Flash CIDNP investigation of a cyclic photoreaction

ChcmicalPhysics 147 (1990) 143-154 North-Holland

Flash CIDNP investigation of a cyclic photoreaction MartinGoez Inrtitut @rPhysikalischeund TheoretischeChemie, T~hnische UniversitdtBraunschweig HatwSommer-Strawe 10,D3300 Brunswick,FRG Received 3 May 1990

The cyclic photoreaction between 9,lO-anthraquinone and N,Ndimethylaniline (DMA) in acetonitrik& has been studied between 237 and 296 K by time resolved measurements of chemically induced dynamic nuclear polarization (CIDNP). A generally applicable kinetic treatment including the calculation of absolute CIDNP signal intensities is presented. For the dimethylamino protons in the &nor radical8 a mean nuclear spin relaxation time of 103 ps ( &25%) was found An activation energy of 11.3 kJ/mol ( + 10%) was determined for the dqenerate electron ex&mge between DMA and its radial cation.

1. Introduction

The products of a chemical reaction carried out in a magnetic field may be formed with a nonequilib rium population of their nuclear spin states. Transient changes of NMR line intensities (emission or enhanced absorption) are observed as a result of this so-called chemically induced dynamic nuclear polarization (CIDNP) [l-3 1. The accepted qualitative explanation of this phenomenon has been given by Closs [ 4 ] and Raptein and Oosterhoff [ 5 ] by a spin sorting mechanism taking place in an intermediate electron spin correlated radical pair. During the lifetime of this pair ( = 10 ns) intersystem crossing occurs with a nuclear spin dependent probability. In this way, opposite nuclear spin polarizations are created in the singlet and trip let states of the radical pair. These polarizations are transferred to diamagnetic species through multiplio ity dependent reaction channels. In most cases, geminate recombination regaining the educts can occur from the singlet state only, while the formation of free radicals ultimately leading to the products is possible from all multiplicities. Theoretical models for a quantitative description of CIDNP have been presented by several groups of authors [ 6- 15 1. Since the polarizations are conserved in the products for the spin-lattice relaxation time T, (of the order of seconds for protons), CIDNP studies of fast 0301-0104/90/$03.50

0 1990 - Elsevier SciencePublkhenB.V.

radical reactions in solution are feasible in spite of the slow timescale of NMR measurements. In CIDNP investigations of photoreactions, steady-state illumination is conventionally employed. These measurements yield valuable information about the reaction mechanism. Even more meaningful is the time resolved variant of the experiment, “Sash CIDNP’ [ 16-25 1. In this case, the chemical reaction is started by a flash, usually from a pulsed laser. The nuclear spin states of the products are probed aikr a delay A with a radiofraquency (rf) pulse from an FT-NMR spectrometer. A kinetic profile is obtained by carrying out a series of experiments with varying A. Ifdeconvolution methods are used, polarizations can be measured on a submicrosecond timescale with commercially available NMR spectrometers [22,25 1. Thus, diffusion controlled bimolecular reactions are observable, if low reactant concentrations can be employed. In a cyclic photochemical reaction, where reae tants and products are identical, geminate recombination and free radical formation finally lead to the same chemical species In this case, only (usually very weak) signals caused by nuclear spin relaxation in the radicals are observed in steady-state CIDNP experiments; in the absence of relaxation complete cancellation of the polarizations from the two reaction channels occurs. On the other hand, in time resolved experiments strong transient CIDNP signals are de(North-Holland)

144

M. Goes / CIDNPin a cyclicphotoreaction

tected, since geminate recombination and reactions of the free radicals take place on different timescales

1261. In the present investigation, nuclear spins polarized by the CIDNP effect serve as labels to distinguish reactants and products of a degenerate electron transfer. Due to the very small Zeeman energies, the course of this reaction is not influenced by the magnetic field. This detection method is thus an altemative to time resolved CIDEP experiments [ 27-29 1, as well as the usual indirect determination of the rates of such processes by measurements of the ESR [ 301 or NMR lineshape [ 3 11. The activation barriers for degenerate electron exchange reactions are fundamental parameters in the cur&t theories, of homogeneous electron transfer [ 32-341. In this work, the measurement of such an activation barrier by means of flash CIDNP experiments is reported for the first time.

