J. Phys. Chem. 1991,95, 5529-5532
5529
Picosecond Transient Absorption Measurements of Gemlnate Electron-Catlon Recombination Charles L. Braun,* Sergei N. Smirnov,f Steven S. Brown, Department of Chemistry, Dartmouth College, Hanouer, New Hampshire 03755
and T. W. Scott* Corporate Research Science Laboratories, Exxon Research and Engineering Company, Annandale, New Jersey 08801 (Received: January 17, 1991) Durene (1,2,4,5-tetramethylbenzene)dissolved in n-hexane was photoionized by 35-ps light pulses at 266 nm. Transient absorption at 1064 nm arising chiefly from geminate electrons was detected and used to monitor the recombination of the electron-cation pairs produced by two-photon ionization. An excellent fit to the recombination kinetics at 208 K was obtained by assuming that the distribution of initial electron-ation separations was of the form 9EXP = 9/(2L3) exp(-r/L) with a mean radius 3L = 5.7 nm.
Introduction Photoionization of molecules in condensed media leads to the creation of excess electrons which are expected to thermalize in less than 1 p.' In liquid hydrocarbons, thermalization distances are found to be in the range 2-1 5 nm.2-5 Because these initial separations of the electron and cation are much smaller than the Onsager radius r, = $/(4meok7'), the distance at which the Coulomb binding energy equals kT,a majority of the electrons recombine with their parent cation radicals, Le. geminately. The recombination kinetics of geminate electron-tion pairs depend on the initial separation only for times much shorter than r 2 / D where D, the sum of electron and cation diffusion constants, is dominated by the large diffusion constant of the electron.&' The first picosecond rec~mbination'*~.~ experiments on the geminate electron-cation pairs produced by photoionization were done with a highly sensitive conductivity techniq~e.~ With this method, it was shown that (a) there are no long-lived (>5 ps) precursors of the geminate charge pairs,' (b) the diffusion constant of the electron as measured in timeof-flightmobility experiments governs the recombination kinetics? and (c) the distribution g(r) of initial cation-electron separations is fairly b r ~ a d . ~ . ~ Despite the high sensitivity of the conductivity technique, it suffers from probable bias8 in detecting geminate pairs of varying radii. Thus, attempts were made to record the picaaxnd kinetics of geminate electro-tion recombination using optical absorption by geminate electr0ns1Oor cations." Those experiments suffered from high levels of interfering transient absorption produced by background neutral states. A similar problem appears to exist for the femtosecond experiments on ionization of neat octane by Bowman et aI.l2 although their isooctane decay curve may be largely free of extraneous absorption. Here we report picosecond transient absorption measurements of geminate electron kinetics in cold liquid hexane along with the temperature dependence of the photocurrent produced by pairs that separate. Geminate pairs were produced by two-photon photoionization of 1.2.4,s-tetramethylbenzene (durene) at 266 nm. We show that the decay kinetics can be fitted by Hong and Noolandi's solution' of the timedependent Onsager problem with exp(-9/G2) ') or GEXP = either the JJGAUSS = 4 9 5 / ( ~ ~ / ~ G G/(2L3)exp(-r/L) initial distribution of electron-cation separations. However, the GEXP function allows a somewhat better fit. In either case, the distribution function gives the probability that the initial separation (thermalization radius) lies between r and r + dr. To whom correspondenceshould be a d d r d . Permanent address: Institute of Chemical Kinetics and Combustion, Novaibink 630090. USSR. *Permanent addreas: Department of Chemistry, New York University, New York, NY 10003.
