9310
J. Phys. Chem. 1992, 96, 9310-9315
(29) Benzon, S. W.; O"ea1, H. E. Kinetic Data on Gas Phase Unimolccular Reactions. NSRDS-NBS-21, U S . Dept. Commerce: Washington, DC, 1970. (30) Batt, L. In?. J. Chem. Kine?. 1979, 11, 977. (31) Benson, S.W. ThermochemicalKinetics, 2nd ed.;Wiley: New York, 1976. (32) (a) Indritz,D. PhD Thes!, Princeton University, Princeton, NJ, 1978. (b) Indritz, D.; Rabitz, H. A.; Wdhams, F. W. J. Phys. Chem. 1977,81,2526. (c) Indritz, D.; Sheinson, R. S.;Williams, F. W.; Durant, J. L.; Rabitz, H. A.. Bogan, D. J. Procttdings of the Eastern States Section; The Combustion Institute, Pittsburgh, PA, Nov 1977. (d) Bogan, D. J. Unpublished work. (33) Westley, F.; Herron, J. T.; Cvetanovic, R. J.; Hampson, R. F.; Mallard, W. G. NIST Standard Reference Database 17, Chemical Kinetics Database, Version 3.0. data coverage through 1990, U S . Dept. Commerce, Gaithersburg, MD, 1991. (34) Keiffer, M.; Pilliig, M. J.; Smith, M. J. C. J. Phys. Chem. 1987,91, 6028. (35) Harding, L. B.; Goddard, W. A., 111 J. Am. Chem. Soc. 1980,102, 439. (36) Miller, R. G.; Lee, E. K. C. J. Chem. Phys. 1978,68,4448. (37) Halpern, A. M.; Ware, W. R. J . Chem. Phys. 1971, 54, 1271. (38) Grcenblatt, G. D.; Ruhman, S.; Haas, Y. Chem. Phys. Le??.1984, I12,200. (39) Copeland, R. A.; Crosley, D. R. Chem. Phys. Lett. 1985,115, 362. (40) Zazlonko, I. S.; Mukoseev, Yu.K.;Tyurin, A. N. Kinet. Curd. 1988, 29, 244 (original Russian, p 283). (41) Data and sources for Figure 1. Values of AI6'm in kcal/mol are as follows: 2,3-dimethyl-2-butene, -14.2 (ref 18); acetone, -52.0 (ref 18); tetramethyl-lJdioxetane, -35 (refs 8a, 16, 19). Excitation energies in kcal/mol are as follows: OZ('&), 22.6 (ref 20); acetone (TI), 78; acetone (SI),85 (ref 2lb). Activation energies in kcal/mol are as follows reaction la, 8.6 (this work); reaction Ib, 26 (ref Id). (42) Data and sources for Figure 6. All ionization potentials were taken
from: Lias, S.G.; Bar", J. E.; Liebman, J. F.;Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data 1988,17, Supplement No. 1. The values, in eV, are as follows: ethene, 10.51; 2,3-diiethyl-2-butene,8.27; 2-methyl-l-(N,N-dimethylamino)propene, 8.15; methoxyethene, 8.93; ethoxyethene, 8.80; 2-methoxypropene, 8.64; ketene, 9.61; allenc, 9.69; chloroethene, 9.99, l,l-dichloroethene, 9.90, fluoroethcne, 10.36; l , l d ~ ~ o c t h c n e , 10.29; trifluoroethene, 10.14; tetrafluoroethene, 10.12. The cycloaddition activation energies, in kcal/mol, are as follows: ethene, 21.4 (ref 8b,c); 2,3-dimethyl-2-butene, 8.6 (this work); 2-methyl-l-(NJV-dimethylamino)propene, 2.6 (ref 8b); methoxyethene, 13.5 (ref 8b); ethoxyethene, 12.5 (ref 8b); 2-methoxypropene, 11.8 (ref 8b); ketene, 15.3 (ref 8b); allene, 18.6 (ref 8b); chloroethene, 15.5 (ref 8a); 1.1-dichloroethene, 16.9 (ref Sa); fluoroethene, 18.3 (ref 8a); 1,l-difluoroethene, 16.3 (ref 8a); trifluoroethene, 15.6 (ref Sa); tetrafluoroethene, 17.9 (ref 8a). (43) Data and sources for thermochemistry, eqs 4, 7, and 8. Acetone, O#&), and TME were taken from ref 41. Methyl and hydroxyl radicals were taken from Baulch et al. (Baulch, D. L.; Cox, R. A.; Hampson, R. F., Jr.; Kerr,J. A.; Troe, J.; Watson, R. T. J . Phys. Chem. Ref. Data 1984,13, Supplement 2, 1259) as was ethylene @298(C-H) = 108 kcal/mol used