2. Experimental 9,10-anthraquinone ( AQ ) (Fluka ) was sublimed twice in vacuum, N,Ndimethylaniline (DMA) (Aldrich) was doubly distilled under reduced pressure. Since the photo&ox system was not stable under, _illumination in the presence of even small amounts of water, solutions of the reactants in acetonitrile-d, (99.896, MSD) were dried prior to use over 3 A molecular sieve (Merck). They were handled with syringe techniques in an inert atmosphere, degassed by, the freeze-pump-thaw method directly in the NMR,tubes, and these were sealed. The residual water content was below 5 x 10e4 M, as determined by NMR spectroscopy. In all experiments, the concentration of AQ was 8 x 10m4M; amine ,concentrations ranged from 2 x 10e4 to 2 x 1O- 3 M,. The experimental setup for the flash CIDNP measurements consisted of a Bruker WM 25O’NMR spectrometer with Aspect 2000 computer, and an excimetlaser (EMG 101, Lambda Physik, XeCl, 308 nm, 1.00-l 20 mJ/pulse, 15-20 ns pulse width) which was used to pump a two-stage dye laser (home made from Spindler & .Hoyer parts). The energy output at the excitation wavelength 2 ,=343 nm (pterphenyl) was 5-10 mJ/pulse; energy fluctuations amounted to +3%. Side-on illumination of the NMR tube was

performed as in ref. [ 17 ] with a quartz rod and suprasil prism inserted into the NMR probe head. For low optical losses the touching faces of these parts were highly polished so that they could be joined by adhesion. With this configuration, an optical efficiency of 70% at Iz, was reached, as determined actinometrically. In all CIDNP experiments the background magnetization was first removed by application of a 50 ms noise modulated decoupler pulse [ 18,351. The laser was then triggered by the NMR data system, and the probing rf pulse applied after a computer controlled variable delay which could be changed in 100 ns steps. The delay between trigger pulse and laser discharge ( z 1.5 ps) is weakly dependent on the age of the laser filing and the high voltage applied. Since this delay must be accurately known for the evaluation of other than mono-exponential kinetics it was routinely determined with a fast photodiode (LF 200, Lambda Physik) before and after a set of measurements. The short time jitter of the pulses was found to be f 5 ns. The duration of the NMR observation pulse was either 0.5 or 1 ps (experimentally determined flip angles 6” or 17 ‘, respectively). The temperature in the probe head could be controlled to f0.3 K. The apparatus for the performance of the laser flash photolysis (LFP) experiments has been described elsewhere [ 361.

3. Results and discussion 3. I. Mechanism and chemical kinetics In scheme 1, a general mechanism for the photoreaction between an excited acceptor A and a donor D in a magnetic field is shown. All steps in this scheme without explicitly given rate constants are too fast to be observable with the time resolution of the flash CIDNP apparatus ( 100 ns). For the investigated redox system (A=AQ and D= DMA) the evidence for the proposed mechanism is summarized in the following. No changes in the UV-VIS and NMR spectral parameters of solutions of DMA and AQ in acetonitrile were observed upon mixing, so ground state complexation was ruled out. At the excitation wavelength

M. Goes/ClDNP ina cyclicphotoreaction

Tz

‘A+0

-

k ddf

3

A’ D+ -

h+

\

-A+D

/

1

A:

Scheme

Dt-A’D

1.