OO22-3654/91/2095-5529$02.50/0
Experimental Section The laserg and the apparatus used for photocurrent measurem e n t ~have ~ * ~been described earlier. Transient absorption experiments employed 35-ps pulses of 0.24.6 mJ at 266 nm. The excitation pulse was focused by a 1-m lens to a diameter of about 0.5 mm. The IR probe beam at 1.06 pm was attentuated to approximately 5 pJ. n-Hexane from Burdick and Jackson (UV cut at 192 nm), durene (1,2,4,5-tetramethylbenzene) from Matheson, Coleman and Bell (quality I), and perfluorohexane (PFH) from Aldrich were used without additional purification. Both conductivity and absorbance experiments could be made in the same cell, which had an electrode gap of 0.8 mm and a light path length of 1.O cm and was constructed of Macor ceramic and stainless steel. Solution was continuously flowed through the cell from a 75-cm3 reservoir in order to mitigate the effects of durene photolysis. Durene solutions in hexane had an absorbance of about 0.9 at 266 nm in a 1-cm cell (1.9 X mol/L) and were deoxygenated by bubbling with N2 gas. Cell temperature was controlled by flowing N2gas and was measured by thermocouples immersed in solution upstream and downstream of the cell. The two temperatures generally agreed to within 1 O C at the time measurements were made. The temperature dependence of the yield of separated charge was measured by two methods, the first of which was integration of the current pulses produced by lowintensity, 3-11s pulses of 266-nm light. At higher intensities, second-order recombination caused ion currents to decay on the microsecond time scale, and initial photocurrents were estimated by extrapolation of timeresolved (100-ns resolution) current traces to zero time. Measurements of the cation and anion mobilities as a function of temperature allowed computation of the number of charge carriers. Ion mobilities were determined by direct time-of-flight measurement using the conductivity cell described above. The solution volume excited by 3-11s pulses of 266-nm light was defined by a movable slit which could be positioned to allow irradiation of any 50-pm-wide slab between the electrodes. The slit was usually positioned so that a slab immediately adjacent and parallel to an M.NATO Adu. Study Inst. Ser., Ser. C 1982,86,433. (2) Choi, H. T.; Sethi, D. S.;Braun, C. L. J . Chcm. Phys. 1982,77,6027. ( 3 ) Holroyd, R. A.; R w l l , R. L. J. Phys. Chem. 1974, 78, 2128. (4) Braun, C. L.; Scott, T. W. J. Phys. Chem. 1983,87,4776. ( 5 ) Yakovlev, B. S.; Lukin, L. V. Ado. Chem. Phys. 198S,aO, 99. (6) Mommder, A. 1. Chcm. Phys. 1w8,48, 1659. ( 7 ) Hong, K. M.;Noolandi, J. J . Chcm. Phys. 1978,68,5168; 1978,69, 5026. (8) Scott, T. W.; Braun, C. L. Can.J . Chem. 19W, 63,228. (9) Scott, T. W.; Braun, C. L. Chem. Phys. Lett. 1986,127,501. (10) Braun, C. L.; Scott, T. W. J . Phys. Chcm. 1987, 91,4436. (1 1) Hirata, Y.; Matap, N.; Sakata, Y.; Mbumi, S. J. Phys. Chem. 1986, 90, 6065. Miyasaka, H.; Matap, N . Chem. Phys. Lett. 1987, 134, 480. (12) Bowman, R. M.;Lu, H.; Eisenthal, K. B. J. Chem. Phys. 1988,89, 606. (1) Warman, J.
Q 1991 American Chemical Society
5530 The Journal of Physical Chemistry, Vol. 95, No. 14, 1991
Braun et al. 8
0.06:
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Figure 1. (0)Transient absorption at 1.064 pm of 1.9 X 1V3M durene in n-hexane excited at 266 nm; T = 295 K. (A)Same solution but with 0.1 M perfluorohexane added as electron scavenger. The smooth curve is based on the assumption that the residual transient absorption arises from durene SIstates; see text for details.
3
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rima (na)
i
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T I N (nr)
Figure 2. (0)Transient absorption at 1.064 pm of 1.5 X M durene in n-hexane excited at 266 nm; T = 208 K. (A) Same solution but saturated (a. 0.03 M) with PFH. The smooth curve is once again based on the assumption that the residual absorption arises from durene SI states.
electrode was excited. Fluorescence lifetimes of hexane solutions of durene both with and without added PFH were needed to correct transient absorption results for a background absorption from excited states. The lifetimes were determined with a time-correlated photon counting apparatus.
