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NMR relaxation studies and internal molecular rotation in liquid nitromethane
J O U R N A L OF M A G N E T I C R E S O N A N C E 33, 389-399 (1979)
NMR Relaxation Studies and Internal Molecular Rotation in Liquid Nitromethane* W.
SUCHANSKIt
AND
P.
C.
CANEPA
Department of Physics, University of Florida, Gainesville, Florida 32611 Received April 29, 1978 Studies of the deuteron and proton relaxation rates of liquid nitromethane were made at various temperatures. The separation of the proton-proton intermolecular relaxation was accomplished by a dilution study in nitromethane-d3. It was found that the spin-rotation interaction contributed significantly to the intramolecular relaxation. The spin-rotation interaction contribution is discussed in terms of different models for the spin-internal and spin-overall rotation coupling. The resulting spin-rotation relaxation times offer evidence for large spin-rotation effects due to the internal rotation of the methyl group.
INTRODUCTION
In connection with our studies (1, 2) in determining the contributions of the spin-rotation interaction to the relaxation mechanism of protons in methyl groups with a low barrier to internal rotation we have investigated the relaxation of nitromethane. From microwave studies (3) of nitromethane, in which the potential barrier to CH3 group rotation is sixfold, we know that the barrier value is 6.03 cal/mole. In this work we measured the temperature dependence of the proton and deuteron relaxation times in nitromethane and nitromethane-d3. Previous workers have measured room temperature relaxation times for H (4, 5) and the temperature dependence of the self-diffusion coefficient Ds (5, 6). For protons various competing mechanisms may contribute to the net relaxation. The most important of these are the inter- and intramolecular dipole-dipole, and the spin-rotation interaction, whose characteristic relaxation times will be denoted respectively as (T1)d, inter, (T1)d, intra, (T1)sr. If one is to make use of the data from relaxation time studies the contributions of each of the above mechanisms must be separated. The separation of intermolecular and intramolecular contributions to proton relaxation has been carried out by measuring T1 of the methyl protons in nitromethane at different isotopic concentrations in nitromethane-d3. The separation of ( T 1 ) d , intr a from (T1)sr is more complicated since the protons are localized in an internal rotator, able to perform internal rotation in addition to reorientation with the molecule as a whole. * Research supported in part by National Science Foundation Grant DMR 77-08658. t Visiting scientist from the Institute of Physics, A. Mickiewicz University, Poznan, Poland. 389
0022-2364/79/020389-11$02.00/0 Copyright © 1979 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain
390
SUCHANSKI AND CANEPA
The theoretical interpretation dealing with the question of overall and internal rotation in nitromethane is based on the work of Woessner and Snowden (7), Hubbard's work (8) on the spin-rotation interactions and work by Burke and Chen (9) for the spin-rotation interactions in molecules with internal motion are used to explain the temperature behavior of T1 due to the methyl protons. EXPERIMENTAL
Nitromethane was obtained from E. D. Merck, and sealed under vacuum in a Pyrex tube after degassing by the freeze-pump-thaw technique. For these measurements, the liquids under investigation were in tubes of a similar design to that used by Tison and Hunt (10). The liquid region was approximately 5 mm long and was situated in the center of the 12 mm rf coil of a NMR probe. With the liquid in the capillary section extending above the top of the coil, this arrangement minimized the problem associated with vapor to liquid exchange (11). Measurements of 1H spin-lattice relaxation times were performed in the Institute of Physics, A. Mickiewicz University of Poznan, using a 25 MHz c-w high resolution NMR spectrometer by applying a null-method developed in this laboratory (12) over a temperature range extending from approximately 230 K up to about 400 K. The temperature of the sample was controlled by a gas-flow cryostat and monitored with a thermocouple to an accuracy of about 1 K. Measurements of the deuteron relaxation times were made at the University of Florida using pulse NMR apparatus employing repeated 180°-90 ° pulse sequences, at a frequency of 6.5 MHz. The sample was contained in a copper cell in a temperature-control cryostat, which provided temperature stability of better than 0.1 K and an absolute accuracy of 0.5K. RESULTS AND DISCUSSION
1. General Approach For most spin ½nuclei the relaxation rate R1 -= (T1)-1 is determined by a combination of mechanisms: (R1)exp = (gl)d, inter "[- ( e 1)d,intra "b (R1)sr.
[1]
In Fig. 1 the logarithm of proton, deuteron and nitrogen-14 spin-lattice relaxation times are plotted versus the reciprocal temperature. The proton relaxation data indicate that all three mechanisms contribute to the proton relaxation time. The standard type of analysis on the dilution data, CH3NO2 in CD3NO2 allows us to eliminate (R1)d, inter from Eq. [1]. But to eliminate (R1)d,intra from (R1)sr is not so easy. Various activation energies and values of correlation times resulting from deuteron and nitrogen-14 spin-lattice relaxation times clearly indicate that the methyl group is able to perform internal rotation in addition to reorientation with the molecule as a whole. Therefore the internal and overall rotational diffusion coefficient must first be determined in order to separate the intramolecular dipolar contribution from the spin-rotation contribution.
RELAXATION IN LIQUID NITROMETHANE 30
i
I
I
391 300
I
20
200
"
"
"-"
E
~s
50 "2 3
30
2-
20
I
2.5
3.0
3.5
4.0
4.5
I0
IO00/T (*K "1) FIG. 1. The experimental temperature dependence of the 1H, 2D and 14Nspin-lattice relaxation times in nitromethane. Hydrogen relaxation: C), pure CH3NO2; A 36% CH3NO2 in CD3NO2. Deuteron relaxation; U], Ea = 1.4 kcal/mole. Nitrogen-14 relaxation; O, Ea = 1.9 kcal/mole (after Moniz and Gutowski).