the extinction coefficient of DMA is at least a factor of 50 smaller than that of AQ. Comparable concentrations of AQ and DMA were employed in all experiments. Thus, the primary step of the reaction must be electronic excitation of the acceptor. The intersystern crossing quantum yield for AQ is nearly unity [ 37 1. The first excited singlet state of the quinone is too short-lived to be appreciably quenched by DMA under the experimental conditions of this work. It follows that the chemical reaction occurs from a trip let state of AQ. In LFP experiments with AQ in acetonitrile a transient was observed which disappeared when the solutions were saturated with oxygen. Therefore this signal was assigned to 3AQ. The absorptionspectrumofthisspecies(L,=370mn)was identical to that obtained by pulse radiolysis of AQ in acetonitrile [ 38) and other solvents [ 39,401. In dry solutions the triplet decayed. monoexponentially; the observed lifetime (4.7 us) was almost twice as long as that given in ref. [ 38 1. In the presence of 2 x lo-’ M Dh4A no change in the absorption at 370 nm could be detected tier the dead time of the LFP apparatus ( 100 ns). Instead, strong transient absorptions in the visible range were found, which decayed according to a bimolecular rate law. From the occurrence of CIDNP during the reaction it is evident that radicals are formed. The observed extinction maxima at 470 and 550 nm are consistent with a 1 : 1 superposition of the known spectra of the radical cation of DMA [ 4 l-431 and the anthrasemiquinone radical anion [ 44,451. CIDNP data strongly corroborate this evidence for the generation of ions. Experimentally, an emission signal is found for the aliphatic protons of DMA formed by geminate recombination. The radical pair is initially produced in the triplet state. Si,nce the triplet energy of DMA (286 kJ/mol [46] ) is higher

145

than that of AQ (265 kJ/mol [ 47]), in-cage reaction to an electronically excited species is very unlikely; geminate recombination is assumed to proceed exclusively from the singlet state of the pair. Both in the case of neutral radicals, as well as radical ions, the electronic g factor in the aniline species is smaller than that in the semiquinone. However, the hyperfine coupling constant (hfc) is positive in an anilinium cation and negative in a neutral anilinoalkyl radical. From Kaptein’s rules [48] it follows that the observed polarization in the cage product can only be explained by the appearance of radical ions as intermediates [ 49 1. The free enthalpy for radical ion pair formation can be estimated from the redox potentials of the reactants and the triplet energy of the acceptor [ 501. It is strongly negative (E(AQ/AQ-‘)=-0.96 V [51], E(DMA+‘/DMA)=0.81 V [52], both in acetonitrile versus SCE) , so diffusion controlled quenching with & according to the Smoluchowski equation [ 53 ] is assumed &

= 4xuDL

(1)

(a sum of the radii of both reactants, D interdiffusion coefficient, L Avogadro’s number). Encounters of the free ions are also diffusion controlled. The respective rate constant k_ is taken as kdiffyI1,where the Debye factor w [ 541 considers the Coulombic attraction between the ions 1 z*zue2 YnD=41tgc,akTexp(z,z,e2/4~~~~uk~

-

1’

(2)

( ZA, zB ionic cbi?irges,,f?elementary charge, e0VaCUUm permittivity, er relative permittivity, k Boltzmann constant, T temperature). The degenerate electron exchange between a donor molecule and the corresponding radical ion (rate kDD) results in no net chemical change, but transfers CIDNP created in the free radicals to the observable species DMA. Since AC for this process is zero, k,, is expected to be significantly smaller than b,+ According to Kaptein’s rules the resulting polarization should be enhanced absorption. Fig. 1 shows typical time resolved spectra obtained by a flash CIDNP measurement of the photoreaction between AQ and DMA. From the preceding discus_ sion it is evident that the diffusion controlled quenching of 3AQ is responsible for the fast rise of

M. Goez/ CIDNP in a cyclicphotoreaction

146

Fii 1. Time reso1ve.dCIDNF’ spectra of the photorawtion of 8.0 x lo-’ M anthmquimme with 3.2 x 1O-4 M N,Ndimcthylaniline in acctonit&-& (T=257 K, 1 _= 343 mu, width of rfpulse 0.5 w 256 scans per delay). The inverted power apa%rmn~rcscntatio~~ of the signal from the dimethylamino protons is shown as a function of the delay b between laser diHargc and NMt observation pulse.