Results and Discussion The chief problem in picosecond transient absorption measurements of geminate electron-cation recombination has been excited neutral state absorption at the wavelength of the probe To overcome this problem, the solute should have (a) a high SIextinction coefficient at 266 nm to allow efficient two-photon ionization and (b) negligible extinction coefficient of SIand S, states at the probe wavelength. Absorption by the solute cation radical would make an additional contribution to the geminate pair signal but is undesirable given our method of correcting for the effects of SIabsorption on the geminate pair kinetics (vide infra). While no solute investigated in preliminary experiments satisfied criterion b entirely, durene proved to be the most satisfactory. The upper curve of Figure 1 shows the 1.06-pm transient absorption from a 1.9 X M solution of durene in n-hexane excited at 266 nm at room temperature. The early time decay of the upper curve is attributed to optical absorption by geminate electrons. The lower curve shows the effect of adding perfluorohexane (PFH) as an electron scavenger. The smooth curve is a convolution of an exponential decay with the 3 5 9 excitation and probe pulse widths of the laser. The lifetime of the exponential is 4.4 ns, the measured fluorescence lifetime of a durene solution quenched by 0.1 M PFH. The small peak in the lower curve over the first 100 ps is presumably the result of absorption by unscavenged electrons. For longer times, the assumption that the signal decay is governed by the lifetime of SIfor durene appears reasonable. At room temperature (Figure l), the geminate charge pair decay is not fully time resolved and we omit attem ts to fit the decay kinetics. However, as we have observed before!&’o reduced temperature results in a smaller electron mobility” which leads to a slower recombination rate. This allows the kinetics to be resolved in time. The upper curve in Figure 2 is the transient absorption by geminate charge pairs at 208 K, using a 5-ns time base. The lower curve is for the same solution after saturation (ca.0.03 M)with PFH. In the lower curve, absorbance after 1.5 ns is thought to be due largely to SIof durene and is fit (as in Figure 1) by an exponential lifetime of 10.3 11s appropriate to the PFH-quenched fluorescence lifetime of that state at 208 K. The rise in absorbance (lower curve) after 3.5 ns is not understood but could result from cation dimers of durene. Cation dimers of (13) Nyikor, L.; Zador, E.;Shiller, R. In Proceedings of rhe 4th Tihany Hungarian S y m p i u m on Fdfarion Chemisrv, H d g , P.,Shiller. R.,We.; Academy of Sciences: Budapest, 1977; p 179.
0
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Figure 3. Transient absorption from Figure 2 corrected for the effectsof durene SIabsorption as described in the text. The smooth curve was calculated from the theory of Hong and Noolandi’ using an electron diffusion constant” at 208 K of 9.7 X 1W5cm2/s and the 9EXP distribution function with a mean radius of 5.7 nm. Both the UV and IR pulses are assumed to be Gaussian with a full width at half-maximum of 35 ps.
several methyl-substituted benzenes are known to absorb in the near-IR region.14 Figure 3 gives the upper curve in Figure 2 corrected for the effects of background absorbance. In the correction it is assumed that only durene SIstates contribute to the background absorbance and that their lifetime is 15 ns, the value measured for the fluorescence decay of a durene solution which was bubbled with N2as was the solution of Figure 2-we measured longer lifetimes for rigorously deoxygenated solutions, but for lifetimes >10 ns the precise value of the lifetime has little effect on the correction. The amplitude of the exponential used in the background subtraction is that of the lower smooth curve in Figure 2, but increased by 9% to reflect the slightly higher intensity that was used during the measurement of the upper curve in Figure 2. The smooth curve of Figure 3 is that expected for a particular initial population of geminate charge pairs assuming that diffusion within the Coulomb well governs the decay rate. The theory is that of Hong and Noolandi.’ As in our earlier work, it is impossible to fit the data by assuming that all geminate pairs have the same initial radius. In Figure 3, we assume that the distribution of initial electron-cation separations g(r) is given by the function 9EXP = 9/(2.L3) exp(-r/l) where the mean radius of the distribution is 3L = 5.7 nm. In order that the absorbance decay of Figure 3 match that of the geminate electron population decay, the electron absorbance at 1064 nm must depend neither on time nor on the separation (14) Badger, B.; Brocklehurst, B Trans. Faraday Soc. 1969, 65, 2582.