2. Nitrogen-14 and Deuterium Relaxation Since the quadrupole relaxation mechanism is usually several orders of magnitude more efficient than other competing mechanisms, m e a s u r e m e n t s of relaxation times of quadrupolar nuclei have extensively been used to obtain details of molecular reorientation in liquids. For nuclei with spin I = 1, such as nitrogen-14 and deuterium, the relaxation rate due to quadrupolar interactions is given by the expression (•3): (Ra)o = 3(1 + ½r/z)\2rr(
ro
[2]
where rt is the asymmetry parameter, (eZQq/h) the nuclear quadrupole coupling constant, and To is the reorientational correlation time. Figure 1 shows the t e m p e r a ture dependence of 14N and 2D relaxation for CH3NO2 and CD3NO2 respectively. Using Eq. [2], together with an experimentally obtained (14) 7"1value of 22 ms at 25°C, a quadrupole coupling constant (15) of 1.695 M H z and asymmetry p a r a m e t e r rt = 0.424 (15), a correlation time of 1.03 x 10 -12 s are obtained for CH3NOz. Nitromethane has an electric dipole moment. Consequently, nitromethane exhibits dielectric dispersion, and dielectric relaxation times can be obtained. But the relaxation time associated with the macroscopic polarization measured by dielectric relaxation is somewhat different than the microscopic molecular correlation time. Taking into consideration this fact Powles (16) has shown that: M "rdiel
(3Co) 2Co q- Coo 7"diel
[3]
392
SUCHANSKI AND CANEPA
where e0 and coo are the dielectric constant at zero and infinite frequency respectively, ~'die, M is the macroscopic correlation time, and "/'diel is the microscopic correlation time. Dielectric relaxation times were recently reported (17) for nitromethane. Using this data we obtained a microscopic dielectric correlation time at 25°C of 2.7 x 10-12s, which is approximately 2.7 times the nuclear correlation time. If the reorientation occurs by a rotational diffusion mechanism, the ratio of dielectric correlation time to nuclear correlation time is predicted to be three (18). From this it appears that the overall reorientation in nitromethane, to a first approximation, can be described by a rotational diffusion process. The electric dipole moment in nitromethane is directed along the symmetry axis of the molecule, so that the dielectric relaxation time is dependent only on the rotational diffusion constant about an axis perpendicular to the symmetry axis. Then the dielectric relaxation times give us D . because in the diffusion limit: D . = (2rdie,) -1.
[43
The experimentally determined 14N correlation time is more connected with the overall rotation diffusion constant Do because the large value of the asymmetry parameter does not permit us to assume that the electric field gradient is axially symmetric and parallel to the symmetry axis of the molecule. Thus for 14N correlation time we get: Do = (6~'u)-'.
[S]
It seems that the close correlation between D± and Do determined by dielectric and a4N relaxations, as it follows from Fig. 2 allows us to assume that the overall reorientation in nitromethane is isotropic. Additional support for this assumption is the fact that activation energies following from dielectric and 14N relaxations have the same value. Hence, comparison of the dielectric relaxation time and the experimentally determined ~4N correlation time as well as the apparent activation energies suggests that a rotation diffusion mechanism and the assumption D . - DIL = Do are reasonably consistent with the experimental data. Now making use of Do along with the 2D relaxation times (Fig. 1) and following the procedure of Woessner and Snowden (7), we are able to calculate the internal rotational diffusion constant D/taking the quadrupole coupling constant as 164 kHz (5) for the methyl deuterium in nitromethane and neglecting the asymmetry parameter. Woessner and Snowden (7) give the following expression for the effective correlation time: re~ = ¼(3 cos 2 0-1)Z(6D0)-a + 3 sin 2 0 cos 20(Oi + 5D0)-1 + ] sin 20(4Di + 2D0) -1
[6] where 0 is the constant angle between the relaxation vector and the symmetry axis. We find Ea (D0 to be 0.92 + 0.2 kcal/mole, and we find that internal reorientation is about 6 times faster than overall reorientation at 25°C. The derived values of Di yield reorientational correlation times rl = (69/) -1 that can be compared with the classical free rotor reorientational time zo = ](I, J k T ) 1/2 in
RELAXATION IN LIQUID NITROMETHANE I
I
I
I
~t=.
393
I
CD3NO z
lOle
~10" P~~' '~ Iz Om~
O° I
I
I
I
I
2.5
3.0
3.5
4.0
4.5
IO00/T
(K - I )
FIG. 2. The temperature dependences of the rotational diffusion constants for nitrometbane found from analysis of the deuteron and nitrogen-14 relaxation data. The dielectric results are labelled ©.
the so-called X test (19). Thus: "ri
5
(k_T~1/2
xi . . . .
rfi
18Di
[73
and X >> 1 for the rotational diffusion to apply. One calculates that Xi changes from 2.8 at low temperatures to 1.6 at the upper limit of the measured t e m p e r a t u r e range in CD3NOz. The values of )t'i indicates that in the measured t e m p e r a t u r e range one could expect strong inertial effects in the internal rotation of the CD3 group.
3. Proton Relaxation A. Proton Intermolecular Dipole-Dipole Interaction If we assumed that the relaxation of a spin is due to the uncorrelated motion of all its intermolecular spin pairs, only relative translation motion changes the intermolecular dipole vector, the molecules are spherical and have a single distance of closest approach independent of relative orientation, then we get the following theoretical expression for (R1)d, inter: (R1)d,i.t~= ~rrh 1 ZNa -3 yH['yHrlH+~.~,'y[nfIf(If+ z z 8 2 1)]" rt
[8]
where yri is the gyromagnetic ratio of the proton, Yt is the gyromagnetic ratio of the nonresonant nuclei, nil, n~ is the n u m b e r of protons or f nuclei per molecule, r, is the
394
SUCHANSKI AND CANEPA
translation correlation time, N is the number of molecules per unit volume, and a is the effective radius of the molecule• The temperature dependent proton relaxation times are shown in Fig. 1 for pure CH3NO2 and for a mixture containing 36 mole % CH3NO2 in CD3NO2. For this mixture the intermolecular relaxation rate is: H H-H H-D H-N ( R 1) d,inter = (R1)d, lnter+ ( e 1) d, inter -1"-( e 1) d,inter
[9]
Since 7 2 = 4 2 . 5 y ~ and the spin values are different, the deuterium in CD3NO2 will • 1 contribute only 5 as much to the intermolecular relaxation as do the hydrogens, and because YN/YH 2 2 = 5.3 X 10 -3 the effect of the nitrogen nucleus may be ignored. The total proton relaxation rate is then: (R1)exp = [(23C + 1)/24](R 1)H-H d,inter q- (R 1)d, intra "~- (R 1)sr
[lo]
where C is the mole fraction of the protonated nitromethane. Thus plotting (R1)exp vs 2 3 C / 2 4 gave a slope of (R 1)U,inter. Values of (R1)a,l,ter calculated by this method at regular intervals of 1 0 0 0 / T using smoothed proton relaxation data, are shown in Fig. 3. The data shows Arrhenius behavior with an activation energy of 3.0 kcal/mole. We express the translation correlation time as: 121ra2~7 rt
I
lO-I
1
[11]
kT
I
-
// I
I
,4,/"
1O- !