emissive polarization in the dimethylamino protons. This signal is slowly compensated by an absorptive component mainly caused by the polarization tram+ fer due to the degenerate electron exchange. Relaxation in the free radicals manifests itself by a remaining emissive signal at long times. In rigorously dried acetonitrile, the system AQ/ DMA was fairly stable under illumination. After the absorption of 5- 10 J of laser radiation, about 2 x 10-s moles of the reactants had been consumed, corresponding to a quantum yield of less than 0.1%. Not even weak CIDNP signals assignable to products of side reactions (e.g., hydrogen abstraction as found with aliphatic amines [ 491) were observed. Especially, no evidence for the formation of N,N,N’,N’tetramethylbenxidine was detected. When radical cations of DMA are generated electrolytically, this reaction is predominant, so that only the ESR speo trum of the coupling product can be recorded [ 55 1. The diffusion controlled recombination of DMA+ * and AQ- ’ presumably suppresses this dimerixation under the experimental conditions of the present work. A closed form solution for the chemical rate law resulting from scheme 1 exists, if the quenching may be assumed to be a first-order process (i.e. [D] z+ [3A]).Duetothestoichiometryonethenhas $

[3Al=-~[3Al,

(3)

-$D+*]=k,[3A]-k2[D+*]2

.(4)

with b=t

(5)

+&Do,

k,=k,mDo,

(6)

b=kncf,

(7)

where 3~is the triplet lifetime, Do denotes the donor start concentration and f is the so-called spin statistical factor cfm 0.25 ). This factor takes into account that-apartfromthesmallCIDNPe&cts-radical pairs are only capable of recombination from the singlet state. It is approximately the probability that a random encounter of free ions leads to a correlated singlet pair. Following Chien [ 56 ] who treated an almost identical kinetic problem, one obtains [3A]=3A06,

(8)

ID+*]=+=

(9)

with Lexp(

-k&

,

(10)

~=kJ%,

(11)

jY= 3A04k, k,/k; ,

(12)

M. Goez/CIDNP in a cyclicphotweciction

r=a/m~,(Jib

(13)

9

where Z, and K,, are the modified Bessel functions of the first and second kind of order II, and ‘,&, is the triplet start concentration. Since the argumencfl is small and decmases with increasing time an approximation of eq. (9) can be obtained. With the asymptotic expressions for the Bessel functions [ 57 ] one gets [D+‘] =a

b-exp(

-&)

(14)

c+t

with a= ~Pl&

,

(15)

b=WB, c=Vkb(

(16) l/r-h/%

(17)

.

The difference between eqs. (9) and ( 14) is less than 3% under the experimental conditions of this paper. The approximation becomes exact in the limit of very long times. For sufficiently small #Z(i.e. ion recombination slow compared to triplet decay) an even simpler relation can be found by insertion of the asymptotic value for 15 [D+‘l=A

l-exp(--kot) B+t

’

(18)

where A=l/k,,

(19)

B=2/M2/8-ln,/%.

(20)

147

status r of exponential terms in the polarizations are left unchanged by the convolution, but the amplitude of such terms is diminished with decreasing T. This effect is pronounced if T is smaller than or comparable to the duration of the rfpulse. Signals observed at to=0 arc also caused by the convolution; due to the presaturation, the true CIDNP magnetization starts from zero at the time of the laser tlash. In the following, the time dependence of the donor polarizations for a CIDNP net effect will be derived from the kinetic scheme. The treatment is an extension of earlier work by other groups [ 58,201. It can be modified in a straightfonvard way for the calculation of acceptor polarizations. The reaction rates of the radical pairs depend on the nuclear spin states. The probabilities of geminate product formation from a radical pair with a triplet precursor, or generated by an encounter of free radicals are denoted as F,,,,(T) and F,,(F), respectively. The first subscript refers to the nuclear spin state of the donor D, the second to that of the accep tor A. Concentrations of a molecule in a particular nuclear spin state are marked with an index. Without an index, total ~ncentrations are meant. The following system of Merential equations is readily obtained from scheme 1, when relaxation in the donor radicals (rate 1/T,, equilibrium concentration [ D$ * ] ) is considered additionally.

$ 13Al= -(; ;

+kidW)13Al

,

(21)

ID,]=- &dDjl 7 ( 1-F,I(T) 1f3&l

3.2. CZDNP kinetics

+k,[Di+‘l T F,I(F) [Ai’1 The experimentally determined time dependence of the CIDNP signal intensities for the dimethylamino protons in aniline is excellently describable by a superposition of two exponentials (see fw 2a) and a very small constant term. If larger concentrations of DMA and longer rf pulses are used, the fast component cannot be resolved and a quasi mono-exponential curve results (fig. 2b). The observed magnetization in these flash CIDNP experiments is given by a convolution integral of rf pulse and true kinetic magnetization [ 251. This has been taken into account in fig. 2 by iterative reconvolution with the known pulse shape. The time con-

=-;[,I-&

~~D_i+~l-~Dj&~l>.