to estimate &I(2-propenyl) = 60 kcal/mol. The following standard enthalpies of formation in kcal/mol were estimated by using group additivity rules according to ref 3 1: 2,3-dimethyl-3-buten-2-01, -57; 2,3-dimethyl-3-hydroperoxy-1-butene, -40; 3-methyl-3-buten-2-one, -36. The estimate for 2,3dimethyl-3-buten-2-01together with @2g8 (alcohol &H) = 104 was used to obtain Ad@r(2,3-dimethyl-3-buten-2-oxy radical) = -5. One of the group values used was not available from ref 31 and was estimated. This was grOup[C(O)(Cd)(C)z] -5.1 = 1.5 grOUp[c(o)(c)~]. This basis Of the estimate is that Benson" has given two examples of group valuca where the effect of a similar substitution of cd for C can be obtained. In one case = 1.6 + gro~p[C(0)(C)(H)~], and in the other case, gro~p[C(O)(C~)(H)~l grouP[C(CO)(Cd)(H)z = 1.4 -+ group[C(CO)(C)(HM. (44) Benson, S.W.; Nangia, P. S . Acc. Chem. Res. 1979, 12, 223. (45) Sheinson, R. S.;Williams, F. W.Combust. Flame 1973, 21, 221.
Photooxidation of Zinc Tetraphenyiporphyrin by Benzoquinone: A Fourier Transform Electron Paramagnetic Resonance Investlgation Mane Ebersole,+Patricia R. Levstein,* and Hans van Wagen* Department of Chemistry, University of Massachusetts at Boston, Boston, Massachusetts 02125 (Received: April 13, 1992; In Final Form: August I I , 1992)
Fourier transform electron paramagnetic resonance (IT-EPR) has been used to study the photooxidation of zinc tetraphenylporphyrin (ZnTPP) by benzoquinone (BQ). A method was developed for the analysis of the time dependence of the IT-EPR spectra, following pulsed laser excitation of ZnTPP, that gives rate constants for the electron-transferprows as well as for the spin-polarization evolution in paramagnetic species involved in the reaction. It is found that the rate constant of electron transfer from photoexcited triplet ZnTPP to BQ in ethanol is concentration dependent. The data yield a value for the electron-transfer-reactionradius of triplet ZnTPP, the limiting rate constant that would obtain for [BQ] 0, and the radical pair lifetime. In addition, values are found for the spin-lattice relaxation times of the BQ- anion radical and triplet porphyrin precursor and for electron transfer from BQ- to BQ.
-
Lntroduction Fourier transform electron paramagnetic resonance1(FT-EPR) has proven to be ideally suited for time-resolved studies of photochemical reactions generating (transient) free The method can be used to identify free radicals and to determine the kinetics of their formation and decay. Furthermore, the time evolution of the spectra is determined, in part, by chemically induced electron polarization (CIDEP) mechani~ms.~These CIDEP effects give an insight into reaction mechanisms and can be used to derive information on spin-state dynamics of paramagnetic species involved in photoinitiated reactions. A number of FT-EPR studies have been concerned with photoinduced electron transfer from zinc tetraphenylporphyrin (ZnTPP) to duroquinone (DQ) in ethanol.24 The measurements have yielded values for the rate constant (keJ of the electrontransfer reaction, the spin-lattice relaxation time ( TIR) of the 'Present addrew Freie Univcrsitiit Berlin,Institut for Experimentalphysik, lo00 Berlin 33, Germany. $Present address: INTEC, Giiemcs 3450,3000 Santa Fe, Argentina.