¢(/ F'a= 3 . 0 Kc01/m0hl
I
i
i
I
L
2•5
3,0
3.5
4.0
4.5
I O 0 0 / T (K -j) FIG. 3. The temperature dependences of the proton inter (O) and intramolecular (A) relaxation rates obtained from the proton data for 100% CH3NO2 and 36% CH3NOa-64% CD3NO2 samples, Included is the theoretical plot for (T1)dJ.ter - - -
R E L A X A T I O N IN L I Q U I D N I T R O M E T H A N E
395
TABLE 1 GEOMETRIC PARAMETERS AND MOMENTS OF INERTIA FOR NITROMETHANE a rc-H (10 -8 cm) rc-N (10 -8 cm) r~_o (10-8'cm) rH-H (10 -8 cm) rH-N (10 -8 cm) < H-C-N
1.088 b 1.4896 1.224 b 1.800 2.087 107.2 ° b 125.3 °b 62.9 b 79.6 b 124.8 b 5.5
a Those not given in the reference were derived. b p. A. Cox and S. Waring, J. Chem. Soc. Trans. 11, 68, 1060, (1972).
Then
Eq. [8] looks
Faraday
as follows:
6 zr2h2r~in×[nHON0]
(el)d,inter
5
kT
[12]
M
where p and M are, respectively, the density and the molecular weight of the liquid. For nitromethane, the densities and viscosities were obtained from Ref. (20). The temperature dependence thus obtained is shown in Fig. 3. From Eq. [12] a theoretical activation energy of 2.9 kcal/mole can be calculated. Therefore, in this case, the intermolecular theory yields close agreement to experiment, perhaps fortuitous in view of the questionable assumptions used in its derivation. B. Proton Intramolecular Dipole-Dipole Interaction
Separation of (R1)d, intra from (Rx)sr c a n be accomplished using a theoretical equation for (R1)d, intra:
(R1)d,intra=~h '~H--(~ 3242
Z
n
i>i
6 r~ Ire(H-H)
[13]
/
where re(H-H) is the effective correlation time for reorientation of the proton intermolecular vector and can be calculated using Eq. [6] with 0 = 90 °. Using internuclear distance given in Table 1 we obtained: ( R 1)d, intra = 5 . 0 0 X
101°re(H-H)
[14]
The values of Di appropriate to CD3NOz (Fig. 2) have been corrected for the ( e l ) d , intra calculation on the CH3NO2 case. The correction to Di in moving from CD3NOz to CH3NO2 was made by noting that in the inertial limit Di - (i~)1/2 (21). The resulting (R1)d.intra is shown in Fig. 4.
396
SUCHANSKI AND CANEPA I00
~
,~
I
I
I
3.5
4.0
4.5
50
20
I0
I
2.5
3.0
IO00/T (K -I) FIG. 4. The total proton intramolecularrelaxation time (A) of nitromethane and its separation into its intramolecular dipole-dipole (Eo = 1.55 kcal/mole) and spin-rotation relaxation times (O, Eo = -0' 94 kcal/mole).
C. Proton Spin-Rotation Interaction Then it is possible to calculate (R 1)st by subtracting (R 1)a,i,tra from experimentally determined (R1)intra. These are also given in Fig. 4. This provided a basis for our attempt to interpret the temperature dependence of the proton Tt data for the methyl group in nitromethane. As a first step we assumed that the spin-rotation contribution results from end-over-end reorientation. The overall spin-rotation contribution to T~ for a spherical molecule has been derived by Hubbard [8]:
8¢rkT 2 (Rt)sr = - - ~ I a v ( 2 C ± + CI~ )~-j
[15]
where Iav is the average moment of inertia of the molecule, C± and CII are diagonal components of the spin-rotation interaction tensor, and rj is the angular velocity correlation time. cj is related to ro in the diffusion limit by the relation: I
rI.ZO=6k T
[16]
Thus, one can use Eqs. [15, 16] to evaluate C 2en = (2C 2 + C~)/3 to obtain the spin-rotation interaction constant C ~ from relaxation. Using an approach introduced by Smith and Powles (22), at the maximum of the plot of In (R1)intra vs l/T, l ( R 1 ) i n t r a = (gl)d,intra = (R1)sr. For nitromethane (Rt)intra = 0.05 S-1 at 0.00315 K -1, the average moment of inertia I~v = 9 5 . 1 0 -40 g. cm 2, one calculation Cee~= 8.8 kHz for protons. The experimental value of C~erfor the nitromethane is not known. From the chemical shift data by using the average moment of inertia in the relevant expression (see Ref. (23)), (C~) 1/2= 1.47 kHz can be calculated. In spite of the fact that large differences in magnitude between the spin-rotation constant obtained from relaxation data and chemical shielding data have previously been observed (23, 24) we think that the value C~fe= 8,8 kHz for protons in nitromethane is rather
RELAXATION IN LIQUID NITROMETHANE
397
unrealistic. This fact and both the deuterium and nitrogen-14 relaxation measurement together with experimentally determined (3) very low barrier to internal rotation for the CH3 group in nitromethane suggest that spin-internal rotation coupling plays an important role in the spin-rotation interaction. Burke and Chan (9) have shown that the spin-rotational contribution for a nucleus located on an internal rotator in the so-called uncorrelated model is given by the following expression:
8rc2kT
(R1)sr-- ~
2 8~'2kTI~C~ IoCoTJ + (1--I"~ ~'~ \ I,J 3h 2
[17]
where I0 is the overall moment of inertia,/~ a n d / ~ one of the moments of inertia of the top and whole molecule about the symmetry axis, Co and Ca are the overall and spin-internal rotation coupling constants. The first term in Eq. [17] corresponds to the contributions from the spin-overall rotations with the correlation time rj defined by Eq. [16] and second terms represent the contribution of the spin-internal rotation coupling with the correlation time ri. The ~'i was assumed to be a correlation time for a free rotation (9): [ ~-I~\ 1/2
= n cf-f }
[18]
where ni is an empirical constant obtained from fitting the experimental data. On the basis of Anderson and Ramsey's (25) data, Burke and Chan (9) have calculated 14.4 kHz for C,~ for a CH3 top. On the basis of the uncorrelated model two interpretations of the experimental data are possible. The first one was used by Parker and Jonas (24) in their explanation of the temperature dependence of the spin-rotation contribution for the methyl group in toluene. They assumed a temperature dependence of the spinrotation contribution which is much stronger than follows from the second term in Eq. [17] combined with Eq. [18] is connected with overall reorientation. Using this method we have been able to obtain the best agreement between the observed and calculated relaxation rate using Ca = 14.4 kHz, nj = 1.5, and (C 2)1/2= 5 kHz. It seems that the value of (C 2 )1/2 = 5 kHz obtained by adjusting to give the best fit for (R1)sr is still too high as compared with (C~) 1/2= 1.47 kHz obtained from chemical shielding. While comparing the activation energy Di (0.92 + 0.2 kcal/mole) with the activation energy of (R1)sr (-0.94+0.2 kcal) another alternative for interpreting the temperature dependence of the spin-rotational contribution suggests itself. Both Deverell (23), and Powles (26) have presented qualitative arguments that the product of the reorientational correlation time and the spin-rotation correlation time about a single axis of the molecule is proportional to the moment of inertia about that axis divided by kT. This predicts (27) that if the internal rotation of the CH3 group is the motion causing spin-rotation effects, the exponential factor for (T1)sr will be expected to be equal to the negative of that of Di. This result can therefore be viewed as evidence that the internal rotation of the CH3 group in nitromethane is the principal source of the large spin-rotation relaxation.