(23)

The spin statistical factor of eq. (7) is contained in the terms F,,(F). In the third term on the right of eq. (22) addition and subtraction of kuu[ D_,?’] [ Dj]

M. Goez/CIDNP in a cyclicphotoreaction

148

1,

A

nob

a

m go-

w110-

70-

w-

UJO-

SO?-

LO30-

clo-

2070l@

.,.,.,.,.,.A

w-p,.,

0200m6008001ocol2w%al

IK

I&

0

loo2003004alsm600700

Fig. 2. The solid lines shsw best fits of a b&exponential (a) and mono-exponential (b) function to the measured CIDNP signal intensities (intghls) at diffen+ delays t,, for the following experimental parameters: (a) as in fw 1, (b) similar, but 1.0~ lo-” M DMA, width of d pulse1.Ops, 128 scans per delay. For convenience, the signal phasea have been inverted.

leads to a replacement of the sums by total concentrations. As only the polarization of D is observed in the experiments, one has to sum over all nuclear states 1of 3A and A- *. The concentrations of X,, where X = 3A or X =A-‘, are expressed with the respective total concentrations, the partition function Z, and the statistical weight gl of the nuclear spin’state I, as [Xl,=

+

[Xl.

(24)

Due to the presaturation applied before the start of the photoreaction, this relation is exact for ‘A. It is also an excellent approximation for A-’ in the pre+ ent case, since relative deviations from the equihbrium populations are small because of the small .hyperllne coupling constants in the semiquinone radical anion. One defines Fi( T or F) =

T

gF,,(TorF) A

.

(25)

In an analogous manner, one performs a summation over all spin states of nuclei in D and D + * (in this work: ring protons, i4N) which are not observed and do not show a scalar coupling to the observed protons. In the following, an index i refers to the states of the remaining spin system, with their respective degeneracies gi and the partition function Z. The folIowing stoichiometric relations apply: [D+‘] = [A-‘] ,

(26)

[D]+[D+‘]=D,,.

(27)

The loss of polarization by relaxation in the donor radicals of spin state i is denoted as Lt. The terms Li canbe positiveor negative; their sum over all i is zero. Due to the presaturation [D,]+[DI+‘]+[L.]- 1-

g’D 0.

Z

(28)

M. Goez/ CIDNP in a cyclicphotoreaction

Eqs. (22) and (23) yield 2 [Dil= -kditr(1-~i(T))[D,l[3Al +kd’iW

Pt’l

+km@‘o

ID+‘1

- M)[DI

(]Di”]-

-41&l]

5 [D+*]).

9

(29)

(31)

In general, pulse excitation of nonequilibrium states (e.g., caused by CIDNP) has to be described by density matrix theory [ 59 1. However, if flip angles below 20” are used, approximately the same relative intensities of spectral lines are obtained as in slow passage spectra. For the dimethylamino group, the contributions of the different transitions to the total signal strength of the singlet are always given exactly by the CW transition probabilities, since the operator for the scalar coupling between magnetically equivalent nuclei commutates with all propagators and observable operators [ 601. With the transition probabilities P, one obtains for the integrated CIDNP signal S of the observed spin system ~=~,MPr1-[Q1).

(32)

The summation has to extend over all pairs rs where m, the value of Z,, changes by - 1 in the transition. The constant of proportionality p comprises the sensitivity of the NMR spectrometer. The sum of the intensities of all the transitions from a particular spin state of quantum number m differs from the sum of the intensities of all transitions to that state by twice the value of m [ 6 11. It is therefore possible to convert eq. (32) by pairwise combination of states n and k of equal symmetry, but opposite m into S=g, C PA,

(33)

where 4=P,l-[JAI

P,=m(n).

