J. Phys. Chem. 1995, 99, 2782-2787
2782
C ~ Triplet O Excimers: Evidence from Transient Absorption Kinetics H. Thomas Etheridge, IIIJ and R. Bruce Weisman" Department of Chemistry and Rice Quantum Institute, Rice University, Houston, Texas 77251 Received: August 12, 1994@
Time-resolved absorption measurements on solutions of pure C70 in toluene reveal complex kinetics that vary strongly with sample concentration and probe wavelength. These observations suggest efficient association between triplet and ground state C70 molecules to form triplet excimers. Decay data measured with sample O monomer is at least 12 concentrations near and below 1 ,LAMshow that the intrinsic lifetime of the C ~ triplet ms. Data at higher sample concentrations are fit by a kinetic model in which triplet monomers rapidly preequilibrate with shorter-lived excimers, causing strong apparent self-quenching of the triplet excitation. The rate constants for excimer formation, dissociation, and deactivation in this model are deduced to be approximately lo9 M-' s-l, lo5 s-l, and lo4 s-', respectively. Because the equilibrium constant for association lies near lo4 M-l, many photoexcited solutions of C70 may be expected to contain not only monomer, as normally assumed, but also significant concentrations of excimer.
Introduction The rapid broadening of research into properties and reactions of fullerenes has led to deeper interest in their photoprocesses. It is now known that excitation of fullerenes by light can induce such processes as photochemical reactions,',* optical limiting b e h a ~ i o r ,and ~ , ~p~lymerization.~,~ All of these seem intriguing at a basic level and also potentially relevant to real-world applications. In trying to understand and control fullerene photochemistry and photophysics, one naturally focuses on those electronically excited states that are most abundant and persistent. It is TI, the lowest-lying triplet state, that plays the dominant role in photoprocesses of c60 and c70. For C ~ Othe , second most common member of the fullerene family, basic photophysical measurements have been reported for the rate of S1 d e ~ a y , ~the- ~quantum yield of TI formation,IO." the T, T1 absorption ~ p e c t r u m , ~and - ' ~ the T1 lifetime.7~9~10~12~'4 Even more than in the case of c60, accurate triplet lifetime measurements for C70 are hampered by interference from oxygen quenching, impurity quenching, triplet-triplet annihilation, and encounters with unexcited fullerene molecules. These effects are probably responsible for the variation, from 93 to 250 ,us, in values reported for the intrinsic T1 lifetime in room temperature solution. Previous transient absorption studies from this laboratory used sensitive detection coupled with careful oxygen exclusion and low concentration samples to obtain an improved view of C ~triplet O decay.15J6 It was found from those studies that C70's intrinsic triplet lifetime in room temperature solution exceeds 4.8 ms, that triplet excitation is efficiently and reversibly transferred between c70 and c 6 0 in mixed solutions, and that the triplet lifetime depends rather strongly on ground state concentration. We report here further, more detailed studies on pure c 7 0 solutions using a method that can be called "high-definition'' transient absorption kinetics. In this approach small induced absorptions are measured with high precision and accuracy, and the resulting kinetic traces are then fit precisely to simulated traces computed from detailed kinetic models. The kinetic data's high information content is thereby extracted to clarify subtle relaxation channels. Our studies show surprisingly
-
' Present address:
Hewlett-Packard Co., 1000 NE Circle Blvd., MS
3UE4,Corvallis, OR 97330. @Abstractpublished in Advance ACS Abstracts, February 1, 1995.
complex, concentration-dependent triplet kinetics that strongly suggest the facile formation of triplet excimers through encounters of triplet and ground state C70 molecules. We also find that the intrinsic triplet lifetime of C70 in room temperature toluene solution is at least 11.8 ms, a value 83 times longer than that of c60. From modeling of data taken at various concentrations we are able to deduce some key kinetic and thermodynamic properties of the C70 excimer. Our finding that significant quantities of triplet excimer can be formed in photoexcited C70 solutions implies that a number of prior experimental results may require reexamination.