398
SUCHANSKI AND CANEPA
Additional support for this interpretation arises from the fact that, when we assume Co= C~,= 1.47 kHz then the first term in Eq. [17], is equal ~ of the experimental value (R1)sr. Thus the contribution from spin-overall rotation is practically of no relevance. One final observation should be made. Our interpretation is only approximate. First, a small error in (T1)exp causes large changes in the calculated value of (Tx)sr in the lower range of temperatures. Secondly, as noted by Parker and Jonas (24) in a similar case, interpreting zef~we assumed a rotational diffusion mechanism and then in interpreting the spin-rotation behavior we assumed that the CH3 group behaves as a freely rotating top. It seems that the results of the Xi test for the internal rotational diffusion coefficient in a qualitative analysis justify the procedure. In general, the primary conclusion of this study is that spin-internal rotation coupling provides a major contribution to the proton relaxation above room temperature in nitromethane. This has important implications for 13C nuclear Overhauser enhancement (NOE) (28) implying that there will be a reduction in the NOE of ~3C nuclei in an internally rotating methyl group due to spin-rotation contributions to the relaxation. Indeed, a recent result (29) in nitromethane NOE yields r/C-H= 0.1 which confirms this conclusion. ACKNOWLEDGMENTS The authors wish to thank Professor T. A. Scott and Dr. J. R. Brookeman for helpful discussions and comments. One of us (W.S.) would also like to thank Professor Z. Pajak for helpful discussions and J. Radomski M. Sci. for his assistance in making proton measurements which have been invaluable.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
12. 13. 14. 15. 16. 17. 18. /9. 20. 21.
W. SUCHANSKI AND Z. PAJAK, Chem. Phys. Lett. 26, 182 (1974). J. ANGERER AND W. SUCHANSKI, J. Magn. Reson. 21, 57 (1975). E. TANNENBAUM, R. J. MEYERS, AND W. D. GWINN, J. Chem. Phys. 25, 42 (1956). T. L. PENNDRED, A. M. PRICHARD, AND R. E. RICHARDS, J. Chem. $oc. A. 1009 (1969). D. E. O'REILLY AND E. M. PETERSON, J. Chem. Phys. 55, 2155 (1971). D. W. MCCALL, D. C. DOUGLAS, AND E. W. ANDERSON, J. Chem. Phys. 31, 1555 (1959). D. E. WOESSNER AND B. S. SNOWDEN, Advan. Mol. Relaxation Processes 3, 181 (1972). P. S. HUBBARD, Phys. Rev. 131, 1155 (1963). T. E. BURKE AND S. I. CHAN, J. Magn. Reson. 2, 120 (1970). J. K. TISON AND E. R. HUNT, J. Chem. Phys. 54, 1526 (1971). T. C. FARRAR AND E. D. BECKER, "Pulse and Fourier Transform NMR," Academic Press, New York, 1971. Z. PAJAK, K. JURGA, AND J. JURGA, Acta. Phys. Polon. A38, 263 (1970). A. ABRAGAM, "The Principles of Nuclear Magnetism," Clarendon Press, England, 1961. W. B. MoNIz AND H. S. GUTOWSKt, J. Chem. Phys. 38, 1155 (1963). S. N. SUBBARAO, E. G. SAUER, AND P. J. BRAY, Phys. Lett. 42A, 461 (1973). F. G. POWLES, J. Chem. Phys. 21, 633 (1953). S. CHANDRA AND D. NATA, J. Chem. Phys. 51, 5299 (1969). E. N. IVANOV, Soviet Phys. JEPT 18, 1041 (1964). K. T. GILLEN AND J. H. NOGGLE, J. Chem. Phys. 53, 801 (1970). International Critical Tables of Numerical Data, Physics, Chemistry and Technology,/McGraw-Hill, New York, 1933. W. H. SPIESS, D. SCHWEITZER, AND U. HABERLEN, jr. Magn. Reson. 9, 444 (1973).
RELAXATION IN LIQUID NITROMETHANE
22. 23. 24. 25. 26.
D. W. G. SMITH AND J. G. POWLES, Mol. Phys. 10, 451 (1966). C. DEVERELL, Mol. Phys. 18, 319 (1970). R. G. PARKER AND J. JONAS, J. Magn. Reson. 6, 106 (1972). C. H. ANDERSON AND N. F. RAMSEY, Phys. Rev. 149, 14 (1966). D. K. GREEN AND J. G. POWLES, Proc. Phys. Soc. 85, 87 (1965). 27. K. T. GILLEN, M. SCHWARTZ, AND J. H. NOGGLE, Mol. Phys. 20, 899 (1971). 28. K. F. KUHLMANN, D. M. GRANT, AND R. K. HARRIS, J. Chem. Phys. 52, 3439 (1970). 29. J. R. LYERLA AND D. M. GRANT, J. Phys. Chem. 22, 3213 (1972).
