b
I
CH 3
~
"CH2~
> CHa
~CH2"
]
C~b ~ CH3- -(~H O
CH 3
XXXVI
CH.~ O
XXXV[I
q~CHz x
E and A
(141)
CH3-N-CHC~ CH30 XXXVHI Last, Lepley et al.159 studied the Meisenheimer rearrangement of a tertiary amine oxide. The oxide XXXIX was decomposed thermally to form primarily XLII. Some reduction occurred and N,N-dimethyl benzylamine was also found. As indicated in eqn. (142), proton emission peaks were observed both from the methyl and methylene protons of the product XLII, indicating the existence of XL and XLI. Note that here emission occurs for protons both ~ and fl to the migrating site. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC
NUCLEAR +
347
POLARIZATION
A
~CH2N(CH3)2----~
!
OXXXIX
"N(CH32] :o':- J XL
(142)
6 = 4.6(E) ~---6 = 2.5(E)
[
~bCH2" :N(CH3)2 ~
o
:~ q~CH2ON(CH3) 2
J
XLI
XLII
Overall, it seems that CIDNP is well suited for the detection of radical pair intermediates in intramolecular rearrangements of this sort. Detailed analysis of these spectra in terms of the theories above should yield additional information. F. Nuclei other than protons
Several CIDNP experiments involving 19F nuclei have been reported. The first mention was by Bargon and Fischer 14s who thermally decomposed benzoyl peroxide in three fluorine-containing solvents: p-fluorobenzaldehyde, p-fluorostyrene and p-fluoronitrobenzene. During the reactions, 40 MHz 19 F NMR spectra were recorded. With the first two solvents, strong absorption signals were recorded and attributed to products of the radicals F-C6H4C(O) • and F-C6H4(~HCHz~b; the former is produced in a radical transfer reaction, the latter in an addition reaction with qS.. In both cases, the polarization is long range, extending over at least four atoms from the nominal location of the unpaired electron. This suggests the possible use of 19F as a spin probe for aromatic radicals and radical pairs in much the same way that a 9F is used with non-reacting systems. Last, we note that fluorine polarization cannot be produced in the original radical (q~.) and transferred suddenly 67 to F-C6H4C(O)'; however, polarization in both systems can be understood in terms of the radical pair theory. Polarization was also observed with p-ftuoronitrobenzene and this polarization is more difficult to understand since it is not known for p-fluoronitrobenzene to react with pheny| radicals. If the product here is biphenyl and p-FC6H4NO 2 does not enter the reaction but only forms the solvent cage, this would provide the first example of solvent polarization, an effect not predicted by any theory to date. On the other hand ifp-FC6H4NO2 is involved in the reaction, nothing new is added. Obviously, additional data, including accurate product analyses, are necessary to understand this system completely. A second example of a9F CIDNP was given by Rakshys 16° who studied the reaction ofp-fluorobenzyl chloride with n-butyl lithium. Advan. Mol. Relaxation Processes, 4 (1972) 229-354
348
J. P O T E N Z A
p-FC6H4CH2CI+n-BuLi EtOEt).(p-FC6HaCH2)z
(143)
XLII [ +p-FC6H4(CH2)4CH3 XLIV The reaction was catalyzed with diethyl ether and the major products were XLIII and XLIV. Fluorine signals from both products showed enhanced multiplets; that from XLIV had net negative polarization superimposed, as might be expected from the theory above. However, the 19F NMR of XLIII showed an effect not previously noticed with proton spectra (Fig. 62(a)). Here, the sign of polarization changes at least five times within the multiplet, in contrast to proton spectra where only one change from A to E or vice versa was observed. This complex
I
30 Ht
I
a (a-l) -1 2 a - l a * l l O ( a , 1 )
2al
(a-l)
Fig. 62. (a) ClDNPspectrum of bis(p-fluoro) dibenzyl. (b) Predicted relative intensities for the multiplet components in (a). Reprinted with permission from ref. 160. behavior may be understood by considering one p-fluorophenyl component of the radical pair as an AzB2X spin system where X is fluorine. We would therefore expect the fluorine NMR spectrum to approximate a triplet of triplets, the first triplet arising from F coupling with the m-protons of the ring (A2); this triplet is then split into three by the o-protons (B2). The observed nine-line spectrum was reproduced qualitatively (Fig. 62(b)) using the Kaptein-Closs theory assuming that the hyperfine coupling constant for the ortho protons (Ao) with the electrons of the radical pair is greater than that for the meta protons (Am) and opposite in sign. For many aromatic radicals, including benzyl ~61, spin densities at the ortho and meta positions are found to be opposite in sign. Thus, if the first triplet gives Advan. Mol. Relaxation Processes, 4 (1972) 229-354
349
DYNAMIC NUCLEAR POLARIZATION
E/A corresponding to A,~, the second will give A/E of different magnitude corresponding to Ao, and the general features of the spectrum will be reproduced. An interesting 19F CIDNP experiment was performed by Trozzolo et al. 162 who thermally decomposed fluorine-substituted benzoyl peroxides. rn, p -
C
2
A
b
2 o,m,p-
"
~4 .