Experimental Section Samples were prepared using 99.9+% pure c 7 0 (Bucky USA) that was stored in the dark in a low-oxygen atmosphere. HPLC grade toluene (EM Science) was further purified shortly before use by distillation from L i A l h followed by redistillation from P2O-j. Solutions prepared by adding solid C70 to the distilled solvent were transferred to a sample cell consisting of a jacketed cylindrical fused silica cuvette of 5 cm path length whose filling port had been fused to a Pyrex tube equipped with a greasefree vacuum stopcock and an O-ring flange connector. After a sample solution was introduced into the tube section, the cell was connected through its O-ring flange to a medium-vacuum system. The solution was then subjected to 12 cycles of freezepump-thaw degassing to remove dissolved oxygen. Following this degassing procedure, the cell's valve was closed and the cell was detached from the vacuum line. The sample solution was then tipped into the cuvette section and the cell was mounted in the transient absorption apparatus. Solution concentrations were determined from their absorbance at 381 nm, using the reported molar absorptivity of 29 400 M-' cm-l.l1 As shown schematically in Figure 1, the apparatus used for time-resolved absorption measurements has a Q-switched Nd: YAG laser (Lumonics HY-400) as its excitation source. Nanosecond-scale 532 nm second-harmonic pulses from this laser are attenuated by partial reflection and filtering to give pulse energies in the range 0.4-5 mJ at the sample cell. The excitation beam's diameter is approximately 6 mm. We measure excited state absorption by attenuation of a continuous diode laser beam (Uniphase Model 3501) that counterpropagates
0022-365419512099-2782$09.00/0 0 1995 American Chemical Society
c70
J. Phys. Chem., Vol. 99, No. 9, 1995 2783
Triplet Excimers
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through the excited sample volume at a slight angle to the excitation beam. The probing beam has a nearly Gaussian transverse profile, a diameter of less than 2 mm, approximately 1 mW power, and high amplitude stability. Two separate diode lasers are used to probe at 672 or 758 nm. After emerging from the sample cell, the probing beam passes through an uncoated fused silica substrate (used as a beam combiner), an iris diaphragm, and a Schott OG-570long-pass filter. It then strikes the 5 mm diameter active area of a photoconductive silicon photodiode that has been carefully baffled against stray light. A similar photodiode detects a portion of the excitation pulse to generate a zero-time trigger reference. The photodiode outputs go to the signal and trigger inputs of a Hewlett-Packard Model 54504A digitizing oscilloscope that is controlled over an IEEE-488 bus by an IBM-compatible laboratory computer. A 2.6 kS2 load resistance is normally used at the signal channel’s input to increase voltage at the expense of bandwidth. In this configuration the instrumental response function has a sharp (10 ns) rise and an exponential fall with a time constant of -1.5 ,us. For some measurements this time constant was reduced to 200 ns through the use of a shorter cable and a 1.3 kS2 load resistor. To provide greater sensitivity for induced absorption, we digitally offset the signal channel voltage to the preexcitation level and increase the oscilloscope gain. The oscilloscope averages waveforms representing transmitted probe intensity for 2048 pulses of the 10 Hz excitation laser. The resulting set of voltages in 500 time channels is then transmitted to the controlling computer for analysis. The data acquisition sequence consists of measuring four averaged wave forms: one with both excitation and probe beams blocked, to give an electronic background; one with only the probe beam open, to give an “IO” level; one with both excitation and probe beams open, to give an “I” trace showing excited-state absorption; and one with only the excitation beam open, to measure any excitation-induced background. In processing these raw data, we first subtract the electronic background from all of the others. Using these corrected wave
forms, the excitation-only scan is subtracted from the one taken with both beams open to obtain the net wave form representing induced absorption of the probe beam. We then calculate the AA trace (induced absorbance vs delay) as the negative of the base-10 logarithm of this wave form divided by the probe-only scan. Finally, the AA trace is slightly offset, if necessary, to give an average value of zero at negative delays. We have obtained consistent data with the probe beam copropagating or counterpropagating relative to the excitation beam and with a variety of beam crossing angles and sample cell positions. Our data were also unaffected by the addition of a focusing lens in front of the probe detector to compensate for possible thermal lensing effects in the sample cell. Measurements on blank samples containing only solvent show negligible induced absorbance. In addition, induced absorption data from an air-saturated solution of C70 in toluene show the expected submicrosecond decay to an accurate zero level. We have confirmed the photostability of our degassed C70 solutions under the experimental conditions by observing close agreement between repeated measurements on a single sample. We perform kinetic analysis of the induced absorbance data using a custom program that integrates the differential rate laws of any specified kinetic model. The instrumental response function is accounted for by convolution with the kinetic simulation. Each initial concentration, molar absorptivity, and rate constant in the kinetic model can be held fixed or allowed to vary while the program seeks the best fit between simulated and measured kinetic traces using the Marquardt method.16 Overlaid graphs of the data and simulation as well as a plot of the residuals are displayed on the computer monitor to allow rapid assessment of the fit quality.