0022-365419212096-9310$.03.OO/0
quinone anion radical, the spin-lattice relaxation time (TIT) of (precursor) photoexcited triplet ZnTPP (3ZnTPP*), and the lifetime of the transient radical pair [ZnTPP+*--DQ-]. The work described here concerns a detailed FT-EPR study of the photoinduced electron-transfer reaction from ZnTPP to benzoquinone (BQ) in ethanol. The objective of the study was to develop and apply a comprehensive method of data analysis that would give the values of all parameters that control the time evolution of the FT-EPRspectra. Of interest as well was the resolution of questions regarding rate constants derived in earlier work. For instance, for ZnTPP/DQ in ethanol a k, value of 6 X 109 M-' s-' has been rep~rted.~ This value is sisnificantlyhigher than the rate amstants for electron transfer involving ZnTPP/BQ'O (1.25 X lo9 M-'s-' ) and ZnTPP/DQ" (2.0 X lo9 M-' s-' ) obtained with timetesolved optical spectroscopy. A detailed study of ZnTPP/BQ in ethanol with time-resolved direct detection CW EPR gives 1.25 X lo9M-' s-' at 230 K." Moreover, valuca given for TITof 3ZnTPP* at -250 K range from 505 to 460 ns.3 The lack of agreement between the published values may stem from differences in experimental conditions. Another cause for the Q 1992 American Chemical Society
FT-EPR Study of Photooxidation of ZnTPP by BQ
The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 9311
discrepancies may be the method of analysis of the FT-EPR data. The results presented here show that the electron-transfer rate constant depends on acceptor concentration. The effect can be accounted for with the model for diffusion-controlled excited-state quenching proposed by Stevens.I3 When corrected for the concentration effect, the value of ka derived from FT-EPR spectra is in close agreement with the value given by flash photolysis measurements. The dependence of kd on acceptor concentration is used to determine the reaction radius of 3ZnTPP* and to estimate the radical pair lifetime. A detailed analysis of the time dependence of the amplitudes of three hyperfine components in the spectra of the BQ anion radical from four ZnTPP/BQ samples gives a value of TIT(28 f 10 ns at room temperature) which is in close agreement with the value obtained in the study of ZnTPP/DQS5 It is found that acceptor concentration also affects the apparent T I Rof BQ-. This is attributed to the homogeneous electrontransfer reaction BQ-
+ BQ
lOOOOns L
h
50011s A
Data Analysis Method Figure 1 shows representative FT-EPR spectra from BQ-, generated by photoinduced electron transfer from ZnTPP, for a series of laser pulse-microwave pulse delay-time settings. The spectra were obtained by Fourier transformation of the fid’s followed by the application of a phase correction. The phase correction applied to all 10 spectra was the one that gives two absorption and three emission peaks in the 7d = 1.5 ps spectrum. For 7d < 500 ns the spectra exhibit a dispenive signal contribution. This is attributed to the presence of radical pairs at the time the microwave pulse is delivered. The effect has been discussed in an earlier paper” and will not be considered in this work. As noted previously~the short T2of the counter radical Z n T p P precludes its detection. Of interest in this study is the 7d dependence of the amplitudes of the f i e hyperfine components.To extract numerical data, each fid was processed with two software routines originally developed by Barkhuijsen, De Beer, and van O n n ~ n d t : ’(1) ~ a linear prediction-ingular value decomposition (LP-SVD) routine and (2)
Y
150ns
L A
1 ions
-20
v-
I
1
-10
20
10
0 MHz
Figure 1. FT-EPR spectra of photogenerated BQ- in an ethanol solution of ZnTPP (lo-‘ M)and BQ (lW3 M)for a serk of delay time settings between laser pulse and microwave pulse. Absorption peaks point up; emission peaks point down. Note that the display corresponds to a decrease in magnetic field going from left to right.
ExperimentalSection
ps.
v
v
1500ns
BQ + BQ-
Zinc was inserted into meso-tetraphenylporphine (Strem Chemicals) using published methods.14 ZnTPP was purified by column chromatography and purity was checked with UV-vis spectroscopy. BQ (Aldrich) was purified by vacuum sublimation. Ethanol (10096, Pharmco and Warner-Graham) was used as purchased. Solutions of ZnTPP (1.O X lo4 M) and BQ (0.6 X to 3.0 X M) in ethanol were degassed by several f m p u m p - t h a w sequences on a high-vacuum line (finalpressure Torr or better) and sealed off. When stored in a freezer, samples could be used over a period of months. FT-EPR spectra were recorded with a homebuilt spectrometer described previ~usly.~ The microwave pulse width used was 15 ns, and the free induction decay (fid) of the magnetization was sampled (with two channel quadrature detection) at 200 megasamples/s. A CYCLOPS phase-cycling routine was applied to compensatefor any imbalance in the two detection channels.’ The final signal is the average of 4OOO fid’s (1 0oO per phase) acquired at a repetition rate of 40 Hz. Electron transfer was initiated with a Lambda Physik FL3001 dye laser (560 nm, 2 mJ/pulse, pulse width -15 ns) pumped by a Lambda Physik EMG103 MSC XeCl excimer laser. The time evolution of IT-EPR spectra is monitored by recording the fid for each one of 30 or so delay time (7d) settings between laser and microwave pulses. The 7 d values ranged from 10 ns to 10
“
A
3000ns
-.