399
NMR Relaxation Studies and Internal Molecular Rotation in Liquid Nitromethane* W.
SUCHANSKIt
AND
P.
C.
CANEPA
Department of Physics, University of Florida, Gainesville, Florida 32611 Received April 29, 1978 Studies of the deuteron and proton relaxation rates of liquid nitromethane were made at various temperatures. The separation of the proton-proton intermolecular relaxation was accomplished by a dilution study in nitromethane-d3. It was found that the spin-rotation interaction contributed significantly to the intramolecular relaxation. The spin-rotation interaction contribution is discussed in terms of different models for the spin-internal and spin-overall rotation coupling. The resulting spin-rotation relaxation times offer evidence for large spin-rotation effects due to the internal rotation of the methyl group.
INTRODUCTION
In connection with our studies (1, 2) in determining the contributions of the spin-rotation interaction to the relaxation mechanism of protons in methyl groups with a low barrier to internal rotation we have investigated the relaxation of nitromethane. From microwave studies (3) of nitromethane, in which the potential barrier to CH3 group rotation is sixfold, we know that the barrier value is 6.03 cal/mole. In this work we measured the temperature dependence of the proton and deuteron relaxation times in nitromethane and nitromethane-d3. Previous workers have measured room temperature relaxation times for H (4, 5) and the temperature dependence of the self-diffusion coefficient Ds (5, 6). For protons various competing mechanisms may contribute to the net relaxation. The most important of these are the inter- and intramolecular dipole-dipole, and the spin-rotation interaction, whose characteristic relaxation times will be denoted respectively as (T1)d, inter, (T1)d, intra, (T1)sr. If one is to make use of the data from relaxation time studies the contributions of each of the above mechanisms must be separated. The separation of intermolecular and intramolecular contributions to proton relaxation has been carried out by measuring T1 of the methyl protons in nitromethane at different isotopic concentrations in nitromethane-d3. The separation of ( T 1 ) d , intr a from (T1)sr is more complicated since the protons are localized in an internal rotator, able to perform internal rotation in addition to reorientation with the molecule as a whole. * Research supported in part by National Science Foundation Grant DMR 77-08658. t Visiting scientist from the Institute of Physics, A. Mickiewicz University, Poznan, Poland. 389
0022-2364/79/020389-11$02.00/0 Copyright © 1979 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain
390
SUCHANSKI AND CANEPA
The theoretical interpretation dealing with the question of overall and internal rotation in nitromethane is based on the work of Woessner and Snowden (7), Hubbard's work (8) on the spin-rotation interactions and work by Burke and Chen (9) for the spin-rotation interactions in molecules with internal motion are used to explain the temperature behavior of T1 due to the methyl protons. EXPERIMENTAL
Nitromethane was obtained from E. D. Merck, and sealed under vacuum in a Pyrex tube after degassing by the freeze-pump-thaw technique. For these measurements, the liquids under investigation were in tubes of a similar design to that used by Tison and Hunt (10). The liquid region was approximately 5 mm long and was situated in the center of the 12 mm rf coil of a NMR probe. With the liquid in the capillary section extending above the top of the coil, this arrangement minimized the problem associated with vapor to liquid exchange (11). Measurements of 1H spin-lattice relaxation times were performed in the Institute of Physics, A. Mickiewicz University of Poznan, using a 25 MHz c-w high resolution NMR spectrometer by applying a null-method developed in this laboratory (12) over a temperature range extending from approximately 230 K up to about 400 K. The temperature of the sample was controlled by a gas-flow cryostat and monitored with a thermocouple to an accuracy of about 1 K. Measurements of the deuteron relaxation times were made at the University of Florida using pulse NMR apparatus employing repeated 180°-90 ° pulse sequences, at a frequency of 6.5 MHz. The sample was contained in a copper cell in a temperature-control cryostat, which provided temperature stability of better than 0.1 K and an absolute accuracy of 0.5K. RESULTS AND DISCUSSION
1. General Approach For most spin ½nuclei the relaxation rate R1 -= (T1)-1 is determined by a combination of mechanisms: (R1)exp = (gl)d, inter "[- ( e 1)d,intra "b (R1)sr.
[1]
In Fig. 1 the logarithm of proton, deuteron and nitrogen-14 spin-lattice relaxation times are plotted versus the reciprocal temperature. The proton relaxation data indicate that all three mechanisms contribute to the proton relaxation time. The standard type of analysis on the dilution data, CH3NO2 in CD3NO2 allows us to eliminate (R1)d, inter from Eq. [1]. But to eliminate (R1)d,intra from (R1)sr is not so easy. Various activation energies and values of correlation times resulting from deuteron and nitrogen-14 spin-lattice relaxation times clearly indicate that the methyl group is able to perform internal rotation in addition to reorientation with the molecule as a whole. Therefore the internal and overall rotational diffusion coefficient must first be determined in order to separate the intramolecular dipolar contribution from the spin-rotation contribution.
RELAXATION IN LIQUID NITROMETHANE 30
i
I
I
391 300
I
20
200
"
"
"-"
E
~s
50 "2 3
30
2-
20
I
2.5
3.0
3.5
4.0
4.5
I0
IO00/T (*K "1) FIG. 1. The experimental temperature dependence of the 1H, 2D and 14Nspin-lattice relaxation times in nitromethane. Hydrogen relaxation: C), pure CH3NO2; A 36% CH3NO2 in CD3NO2. Deuteron relaxation; U], Ea = 1.4 kcal/mole. Nitrogen-14 relaxation; O, Ea = 1.9 kcal/mole (after Moniz and Gutowski).