Results and Discussion
Kinetics at Low Concentrations. Accurate lifetimes of longlived triplet states in fluid solution are notoriously difficult to
Etheridge and Weisman
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Figure 2. Induced absorption kinetics measured with 532 nm excitation and 672 nm probing in a sample containing 0.2 pM c70 in toluene. 3. Plot of first-order rate constant vs C70 ground state Points are measured data; the solid curve is a simulation computed as concentration as measured for room temperature toluene solutions. The described in the text. probing wavelength was 672 nm. Points show experimental data, and the solid line is a linear best fit. determine.I8 As the intrinsic triplet lifetime increases, lowconcentration impurities have greater opportunity to quench the I ' " ' ~ " ' ' ~ ' ' ~ ' ~ " " J ' ' excited state and thereby inflate the apparent rate of first-order 0.0010 decay. Even in the total absence of impurities, modest initial triplet concentrations may cause enough second-order decay 8 O.oo08through triplet-triplet annihilation to overwhelm a small firstB 9 order decay component. Systematic errors in measuring intrinsic 5 0.0006triplet decay will generally lead to deduced lifetimes that are -2 too short. 0 . m Earlier studies from this laboratory placed lower limits of 20 pM C,, in toluene 2.2 and 4.8 ms on the intrinsic first-order decay lifetime of C70 758 nm probe dissolved in aromatic ~ o l v e n t s . ' ~ JIn~ order to specify this t important kinetic constant more precisely, we have investigated O.oo00 triplet-triplet absorption in C70 solutions of higher purity and -50 0 50 Io0 150 200 lower concentration. Figure 2 shows kinetic data measured at 672 nm on a 0.2 pM solution. The solid curve drawn through Delay (1s) the data is a best-fit simulation using a phenomenological model Figure 4. Induced absorption kinetics measured with 758 nm probing that includes only concurrent first- and second-order decay. in a room temperature 20 pM solution. Second-order rate constants can be determined only with knowledge of the initial triplet concentration, which is based first- and second-order decays, such as shown in Figure 2 , our on a value for the triplet molar absorptivity. Bensasson et al." transient absorption data measured in more concentrated soluhave reported a triplet absorption spectrum of c70 in room tions using a 758 nm probing wavelength clearly reveal more temperature benzene solution that provides absolute molar complex behavior. Figure 4 shows this observation for a 20 absorptivities at 672 and 758 nm. However, their value of the pM solution of C70 in toluene. We attribute the sharp rise in ratio cmonomer~-~(672 nm)kmonomerT-T(758 nm) differs from our T1 absorption that appears as signal near zero delay to T, experimental value of 2.5. We have therefore chosen cmonomer~-~ optically excited singlet states undergo S, T1 radiationless values of 2500 M-' cm-' at 672 nm and 1000 M-' cm-' at T1 relaxation in C70 has decay. The time constant for S, 758 nm in order to match their average absorptivities over this been reported to be 0.67 ns,7,8 a value shorter than our wavelength range and also give an absorptivity ratio of 2.5. instrumental response function. Following the expected sharp Using this cmonomer~-~(672 nm) value, our kinetic simulation in initial rise component there is a surprising slower increase that Figure 2 gives first- and second-order decay constants of 113 shifts the signal maximum to a delay of 25 ps. s-l and 7.0 x lo9 M-l s-l. The initial decay is 31% first order. This secondary rise must reflect a conversion of one excited When decay data were measured and analyzed for c70 solutions species into another that has a higher molar absorptivity at the with concentrations ranging from 0.06 to 4.4 pM, we found probing wavelength. One possible mechanism for this might very similar second-order rate constants, attributed to tripletbe internal conversion to T1 from a less absorptive higher-lying triplet annihilation, whose average value was (7.0 0.3) x lo9 M-1 s-l triplet state. However, such an explanation seems highly unlikely because it would require a time scale for internal Deduced first-order decay constants are plotted as a function conversion approximately seven orders of magnitude slower than of sample concentration in Figure 3. This concentration is commonly seen. Moreover, Figure 5 shows that the seconddependence is well described by the linear fit shown as a solid ary rise kinetics depends strongly on sample concentration. This line. From the zero-concentration intercept of this line we obtain dependence suggests an underlying process that involves a new estimate for the intrinsic decay rate of C70(T1) in toluene encounters between solute molecules. If we represent the at room temperature: 85 s-l. The inverse of this value, 11.8 excited products of such encounters between triplet and ground ms, should be viewed as a revised lower limit to the intrinsic state c 7 0 molecules as triplet excimers, then the following lifetime. Kinetics at Higher Concentrations. Although prior studies simplified scheme can be considered as a model for the main of triplet kinetics in pure C70 solutions have found only simple kinetic processes: 0