(m(k)=-m(n))t

(34)

(35)

One has to sum over 2 NVI pairs, if the spin system

149

consists of an odd number N of spin-l /2 nuclei. For even N, all states with m= 0 drop out, leaving 2N-1 - f (&) terms. If the spin dependent reaction probabilities I;,( T or F) and Kk (T or F) are equal between pairs of equal m ( n ) , further combination of these pairs is possible. Thus, the sum in eq. (33) comprises only three terms in the case of the dimethylamino group. This encourages further symmetrization (X = T or F, i=kor n, m(k)= -m(n)),

F,(X)=Fo~(X)+s~(m(i))Fl~(X)~

(36)

&=[D,+‘]-[Dk+‘],

(37)

A,= Ll-

Ll

(38)

9

&=[D,l+Pd

(39)

9

u,=[Dn+‘]+[Dk+‘]. Eqs. (29)-(31)

(40)

become

;A”=&+L$+fi+t&+& = -kaitr( 1+Fo.(T)) [‘Al& +k,i&d’U

[3AlG,

+kncf’on(F) P+‘lh +km,l;;n(F)P+‘l~n -kx,(~o4

+ PIL)

,

(41) (42) (43)

The second and fourth term on the right of eq. (41) describe the generation of polarization by quenching of the excited acceptor (4) and raudom*encounters of free radicals ( Sy). $ and 8 represent polarization transfer between radicals and neutral molecules by the same two reactions. The last term comprises polarization transfer by the degenerate electron exchange, and relaxation loss. So far, the relations have been exact. In order to obtain a closed form solution for the system of differential equations (21) and (41)-(43), several approximations have to be made.

M. Goes / CIDNP in a cyclic photoreaction

150

Eq. (2 1) is transformed into eq. (3) by the assumption of a constant donor concentration equal to Do. Under the conditions of most of the experiments in this work the resulting error lies well below 196,in the worst case (high light intensities and small donor concentrations) it approaches 4%. In the donor, population differences of nuclear spin states possessing opposite particle spin are much smaller than total populations. Therefore, the first term on the right of eq. (4 1) can be neglected against the second, especially as 4 starts from zero at t=O where the quenching rate has its maximum. To a very good approximation, &, may be expressed as 4=2$D,,

,

(4)

since for the spin states with m(n) and m(k) (i.e. - m ( n ) ) deviations from the starting populations are nearly symmetrical. This relation is exact at the start of the reaction; at later times the small error caused by the depletion of the donor is partly compensated by the assumption of constant donor concentration ineq. (3). As found experimentally, relaxation losses am small inDMA,so&=d,. Since [D] z+ [D+‘], the ratio of population differences to total spin populations in the radicals 6,/u, is very much larger than that in the neutral molecules A,/&. Furthermore, F,, = F,,, so the term Sy can be neglected against fi. In 4 the radical concentration [D+’ ] is replaced by the maximum radical concentration R, which may be calculated from eqs. (9), (14), or (18). Under the experimental conditions, the decrease of [D+‘] from its maximum value is small (10-2096) during the measurement time. Since * only amounts to about 20% of Q in the worst case, little error is introduced by this replacement. The donor concentration in cbis assumed to be equal to Do. The terms Fon( F). in 4 are nearly independent of IZ, so their mean value which constitutes the spin statistical factorfis substituted for them. With the described approximations and the relation 6.=-@,+A,)

(45)

resulting from eq. ( 28 ) , eq. ( 4 1) yields $.+]-‘A]-k’(d.+l.),

(46)

(47) k’=kcR,f+k,,Do.

(48)

The system of differential equations ( 3 ) , ( 46 ) , ( 42 ) and (43 ) is easily solved by a Laplace transformation. Summation according to eq. ( 33 ) finally yields an expression for the CIDNP signal S,

s=r34~w(--d)( l- &) -exp(-W(l--&)+&F},

(49)

where k= C k,P, ,

(50)

K=k’+l/Tl.