Homogeneous electron transfer contributes to the line width as well. Both effects can be used to measure the rate constant of this reaction. Finally, the measurements give information on the magnitudes of the spin polarization generated by CIDEP mechanisms.
.A
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60
i
I
I
I
I
.’
‘b b
-100 101
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102
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103
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104
TIME (ns)
Figure 2. Time evolution of the amplitudes of the hyperfine components (v,+2; e, +l;A, 0;4 -1; and 0 ,-2) in the BQ- spectrum. The dashed lines represent the result of a least-squares fit of the data points to eq 1.
an iterative nonlinear least-squares method that uses the variable projection (VARPRO) principle. These two programs applied in succession give the frequencies, line widths, phases, and amplitudes of the five hyperfine lines in the EPR spectrum of BQ-. Figure 2 depicts the evolution of the amplitudes of the five hyperfine components given by the LP-SVD/VARPRO analysis of the fid’s given by a sample of ZnTPP (10-4 M) with BQ (1.O X M) in ethanol. The convoluted time dependence of signal amplitudes reflects chemical kinetics, CIDEP effects, and spinlattice relaxation. With the acceptor concentrations used in the measurements, electron transfer involves 3ZnTPP* produced by intersystem crossing from the singlet excited state. Intersystem crossing is a spin-selective process and, in the case of ZnTPP, creates excess pulation in the MS= -1 (T-l) electron spin state of the trip1et.l In the electron-transfer events, spin is conserved and reactions involving 3ZnTPP* in the TPl and T+l spin states give anion radicals with B and a spin statca, respectively. If the rate of electron transfer is of the same order as the triplet spinlattice relaxation rate, triplet spin polarization is camd Over to the doublet radicals. It gives rise to what has been labeled triplet mechanism (TM) CIDEP.9J7 In the reaction considered here, TM CIDEP manifests itself in the form of enhanced absorption signals. Since TM CIDEP is independent of nuclear spin state, the hyperfine components in the BQ-spectrum retain the binomial intensity distribution (1:4641). In Figure 1, the spectra obtained with 7d < 100 ns are dominated by TM spin polarization. Additional spin polarization is developed by electron-transfer events from the 3ZnTPP* To state. The spin state of the radical
P
9312 The Journal of Physical Chemistry, Vol. 96, No. 23, 1992
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levels (T+I,TO, T-1).
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Here, [ATl0 represents the difference between the spin populations of the T-l and T+l triplet sublevels at the time the triplets are formed and [Tolorepresents the initial TOspin population. S = S, denotes the signal amplitude obtained when the system is at thermal equilibrium (t -). In the form the triplet spin-lattice relaxation is introduced in the derivation, it will drive the triplet state to zero spin polarization. Since the TM spin polarization far exceeds the triplet spin polarization at thermal equilibrium? this simplification will not affect the result of the data analysis significantly. The model does not take the back-electron-transfer process into account. At the doublet radical concentrations produced, this proteas does not play a significant role in the time domain considered here.