2. Nitrogen-14 and Deuterium Relaxation Since the quadrupole relaxation mechanism is usually several orders of magnitude more efficient than other competing mechanisms, m e a s u r e m e n t s of relaxation times of quadrupolar nuclei have extensively been used to obtain details of molecular reorientation in liquids. For nuclei with spin I = 1, such as nitrogen-14 and deuterium, the relaxation rate due to quadrupolar interactions is given by the expression (•3): (Ra)o = 3(1 + ½r/z)\2rr(
ro
[2]
where rt is the asymmetry parameter, (eZQq/h) the nuclear quadrupole coupling constant, and To is the reorientational correlation time. Figure 1 shows the t e m p e r a ture dependence of 14N and 2D relaxation for CH3NO2 and CD3NO2 respectively. Using Eq. [2], together with an experimentally obtained (14) 7"1value of 22 ms at 25°C, a quadrupole coupling constant (15) of 1.695 M H z and asymmetry p a r a m e t e r rt = 0.424 (15), a correlation time of 1.03 x 10 -12 s are obtained for CH3NOz. Nitromethane has an electric dipole moment. Consequently, nitromethane exhibits dielectric dispersion, and dielectric relaxation times can be obtained. But the relaxation time associated with the macroscopic polarization measured by dielectric relaxation is somewhat different than the microscopic molecular correlation time. Taking into consideration this fact Powles (16) has shown that: M "rdiel
(3Co) 2Co q- Coo 7"diel
[3]
392
SUCHANSKI AND CANEPA
where e0 and coo are the dielectric constant at zero and infinite frequency respectively, ~'die, M is the macroscopic correlation time, and "/'diel is the microscopic correlation time. Dielectric relaxation times were recently reported (17) for nitromethane. Using this data we obtained a microscopic dielectric correlation time at 25°C of 2.7 x 10-12s, which is approximately 2.7 times the nuclear correlation time. If the reorientation occurs by a rotational diffusion mechanism, the ratio of dielectric correlation time to nuclear correlation time is predicted to be three (18). From this it appears that the overall reorientation in nitromethane, to a first approximation, can be described by a rotational diffusion process. The electric dipole moment in nitromethane is directed along the symmetry axis of the molecule, so that the dielectric relaxation time is dependent only on the rotational diffusion constant about an axis perpendicular to the symmetry axis. Then the dielectric relaxation times give us D . because in the diffusion limit: D . = (2rdie,) -1.
[43
The experimentally determined 14N correlation time is more connected with the overall rotation diffusion constant Do because the large value of the asymmetry parameter does not permit us to assume that the electric field gradient is axially symmetric and parallel to the symmetry axis of the molecule. Thus for 14N correlation time we get: Do = (6~'u)-'.
[S]
It seems that the close correlation between D± and Do determined by dielectric and a4N relaxations, as it follows from Fig. 2 allows us to assume that the overall reorientation in nitromethane is isotropic. Additional support for this assumption is the fact that activation energies following from dielectric and 14N relaxations have the same value. Hence, comparison of the dielectric relaxation time and the experimentally determined ~4N correlation time as well as the apparent activation energies suggests that a rotation diffusion mechanism and the assumption D . - DIL = Do are reasonably consistent with the experimental data. Now making use of Do along with the 2D relaxation times (Fig. 1) and following the procedure of Woessner and Snowden (7), we are able to calculate the internal rotational diffusion constant D/taking the quadrupole coupling constant as 164 kHz (5) for the methyl deuterium in nitromethane and neglecting the asymmetry parameter. Woessner and Snowden (7) give the following expression for the effective correlation time: re~ = ¼(3 cos 2 0-1)Z(6D0)-a + 3 sin 2 0 cos 20(Oi + 5D0)-1 + ] sin 20(4Di + 2D0) -1
[6] where 0 is the constant angle between the relaxation vector and the symmetry axis. We find Ea (D0 to be 0.92 + 0.2 kcal/mole, and we find that internal reorientation is about 6 times faster than overall reorientation at 25°C. The derived values of Di yield reorientational correlation times rl = (69/) -1 that can be compared with the classical free rotor reorientational time zo = ](I, J k T ) 1/2 in
RELAXATION IN LIQUID NITROMETHANE I
I
I
I
~t=.
393
I
CD3NO z
lOle
~10" P~~' '~ Iz Om~
O° I
I
I
I
I
2.5
3.0
3.5
4.0
4.5
IO00/T
(K - I )
FIG. 2. The temperature dependences of the rotational diffusion constants for nitrometbane found from analysis of the deuteron and nitrogen-14 relaxation data. The dielectric results are labelled ©.
the so-called X test (19). Thus: "ri
5
(k_T~1/2
xi . . . .
rfi
18Di
[73
and X >> 1 for the rotational diffusion to apply. One calculates that Xi changes from 2.8 at low temperatures to 1.6 at the upper limit of the measured t e m p e r a t u r e range in CD3NOz. The values of )t'i indicates that in the measured t e m p e r a t u r e range one could expect strong inertial effects in the internal rotation of the CD3 group.
3. Proton Relaxation A. Proton Intermolecular Dipole-Dipole Interaction If we assumed that the relaxation of a spin is due to the uncorrelated motion of all its intermolecular spin pairs, only relative translation motion changes the intermolecular dipole vector, the molecules are spherical and have a single distance of closest approach independent of relative orientation, then we get the following theoretical expression for (R1)d, inter: (R1)d,i.t~= ~rrh 1 ZNa -3 yH['yHrlH+~.~,'y[nfIf(If+ z z 8 2 1)]" rt
[8]
where yri is the gyromagnetic ratio of the proton, Yt is the gyromagnetic ratio of the nonresonant nuclei, nil, n~ is the n u m b e r of protons or f nuclei per molecule, r, is the
394
SUCHANSKI AND CANEPA
translation correlation time, N is the number of molecules per unit volume, and a is the effective radius of the molecule• The temperature dependent proton relaxation times are shown in Fig. 1 for pure CH3NO2 and for a mixture containing 36 mole % CH3NO2 in CD3NO2. For this mixture the intermolecular relaxation rate is: H H-H H-D H-N ( R 1) d,inter = (R1)d, lnter+ ( e 1) d, inter -1"-( e 1) d,inter
[9]
Since 7 2 = 4 2 . 5 y ~ and the spin values are different, the deuterium in CD3NO2 will • 1 contribute only 5 as much to the intermolecular relaxation as do the hydrogens, and because YN/YH 2 2 = 5.3 X 10 -3 the effect of the nitrogen nucleus may be ignored. The total proton relaxation rate is then: (R1)exp = [(23C + 1)/24](R 1)H-H d,inter q- (R 1)d, intra "~- (R 1)sr
[lo]
where C is the mole fraction of the protonated nitromethane. Thus plotting (R1)exp vs 2 3 C / 2 4 gave a slope of (R 1)U,inter. Values of (R1)a,l,ter calculated by this method at regular intervals of 1 0 0 0 / T using smoothed proton relaxation data, are shown in Fig. 3. The data shows Arrhenius behavior with an activation energy of 3.0 kcal/mole. We express the translation correlation time as: 121ra2~7 rt
I
lO-I
1
[11]
kT
I
-
// I
I
,4,/"
1O- !