(51)

n

It is evident that the experimentally observed time dependence of the polarizations, as described at the beginning of section 3.2 is in accord with eq. (49). The fast rise of emissive signal (note that k
M. Goez / CIDNP in a cyclicphotoreaction

t

rs Fig. 3. Comparison between the mmwric solutions (solid lines) of the system of difkrential equations (21 J-(23) and the ap proximate expression of eq. (49) (dotted lines). Curves 8: 3&=l.SxlO-’ M, cmves b: ‘,4,,=7.5~10-~ M, alI curves: 4~3.2~ lo-’ M, I-=296 K, &,=2.0x lo9 M-’ I-‘, T, = 100 W

coefficient of the triplet is about an order of magnitude larger than that of the ground state quinone. However, ‘AA,can be obtained from the absolute signal intensities, if the instrumental factor p and the CIDNPparametersF,,,(T) andfareknown. The former was determined experimentally with a sample of DMA in thermodynamic equilibrium. The spatial sensitivity of the receiver coil in this measurement was assumed to be constant inside the coil, and zero outside. For the CIDNP measurements, the active volume is instead given by the sixe of the laser spot. This was determined directly with the probe head demounted. Effects of inhomogeneous beam profile and nonlinear optical absorption were neglected. An estimated error of about 2096 in 3Aoresults from this approximate treatment. The CIDNP parameters were computed with the refined m-encounter model presented by Vollenweider and Fischer [ 15 1. The mixing strength J -M=JKG%,

151

describes the amount of singlet-triplet mixing in a correlated radical pair. It can be calculated from the electronic g factors g, , g,, hfcs A f , A; in the radicals 1 and 2 with nuclear quantum numbers m i, mf , reaction distance p, interdiffusion coefficient D, magnetic field strength B. and the fundamental constants /Iand fi. The gfactor of AQ-’ is 2.0044, the hfcs are 5.5 pT (4 H) and 9.6 PT (4 H) [62]. For the unknown g(DMA+’ ), the value of the para-substituted tertbutyl derivate (2.0033 [ 631) was taken. The hfcs in the radical cation of DMA have been measured in acetic acid [ 641. It seems questionable whether the data in this protic solvent can be applied to the present problem [ 65,661, especially as other groups reported exclusive formation of benxidine in steadystate ESR experiments with the DMA radical cation [ 55,671. In an investigation of a series of pam-substituted N,Ndimethylanilines where the dimerixation does not take place, Latta and Taft [ 551 discovered an excellent linear relationship between the hfcs in the radicals and the Hammett u+ values of these compounds. Using their data, one can conclude that shouldbe 131,117,54and &I,,A~.N, &I-I ~dki 15 pT, respectively. The unavailable ApH is not crucial for the calculations, since the para proton is not observed. This hfc was assumed to be equal to AeH. The diffusion coefficient of AQ in acetonitrile (1.98x 10s5 cm2/s (681) was taken instead of the unknown one for the anion. Neither the value for DMA, nor that for DMA+ * wcm available, so that of N,Ndimethyl-paraSilllil~ compound the phenylenediamine (1.8~10~~ cm2/s [69]) was used. The Coulomb attraction between the ions was taken into account by multiplying the interditXtsion coefficient with yp (eq. (2 ) ) . The temperature dependence of D follows from the Stokes-Einstein relation [ 701 (54)

(52)

where Q=

where the viscosity 7 (in cP) for acetonitrile is [ 7 I ]

(g1-l?2)BB, 2il

lnq=T 812*4 K -3 . 795 .

(55)

(53) The molecular radii r1,2were calculated from [ 721

M. Goes / CIDNPin a cyclicphotoreaction

152

(56) with the respective molar mass M and density d (&o= 1.419 g/cm3 [73], dDm293K=0.9566 g/cm’ 1741). For a triplet born pair, the CIDNP parameters are only very weakly dependent on the initial separation r. [ 15 1. Thus a crude estimate of r. is sufficient. This was obtained from [ 75 ] ro =p+

dz

37rr7pL’