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similarity of the two annihilation processes and the nearly diffusion-limited magnitude of k5. Remaining to be determined are the ratio c e x c i m e r ~ - ~ / Ponomer~-~ and the rate constants k2, k3, and b. One connection among these three rate constants can be deduced from the kinetic model. If the unimolecular deactivation constants kl and k4 are small compared to k2 [C~O(SO)] k3 , then triplet decay will occur from a preequilibrated mixture of monomer and excimer. In this case the observed first-order decay constant will be given by
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Here, step 1 represents normal unimolecular decay of the triplet state through intersystem crossing to SO. The forward process in step 2 shows the association of triplet and ground state molecules to form a triplet excimer; the reverse process is first-order dissociation of the excimer without electronic deactivation. Step 3 describes the intrinsic radiationless decay of the excimer, with a first-order rate constant different from that of the triplet monomer. Finally, steps 4 and 5 represent triplet-triplet annihilation through encounters of C70(T1) or (C70)2(T1) with another triplet. In these annihilation steps, T represents any triplet species, and [TI is defined as [C70(Tl)] [(C70)2(Tl)]. Although steps 4 and 5 could be replaced by the three specific annihilation reactions, we expect these processes to be quite similar and find comparable parameters in numerical simulations that include three separate annihilation steps. The two-step representation written above should therefore be reasonably realistic and computationally simpler. An important test of this model's validity is its ability to simulate the concentration-dependent profiles of Figure 5 . The nine parameters in our kinetic simulation are the rate constants kl through k6; the concentrations [C70(So)] and [C70(T1)]0; and E ~ ~ ~ ~ ~ ~ T - T / Ethe ~ ~ratio ~ ~ of ~ ~molar ' T - absorptivities T , for (C70)2(TI) relative to C70(T1) at the probe wavelength. Of these, the ground state concentration is known from sample preparation. The initial monomer triplet concentration is deduced from the initial induced absorbance, cell path length, and triplet-triplet molar absorptivity. Analysis of low-concentration kinetic data, described in the preceding section, provides values for kl and ks. Finally, we assume that k.5 equals ks, on the basis of the
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The slope of this self-quenching curve will be given by
In the limit of low sample concentrations the self-quenching curve will approach an intercept of kl with a slope of Ke (k4 - kl). Our measured self-quenching constant of 1.2 x 10' M-' s-l (the slope from Figure 3) must therefore equal (k2/k3)(k4 - kl). Moreover, extension of the self-quenching plot to higher concentrations reveals curvature that when modeled using eq 7 suggests values for k4 and Keq of 17 000 s-l and 7 000 M-l, respectively. Using the excimer formation kinetic model with k l , k4, k5, and k6 set to values near those determined from the above procedures while k2, k3, and E ~ ~ ~ ~ ~ ~ ~ T - are T allowed / E ~ ~ ~ ~ ~ ~ ~ T to vary, we obtain the accurate simulations drawn as solid curves through the data of Figure 5. In this set of simulations, which span a factor of 40 in ground state concentration (from 1.0 to 43.5 pM), the values of k2, k3, and E ~ ~ ~ ~ T-T ~ v"y ~ ~ T - T / by &22%,31%, and 14%, respectively. Despite these variations, which may result from neglected kinetic channels, we view the model as successful in representing the dominant processes revealed by our kinetic data. Figure 6 illustrates the two underlying time-dependent components in the simulation of the 43.5 pM data shown in
2786 J. Phys. Chem., Vol. 99, No. 9, 1995
Etheridge and Weisman
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comparison. Solid curves are simulations computed as described in the text.