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pair formed by encounter of donor and acceptor evolves under the influence of the difference in Larmor frequencies of the unpaired electrons and their exchange interaction. As a consequence, electron transfer involving Ms = 0 triplets generates spin polarization in the doublet radicals. This CIDEP effect, which is known as the radical pair mechanism (RPM), gives rise to nuclear spin-state dependent CIDEP.9v18 The schematic diagram presented in Figure 3 summarizes the praxsses that detemine the time dependence of the BQ-spectrum. It illustrates the model that forms the basis for the data analysis. The model is based on the fact that signal amplitude is a measure of the population difference between @ and a electron spin states in B Q at the time the microwave pulse is delivered. The diagram identifies the possible sources for quinones with each spin state. For example, radicals with +1/2 spin can be produced by electron transfer from a porphyrin triplet in the T+I sublevel with rate constant k,, or from the To sublevel through the RPM with a rate constant ak,,. In a like manner, quinones with -1/2 spin can be produced by electron transfer from a porphyrin in the TV1sublevel of the triplet, also with rate constant k,, or from the To sublevel through the RPM, with rate constant @k,. The rate constant is assumed to be the same for each triplet sublevel so that aket @kd = ka. The values of a and B are nuclear spin-state dependent. As all measurements were performed on samples in which the acceptor is in large stoichiometric excess, k, represents a pseudo-first-order electron-transfer rate constant. Spin-lattice relaxation drives the spin populations in 3ZnTPP* and BQ- toward a Boltzmann distribution with rate constants kT1rand kTI? respectively. The equation giving the time dependence of the signal amplitude for an individual hypefitne line can be derived by solving the differential equations describing contributions from all these processes to the population difference between the two electron spin states of the anion radical: S, = P exp[-(ket+kT,T)t] + Q exp(-k,,it) R exp(-kat) + S
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equation do not reflect a physically realistic situation. Stevens has notedl3that an exciteai-state molecule is m a t likely quenched by its nearest-neighbor quencher. Therefore, he proposes that the flux equation should be solved on the basis of the assumption that the quencher concentration gradient extends only to a dhtancc r, from the excited-state molecules. Here r, denotes the most probable initial nearest-neighbor separation. This model gives an equation for the quenching rate constant kq that includes the reaction radius, R , as well as r,,,,?
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The most probable nearest-neighbor distance is given by r,, = (2rNc)-'/', where c is the quencher concentration and N is Avogadro's number. Hence, the rate constant is a function of quencher amcentration. The equation reverts to the Smoluchowski equation2' at low quencher concentration (rnn>> R ) . Equation 3 predicts that there is a linear dependence of the inverse of the quenching rate constant on c l P
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reaction radius. However, this explanation cannot be correct, because it nquires a reaction radius of -44 k the most probable nearest-neighbor distance for an acceptor concentration of 3 mM. A more likely explanation is that at high [BQ]the rate of donor-acceptor encounters approaches or even exceeds the rate of separation of the radical pair (kwp). In that case the measured electron-transfer rate is not determined exclusively by the encounter rate. A test of this hypothesis is to assume that for [BQ] = 3.0 X lO-' M the measured reaction rate is completely determined by the radical pair lifetime kq-l. This assumption gives a radical pair lifetime of 83 M. The value is in good agreement with the lifetime of 100 ns derived from radical pair signal contributions to FT-EPRspectra of the duroquinone anion radical p r o d u d by electron transfer from ZnTPP.6 From this it is concluded that the leveling off of the rate constant i n d d reflects the fact that cage escape becomes the ratedetermining step. Division of the pudo-fd-order rate constants by the acceptor concentrationsdoes not yield a fmed seamd-order rate constant even in the regime where cage escape does not play a role (cf. Table I and Figure 5B). The rate constants show a significant increase as [BQ]increases from 0.6 to 2.0 mM. Similar results have been obtained in fluorescence quenching studies.sz2 The Smoluchowski equation2)for the rate constant of diffusion-controlled reactions cannot accoullt for this amcentration effect. The failure of the Smoluchowski equation can be attributed to the fact that the boundary conditions used in the solution of the flux
have shown that thisequation accounts satisfactorily for the concentration dependence of fluorescence quenching. The interpretation of the experimental data gives realistic estimates of the relative diffusion coefficients D and reaction radii R . Figure 6 gives a graphical representation of the application of eq 4 in the analysis of the second-order electron-transfer rate collstantp given in Table I. (The data point for [BQ]= 3 X lO-' M has been excluded, vide supra.) It is apparent that there is indeed a linearr c l a t i d p betweenthe inverse of the rate constant and [BQ]1/3. A linear least-squarea fit gives a line with slope -2.50 X 10-9 M2/' s and y-intercept 4.99 X 10-lo M s. The coefficient of determination (the fraction of the variation in y that is a result of variation in x ) for this line is 0.960. The reciprocal of the y-intercept, (2.00 f 0.05) X lo9 M-' s-l, represents the value for the rate constant of electron transfer at infinite dilution of BQ, Le., under the condition that R