(57)

where p is twice the reduced mass of the reactants. The excess energy E was computed according to Weller [ 501. The length of a diffusive displacement was assumed as 1.7 A, the value of the exchange interaction Jo at the reaction distance as 10” rad/s, and the distance r, at which J= 10-5Jo as 2p [ 761. The electron T2 for AQ- ain solution is 1.7 ps [ 77 1. Since T2 for the radical cation is not known, the value for N,N,N’,N’-tetramethyl-para-semiquinonediimine ( 1.O us, calculated from the measurement [ 781 of m& ) was used instead. The uncertainty of the exchange interaction and its distance dependence has the strongest influence on the calculated CIDNP parameters. However, if Jo is varied between lOi and 1014tad/s, and simultaneously r, within a factor of 4, F,,(T or F) only changes by + 50% in the worst case. The triplet start concentrations obtained by the described calculations were at least a factor of 20 lower than the donor start concentrations. Under these conditions, the ion recombination term k&t, fin eq. (48 ) amounted to 20% of It’ at most. Thus, the relative error in the values of kDDextracted from the measurements is expected to be lower than 10%. 3.3. Rates of nuclear spin relaxation and degenerate electron transfer In contrast to time resolved experiments, only extremely weak signals were found in steady-state CIDNP measurements of the investigated system. This shows that with the reactant concentrations used nuclear spin relaxation in the radicals is relatively slow compared to the electron transfer reactions.

Therefore, a determination of the relaxation rates by a brute force fit with eq. (49) is numerically unstable. Instead, a set of measurements with short delays between laser flash and observation pulse was combined with one measurement 50 ps after the tlash. An rf pulse width of 0.5 us was employed in the first case to obtain the necessary time resolution. The loss in sensitivity caused by the very small values of the remaining z magnetization at long times was mitigated by sampling the final value with a n/2 pulse and averaging twice as often in the latter case. After normalization to equal pulse width and number of scans, the value of the plateau was subtracted from the time resolved CIDNP signals. The difference signal was first fitted to a function C{exp( --Kt) -exp( -bt)}, since the weight factors of the exponentials in eq. (49) differ from unity by less than 7% under the experimental conditions of this work. With the obtained approximations for Kand b a preliminary T, was calculated from the constant zmagnetization term. Insertion of the resulting weight factors into eq. (49 ) yielded improved values for the kinetic constants. Within the accuracy limits, selfconsistency was reached after the first iteration. In the investigated temperature range (237-296 K) a mean relaxation time of 103 ~.rsf 25% was found for the dimethylamino protons in D+ ‘. In view of the relatively large error of these determinations no attempt was made to extract a temperature dependence of T, from the data. Comparable relaxation times (between 90 and 120 11s)have been found by other workers for methyl [ 2 11, t-butyl [ 20,231, and benzyl [ 261 radicals. Rate constants kDDwere calcuhted with eqs. (48 ) and (5 1) from the experimentally determined K. In fg 4, an Arrhenius plot for kDD is shown. A frequency factor of 2.0 x 10’ * M-l s-l and an activation energy of 11.3 Id/m01 ( f 10%) resulted from the data. A discussion of the activation parameters for the degenerate electron exchange in DMA and several of its Pam-substituted derivatives with Marcus’ theory of outer-sphere electron transfer reactions [ 321 will be published separately [ 791.

4. conclnsions It has been demonstrated in this paper that flash

M. Goez/ CIDNP in a cyclicphotoreaction

20.0, 3.3

3.5

3.7

3.9

4.1

1OOOK T

Fig. 4. Arrhenius plot for the degenerate electron transfer (mte constant koo) between DMA and its radical cation.

CIDNP experiments allow the determination of nuclear spin relaxation times in radicals, as well as rate constants and activation energies of degenerate electron transfer reactions, even if the recombination of free radicals may not be neglected. Information obtained by this technique is complementary to that from ESR measurements, since the products are observed, not the intermediates. Disadvantages in comparison to ESR experiments are the lower sensitivity of NMR detection and the necessity to use deuterated solvents. On the other hand, time resolved CIDNP measurements yield more information about the reaction mechanism. In contrast to conventional ESR methods they are also applicable, when the radicals are not stable under steady-state conditions, as in the investigated chemical system.

Acknowledgement This work was supported by the Deutsche Forschungsgemeinschaft. Thanks are expressed to Dr. H.-G. Liihmannsriiben for helping with the LFP experiments, and to Professor Dr. H. Dreeskamp for stimulating this project.

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153

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