Figure 5 . Immediately after excitation only the triplet monomer is present. Then, during the first few microseconds, encounters between these triplets and ground state C ~ molecules O create excimers at the expense of triplet monomers. This conversion process increases the measured signal because the excimer's molar absorptivity at the 758 nm probing wavelength is approximately 3 times that of the monomer. After a delay of 30 or 40 ps the ratio of excimer to triplet monomer concentration has stabilized at its preequilibrated value. From then on, decay of the pool of triplet excitation occurs with an effective firstorder rate constant intermediate between the values of kl and k4.
A valid model must also account for the dependence of observed kinetics on probe wavelength. Figure 7 illustrates the large difference between induced absorption traces measured on a 20 pM solution with probing wavelengths of 672 and 758 nm. The computed fits shown in this figure accurately simulate the data using the excimer formation model. In these fits the ratio cexcimerT-T/cmonomer T-T, which is expected to vary with wavelength, equals 1.3 at 672 nm and 3.2 at 758 nm. Individual rate constants differed by less than 7% between the two simulations. We conclude that the excimer model adequately describes the wavelength dependence as well as the concentration dependence of our kinetic data. Interpretation of Kinetic Parameters. The deduced kl value of 85 s-l sets a revised lower limit of 11.8 ms for the intrinsic decay lifetime of C70 in room temperature toluene solution. We note that this lifetime value is only a factor of 4.5 shorter than the 53 ms triplet lifetime reported for C70 in cryogenic solid solutions,14in which bimolecular quenching should be entirely absent. Evidently, the temperature dependence of kl is weak. We also note that in room temperature toluene solutions the intrinsic triplet lifetime of C70 exceeds that of Cm by a factor of more than 80.15The source of this difference remains to be explained. Rate constants k2 and k3 define the preequilibrium between monomer and excimer. Their ratio is an equilibrium constant whose value, which seems to fall in the 5000-15 000 M-' range, dictates an equal partitioning of triplet excitation between the two forms at a ground state C70 concentration of ca. 100 p M . From our kinetic modeling we find values for k2 and k3 near 1 x lo9 M-' s-l and 1 x lo5 SKI, respectively. Note that the large value of k3 ensures that preequilibration will be rapid compared to the first-order deactivation of monomer or excimer, justifying the assumption used in deriving eqs 6-8. The value
of k2 helps to confirm that it is indeed the ground state of C70 that interacts with C70(T1) in step 2 of our kinetic model. If the interacting species were an impurity in the solvent, then its concentration would remain constant with fullerene concentration, and our deduced values for k2 would appear to vary as [C,, (S0)I-l. Such a variation is not observed. If the species were an impurity in the solute, then even if it interacted with the C70 triplet state at a diffusion-limited rate, it would have to compose 10% of the solute to give the measured k2 value. The high purity of our C70 sample excludes this explanation. Only the c 7 0 ground state remains as a plausible reactant in step 2. Deactivation of the triplet excimer is described by k4. whose value seems to be approximately 17 000 s-l. Because this rate constant so greatly exceeds kl, the total loss of triplet energy is accelerated at higher ground state concentrations to give a large apparent self-quenching constant. According to our model and deduced rate constants, C70 excimers lose their electronic excitation by intersystem crossing at one-sixth the rate that they dissociate into ground state