¢(/ F'a= 3 . 0 Kc01/m0hl
I
i
i
I
L
2•5
3,0
3.5
4.0
4.5
I O 0 0 / T (K -j) FIG. 3. The temperature dependences of the proton inter (O) and intramolecular (A) relaxation rates obtained from the proton data for 100% CH3NO2 and 36% CH3NOa-64% CD3NO2 samples, Included is the theoretical plot for (T1)dJ.ter - - -
R E L A X A T I O N IN L I Q U I D N I T R O M E T H A N E
395
TABLE 1 GEOMETRIC PARAMETERS AND MOMENTS OF INERTIA FOR NITROMETHANE a rc-H (10 -8 cm) rc-N (10 -8 cm) r~_o (10-8'cm) rH-H (10 -8 cm) rH-N (10 -8 cm) < H-C-N
1.088 b 1.4896 1.224 b 1.800 2.087 107.2 ° b 125.3 °b 62.9 b 79.6 b 124.8 b 5.5
a Those not given in the reference were derived. b p. A. Cox and S. Waring, J. Chem. Soc. Trans. 11, 68, 1060, (1972).
Then
Eq. [8] looks
Faraday
as follows:
6 zr2h2r~in×[nHON0]
(el)d,inter
5
kT
[12]
M
where p and M are, respectively, the density and the molecular weight of the liquid. For nitromethane, the densities and viscosities were obtained from Ref. (20). The temperature dependence thus obtained is shown in Fig. 3. From Eq. [12] a theoretical activation energy of 2.9 kcal/mole can be calculated. Therefore, in this case, the intermolecular theory yields close agreement to experiment, perhaps fortuitous in view of the questionable assumptions used in its derivation. B. Proton Intramolecular Dipole-Dipole Interaction
Separation of (R1)d, intra from (Rx)sr c a n be accomplished using a theoretical equation for (R1)d, intra:
(R1)d,intra=~h '~H--(~ 3242
Z
n
i>i
6 r~ Ire(H-H)
[13]
/
where re(H-H) is the effective correlation time for reorientation of the proton intermolecular vector and can be calculated using Eq. [6] with 0 = 90 °. Using internuclear distance given in Table 1 we obtained: ( R 1)d, intra = 5 . 0 0 X
101°re(H-H)
[14]
The values of Di appropriate to CD3NOz (Fig. 2) have been corrected for the ( e l ) d , intra calculation on the CH3NO2 case. The correction to Di in moving from CD3NOz to CH3NO2 was made by noting that in the inertial limit Di - (i~)1/2 (21). The resulting (R1)d.intra is shown in Fig. 4.
396
SUCHANSKI AND CANEPA I00
~
,~
I
I
I
3.5
4.0
4.5
50
20
I0
I
2.5
3.0
IO00/T (K -I) FIG. 4. The total proton intramolecularrelaxation time (A) of nitromethane and its separation into its intramolecular dipole-dipole (Eo = 1.55 kcal/mole) and spin-rotation relaxation times (O, Eo = -0' 94 kcal/mole).
C. Proton Spin-Rotation Interaction Then it is possible to calculate (R 1)st by subtracting (R 1)a,i,tra from experimentally determined (R1)intra. These are also given in Fig. 4. This provided a basis for our attempt to interpret the temperature dependence of the proton Tt data for the methyl group in nitromethane. As a first step we assumed that the spin-rotation contribution results from end-over-end reorientation. The overall spin-rotation contribution to T~ for a spherical molecule has been derived by Hubbard [8]:
8¢rkT 2 (Rt)sr = - - ~ I a v ( 2 C ± + CI~ )~-j
[15]
where Iav is the average moment of inertia of the molecule, C± and CII are diagonal components of the spin-rotation interaction tensor, and rj is the angular velocity correlation time. cj is related to ro in the diffusion limit by the relation: I
rI.ZO=6k T
[16]
Thus, one can use Eqs. [15, 16] to evaluate C 2en = (2C 2 + C~)/3 to obtain the spin-rotation interaction constant C ~ from relaxation. Using an approach introduced by Smith and Powles (22), at the maximum of the plot of In (R1)intra vs l/T, l ( R 1 ) i n t r a = (gl)d,intra = (R1)sr. For nitromethane (Rt)intra = 0.05 S-1 at 0.00315 K -1, the average moment of inertia I~v = 9 5 . 1 0 -40 g. cm 2, one calculation Cee~= 8.8 kHz for protons. The experimental value of C~erfor the nitromethane is not known. From the chemical shift data by using the average moment of inertia in the relevant expression (see Ref. (23)), (C~) 1/2= 1.47 kHz can be calculated. In spite of the fact that large differences in magnitude between the spin-rotation constant obtained from relaxation data and chemical shielding data have previously been observed (23, 24) we think that the value C~fe= 8,8 kHz for protons in nitromethane is rather
RELAXATION IN LIQUID NITROMETHANE
397
unrealistic. This fact and both the deuterium and nitrogen-14 relaxation measurement together with experimentally determined (3) very low barrier to internal rotation for the CH3 group in nitromethane suggest that spin-internal rotation coupling plays an important role in the spin-rotation interaction. Burke and Chan (9) have shown that the spin-rotational contribution for a nucleus located on an internal rotator in the so-called uncorrelated model is given by the following expression:
8rc2kT
(R1)sr-- ~
2 8~'2kTI~C~ IoCoTJ + (1--I"~ ~'~ \ I,J 3h 2
[17]
where I0 is the overall moment of inertia,/~ a n d / ~ one of the moments of inertia of the top and whole molecule about the symmetry axis, Co and Ca are the overall and spin-internal rotation coupling constants. The first term in Eq. [17] corresponds to the contributions from the spin-overall rotations with the correlation time rj defined by Eq. [16] and second terms represent the contribution of the spin-internal rotation coupling with the correlation time ri. The ~'i was assumed to be a correlation time for a free rotation (9): [ ~-I~\ 1/2
= n cf-f }
[18]
where ni is an empirical constant obtained from fitting the experimental data. On the basis of Anderson and Ramsey's (25) data, Burke and Chan (9) have calculated 14.4 kHz for C,~ for a CH3 top. On the basis of the uncorrelated model two interpretations of the experimental data are possible. The first one was used by Parker and Jonas (24) in their explanation of the temperature dependence of the spin-rotation contribution for the methyl group in toluene. They assumed a temperature dependence of the spinrotation contribution which is much stronger than follows from the second term in Eq. [17] combined with Eq. [18] is connected with overall reorientation. Using this method we have been able to obtain the best agreement between the observed and calculated relaxation rate using Ca = 14.4 kHz, nj = 1.5, and (C 2)1/2= 5 kHz. It seems that the value of (C 2 )1/2 = 5 kHz obtained by adjusting to give the best fit for (R1)sr is still too high as compared with (C~) 1/2= 1.47 kHz obtained from chemical shielding. While comparing the activation energy Di (0.92 + 0.2 kcal/mole) with the activation energy of (R1)sr (-0.94+0.2 kcal) another alternative for interpreting the temperature dependence of the spin-rotational contribution suggests itself. Both Deverell (23), and Powles (26) have presented qualitative arguments that the product of the reorientational correlation time and the spin-rotation correlation time about a single axis of the molecule is proportional to the moment of inertia about that axis divided by kT. This predicts (27) that if the internal rotation of the CH3 group is the motion causing spin-rotation effects, the exponential factor for (T1)sr will be expected to be equal to the negative of that of Di. This result can therefore be viewed as evidence that the internal rotation of the CH3 group in nitromethane is the principal source of the large spin-rotation relaxation.