2
F
(144)
The product fluorobenzene is formed from three different radical intermediates, each with fluorine at a different ring position. All systems exhibited proton polarization but only the meta-substituted fluorine precursor led to fluorine polarization These results again suggest the possible use of F as a probe for spin transmission effects in aromatic systems. To date, no detailed experimental work has been reported for nuclei other than H or F. However, Kaptein and Oosterhoff 163 have mentioned observing ~3C NMR enhancements during the thermal decomposition of enriched acetyl peroxide. Judging from the signal-to-noise ratio of previously reported spectra, it would seem possible to detect ~3C in natural abundance if l 3C enhancements are larger in magnitude than those of protons. Nuclei such as 31p and 7Li should also be observable. G. Gas Phase CIDNP?
The possibility for observing C1DNPduring gas phase radical reactions should depend on the radical pair lifetime. This is seen most easily from eqns. (85) and (87). If ~ is sufficiently small, the individual w/s, which govern the rate of product formation with nuclear spin state j, should become small and nearly equal. Thus, the enhancement factor Gjk which depends on differences in w, will be small regardless of the magnitude of the mixing coefficients Mj. Kaptein and Oosterhoff 64 used this argument to predict a negligible multiplet effect in the gas phase.
APPENDIX
Since this review was written, there have been major advances both in CIDNP and DNP. With CIDNP, the radical pair theory has become fully established (refs. 164-167) and has been reviewed 16s'169. Multiplet intensities have been considered ~7° and a graphic method for multiplet spectra analysis was given by Miiller TM. A theory of CIDNP equivalent in many ways to that of Closs, Kaptein and Oosterhoff was developed by Adrian 172-174. This theory assumes that encounters between radicals in a radical pair take place via diffusive steps with correlation times of the order of I0-11 sec. A number of these steps in succession then gives the total encounter. Several articles have appeared t65' 175.176 treating Advan. MoL Relaxation Processes, 4 (1972) 229-354
350
J. POTENZA
the anomalous EPR spectra of transient radicals in terms of radical pairs. Theories to account for low field polarization via T~. t - S mixing were proposed and tested (refs. 177-179). Two simple rules 18o for predicting the sign of net enhancement and the phase of multiplet spectra were advanced by Kaptein. These depend on the signs of A, A#, Jis, and whether the polarized product is formed from a singlet or triplet precursor and whether or not the product forms from cage collapse. Kaptein's rules are especially suited for applications of ClDNP. Enhanced 13C and ~5N NMR spectra have also been reported t81' 182 and these may be used to supplement ~H data. Lastly, a number of investigators have reported applications of Clt)NP, some of which are mentioned here 183-195. For DNP, Richards and co-workers have developed a theory 196 relating NMR enhancements to AE, the average electronic excitation energy of the receptor molecule and r, the polarity of the bond containing the receptor nucleus. The theory w a s u s e d 196'197 to interpret high field 3 1 p and ~3C DNP data. Solvation and hydrogen bonding was examined ~9s at five fields and various temperatures using 1H t~NP. With 19F, extrapolated enhancements for substituted fluorobenzenes were related ~99 to the chemical shift, to 7r-n* absorption frequencies and to Hammett's a constant, while another study 2°° gave values for intermolecular hyperfine coupling constants and correlation times. In addition, the effect of radical structure upon low field enhancement was examined TM. The pulse model was applied 2°2 to tri- and pentavalent phosphorus using multifield measurements. With 13C, in addition to a high field s u r v e y ~97, multifield results for benzene and methyl iodide were reported 2°3. Lastly, 7Li salts in solution were examined 204 at low field to study complexation and aggregation.
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Advan. Mol. Relaxation Processes, 4 (1972) 229-354
DYNAMIC 110 Ill 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 15l 152 153 154 155 156
NUCLEAR
POLARIZATION
353
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