and triplet monomers. Although singlet excimers of organic compounds are wellknown in fluid solution, triplet excimers have remained relatively elusive. A recent photophysical study of N-ethylcarbazole by Haggquist and Burkhart presents evidence for the presence of triplet excimers formed through recombination of geminate ion pairs.19 Cai and Lim have reported emission from triplet excimers of the polar compounds carbazole, dibenzofuran, and dibenzothiophene.20.21In addition, Kozlowski and coworkers have proposed that triplet excimer formation underlies the nearly diffusion-limited self-quenching observed for an aromatic thione.22 The situation for triplet excimers of nonpolar aromatic hydrocarbons is more controversial, however. Excimer phosphorescence was reported from phenanthrene solutions in 1968,23but recent searches for triplet excimers of naphthalene have produced both p ~ s i t i v e and ~ ~ -negative ~~ finding^.^^.^^ We note that although C70 is nonpolar, it differs from aromatic hydrocarbons in having much lower-lying excited electronic states and a smaller difference between its electron affinity and ionization potential. Such a reduced difference has been predicted to increase the charge resonance stabilization of a triplet e ~ c i m e r . ~ ~ Further measurements covering a range of temperatures and aliphatic as well as aromatic solvents need to be performed to clarify the properties of C70 excimers. Such experiments may also reveal the need to modify the kinetic model suggested here. Important insights might also be obtained from spectroscopic probes capable of giving structural information about the excimer, and from quantum chemical calculations capable of predicting its geometry and electronic structure.
Conclusions We have deduced that the efficient apparent "self-quenching" in C ~ solutions O masks a more complex process involving rapid formation, dissociation, and deactivation of triplet excimers. Because these excimers have a visible absorption spectrum that is similar to that of C70(T1) (at least near our red probe wavelengths), the observed decay behavior can resemble a weighted average of the long-lived triplet monomer and the shorter-lived excimer. In this interpretation it is the changing balance of these species with ground state concentration that gives efficient self-quenching. Our analysis clearly shows that the C70 monomer's intrinsic lifetime is even longer than had been reported earlier: -12 ms in room temperature toluene solution. The dramatic difference between intrinsic T1 lifetimes of Cm and C70 remains to be understood. Our findings show that important photophysical effects may remain hidden without precise, multiwavelength experimental
c70
Triplet Excimers
studies. In addition, the results have significant implications for fullerene photophysics. We note first that self-quenching also appears to be quite efficient in c 6 0 solutions, suggesting that a search should be made for evidence of triplet excimer formation in c 6 0 . Second, a c 7 0 excimer seems a plausible intermediate species in the recently reported photopolymerization of c 7 0 films.6 Third, the experimental conditions used for prior measurements on the c 7 0 triplet in fluid solution should be examined to determine what fraction of the monitored C 7 0 might actually have been present as triplet excimers rather than the presumed triplet monomers. As an example, the triplet energy transfer kinetics reported from this laboratory for mixtures of C70 and c 6 0 will be reanalyzed to take into account the more complex behavior of pure C70.15 Finally, any future projects involving photochemistry or photophysics of C 7 0 in solution should be designed with the view that many experimental conditions may lead to excited aggregates as well as excited monomers.