398
SUCHANSKI AND CANEPA
Additional support for this interpretation arises from the fact that, when we assume Co= C~,= 1.47 kHz then the first term in Eq. [17], is equal ~ of the experimental value (R1)sr. Thus the contribution from spin-overall rotation is practically of no relevance. One final observation should be made. Our interpretation is only approximate. First, a small error in (T1)exp causes large changes in the calculated value of (Tx)sr in the lower range of temperatures. Secondly, as noted by Parker and Jonas (24) in a similar case, interpreting zef~we assumed a rotational diffusion mechanism and then in interpreting the spin-rotation behavior we assumed that the CH3 group behaves as a freely rotating top. It seems that the results of the Xi test for the internal rotational diffusion coefficient in a qualitative analysis justify the procedure. In general, the primary conclusion of this study is that spin-internal rotation coupling provides a major contribution to the proton relaxation above room temperature in nitromethane. This has important implications for 13C nuclear Overhauser enhancement (NOE) (28) implying that there will be a reduction in the NOE of ~3C nuclei in an internally rotating methyl group due to spin-rotation contributions to the relaxation. Indeed, a recent result (29) in nitromethane NOE yields r/C-H= 0.1 which confirms this conclusion. ACKNOWLEDGMENTS The authors wish to thank Professor T. A. Scott and Dr. J. R. Brookeman for helpful discussions and comments. One of us (W.S.) would also like to thank Professor Z. Pajak for helpful discussions and J. Radomski M. Sci. for his assistance in making proton measurements which have been invaluable.
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12. 13. 14. 15. 16. 17. 18. /9. 20. 21.
W. SUCHANSKI AND Z. PAJAK, Chem. Phys. Lett. 26, 182 (1974). J. ANGERER AND W. SUCHANSKI, J. Magn. Reson. 21, 57 (1975). E. TANNENBAUM, R. J. MEYERS, AND W. D. GWINN, J. Chem. Phys. 25, 42 (1956). T. L. PENNDRED, A. M. PRICHARD, AND R. E. RICHARDS, J. Chem. $oc. A. 1009 (1969). D. E. O'REILLY AND E. M. PETERSON, J. Chem. Phys. 55, 2155 (1971). D. W. MCCALL, D. C. DOUGLAS, AND E. W. ANDERSON, J. Chem. Phys. 31, 1555 (1959). D. E. WOESSNER AND B. S. SNOWDEN, Advan. Mol. Relaxation Processes 3, 181 (1972). P. S. HUBBARD, Phys. Rev. 131, 1155 (1963). T. E. BURKE AND S. I. CHAN, J. Magn. Reson. 2, 120 (1970). J. K. TISON AND E. R. HUNT, J. Chem. Phys. 54, 1526 (1971). T. C. FARRAR AND E. D. BECKER, "Pulse and Fourier Transform NMR," Academic Press, New York, 1971. Z. PAJAK, K. JURGA, AND J. JURGA, Acta. Phys. Polon. A38, 263 (1970). A. ABRAGAM, "The Principles of Nuclear Magnetism," Clarendon Press, England, 1961. W. B. MoNIz AND H. S. GUTOWSKt, J. Chem. Phys. 38, 1155 (1963). S. N. SUBBARAO, E. G. SAUER, AND P. J. BRAY, Phys. Lett. 42A, 461 (1973). F. G. POWLES, J. Chem. Phys. 21, 633 (1953). S. CHANDRA AND D. NATA, J. Chem. Phys. 51, 5299 (1969). E. N. IVANOV, Soviet Phys. JEPT 18, 1041 (1964). K. T. GILLEN AND J. H. NOGGLE, J. Chem. Phys. 53, 801 (1970). International Critical Tables of Numerical Data, Physics, Chemistry and Technology,/McGraw-Hill, New York, 1933. W. H. SPIESS, D. SCHWEITZER, AND U. HABERLEN, jr. Magn. Reson. 9, 444 (1973).
RELAXATION IN LIQUID NITROMETHANE
22. 23. 24. 25. 26.
D. W. G. SMITH AND J. G. POWLES, Mol. Phys. 10, 451 (1966). C. DEVERELL, Mol. Phys. 18, 319 (1970). R. G. PARKER AND J. JONAS, J. Magn. Reson. 6, 106 (1972). C. H. ANDERSON AND N. F. RAMSEY, Phys. Rev. 149, 14 (1966). D. K. GREEN AND J. G. POWLES, Proc. Phys. Soc. 85, 87 (1965). 27. K. T. GILLEN, M. SCHWARTZ, AND J. H. NOGGLE, Mol. Phys. 20, 899 (1971). 28. K. F. KUHLMANN, D. M. GRANT, AND R. K. HARRIS, J. Chem. Phys. 52, 3439 (1970). 29. J. R. LYERLA AND D. M. GRANT, J. Phys. Chem. 22, 3213 (1972).
399