Acknowledgment. This research was supported by the National Science Foundation and the Robert A. Welch Foundation. We are grateful to Kevin Ausman for expert refinement of the kinetic fitting program. References and Notes (1) Zhang, X. J.; Romero, A.; Foote, C. S. J. Am. Chem. SOC. 1993, 115, 11024. (2) Heymann, D.; Chibante, L. P. F. Chem. Phys. Lett. 1993,207,339. (3) Tutt, L. W.; Kost, A. Nature 1992, 356, 225. (4) Wray, J. E.; Liu, K. C.; Chen, C. H.; Garrett, W. R.; Payne, M. G.; Goedert, R.; Templeton, D. Appl. Phys. Lett. 1994, 64, 2785. ( 5 ) Rao, A. M.; Zhou, P.; Wang, K.-A,; Hager, G. T.; Holden, J. M.; Wang, Y.; Lee, W. T.; Bi, X.-X.; Eklund, P. C.; Comett, D. S.; Duncan, M. A,; Amster, I. J. Science 1993, 259, 955.
J. Phys. Chem., Vol. 99, No. 9, 1995 2181 (6) Rao, A. M.; Memon, M.; Wang, K.-A.; Eklund, P. C.; Subbaswamy, K. R.; Comett, D. S.; Duncan, M. A.; Amster, I. J. Chem. Phys. Lett. 1994, 224, 106. (7) Tanigaki, K.; Ebbesen, T. W.; Kuroshima, S . Chem. Phys. Lett. 1991,185, 189. (8) Kim, D.; Lee, M.; Suh,Y. D.; Kim, S. K. J. Am. Chem. SOC.1992, I1 4, 4429. (9) Palit, D. K., Sapre, A. V.; Mittal, J. P.; Rao, C. N. R. Chem. Phys. Lett. 1992, 195, 1. (10) Arbogast, J. W.; Foote, C. S. J. Am. Chem. SOC.1991,113, 8886. (11) Bensasson, R. V.; Hill, T.; Lambert, C.; Land, E. J.; Leach, S.; Truscott, T. G. Chem. Phys. Lett. 1993, 206, 197. (12) Dimitrijevic, N. M.; Kamat, P. V. J . Phys. Chem. 1992, 96, 4811. (13) Lee, M.; Song, 0.-K., Seo, J.-C.; Kim, D.; Suh, Y. D.; Jin, S . M.; Kim, S. K. Chem. Phys. Lett. 1992, 196, 325. (14) Wasielewski, M. R.; O'Neil, M. P.; Lykke, K. R.; Pellin, M. J.; Gruen, D. M. J. Am. Chem. SOC. 1991, 113, 2774. (15) Fraelich, M. R.; Weisman, R.B. J. Phys. Chem. 1993, 97, 11145. (16) Etheridge, In, H. T.; Fraelich, M. R.; Weisman, R. B. in Fullerenes: Physics, Chemistry and New Directions, VI; Kadish, K. M., Ruoff, R. S., Eds.; The Electrochemical Society: Pennington, NJ, in press. (17) Bevington, P. R. Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill: New York, 1969. (18) Linschitz, H.; Steel, C.; Bell, J. A. J. Phys. Chem. 1962,66, 2574. (19) Haggquist, G. W.; Burkhart, R. D. J. Phys. Chem. 1993,97,2576. (20) Cai, J.; Lim, E. C. J. Phys. Chem. 1992, 96, 2135. (21) Cai, J.; Lim, E. C. J. Chem. Phys. 1992, 97, 3892. (22) Kozlowski, J.; Maciejewski, A,; Szymanski, M.; Steer, R. P. J. Chem. Soc., Faraday Trans. 1992, 88, 557. (23) Langelaar, J.; Rettschnick, R. P. H.; Lambooy, A. M. F.; Hoytink, G . J. Chem. Phys. Lett. 1968, 1, 609. (24) Lim, E. C. Acc. Chem. Res. 1987, 20, 8. (25) Locke, R. J.; Lim, E. C. Chem. Phys. Lett. 1987, 138, 489. (26) Locke, R. J.; Lim, E. C. Chem. Phys. Lett. 1989, 160, 96. (27) Nickel, B.; Rodriguez Prieto, M. R. Chem. Phys. Lett. 1988, 146, 125. (28) Huttmann, G.; Staerk, H. J. Phys. Chem. 1991, 95, 4951. (29) Guillet, J. Polymer Photophysics and Photochemistry; Cambridge University Press: New York, 1985. JF'9421545