Geminate Electron-Cation Recombination
The Journal of Physical Chemistry, Vol. 95, No. 14, 1991 5531 0.018
h
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Figure 4. Transient absorption at 208 K corrected for durene SIabsorption. The solid curve assumes that initial geminate pair separations are given by GEXP with a mean radius (3L) of 5.7 nm. The dashed curve arises from &AUSS with a mean radius of 6.1 nm (G = 5.4 nm).
100
50
150
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radius (A)
Figure 5. Normalized distribution functions for initial separations of geminate charge pairs: (-) GEXP with mean radius of 5.7 nm; &AUSS with mean radius of 6.1 nm. (-0)
of the electron and its partner cation. Neither requirement appears to be experimentally established, but both could be examined by transient absorption measurements at different probe wavelengths. The spectrum of the electron in n-hexane, observed following a 50-ns, 10-MeV electron pulse, rises steadily from 700 to 1400 nm with a molar extinction coefficient at 1000 nm of either 6 X lo3 ~ ~liquid or 8.3 X lo3 M-’ cm-I, depending on a s ~ u m p t i o n s . In propane at -185 O C , the electron spectrum has a similar shape and is independent of time over the interval 160 ns to 2 p.I6 The same is true of the spectrum in 3-methyloctane at 127 K over the interval 100 ns to 7 ps.” In methylcyclohexane, the maximum in the electron spectrum recorded immediately following a 10-ns pulse blue-shifts from above to below 2 pm and narrows as the temperature is reduced from room temperature to 132 K.I8 While there are no data directly relevant to our kinetics, it seems possible that the electron spectrum in n-hexane will blue-shift and narrow with time. Whether this results in a significant time-dependent change in the extinction coeftkient at 1064 nm can be determined only by experiment. For the present, we will assume that the time dependence of the electron absorption is an adequate measure of the electron population. Figure 4 shows the highest precision data that we have yet collected. It is an average of four separate decay curve measurements at 208 K (each of which had the same shape within the scatter of the data). Figure 4 has been corrected for background absorption in the same manner as that described for Figure 3. The solid curve assumes that the initial separations are given by ZEXP with a mean radius of 5.7 nm, i.e. the same function used to fit the longer time-base data of Figure 3. The dashed curve depicts the best-fit decay curve which results when the initial radii are assumed to be given by the spherical Gaussian function &AUSS with a mean radius of 6.1 nm. The standard deviation of the ZEXP fit is 8 X l P while that of the &AUSS fit is 1.4 X Figure 5 shows graphs of the normalized radial distribution functions ZEXP and ? G A U S S used to fit the geminate pair decay data of Figure 4. The mean value of the distribution of initial pair separations is expected to depend on the energy of the state that ionize^.^.^ However, for several reasons, one can make only a rough estimate of the maximum energy of an outgoing photoelectron in our experiments. As recently discussed by Hoffman and Albrecht,19 the measurement of the ionization potential for a molecule in (15) Baxendale, J. H.; Rarburn, E. J. J. Chcm. Soc., Faraday Tram. I 1974. - - . ., .70.705. - , .-- .
(16) Gillis,H. A.; Klassen, N.V.; Teather, G. G.; Lokan, K. H. Chcm.
Phys. Lrrr. 1971, IO, 481.
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Figure 6. Temperature dependence of ion yield from photocurrent
measurements: (a) initial photocurrent divided by sum of ion mobilities
for nanosecond excitation; (b) integrated photocurrent for low-intensity nanosecond excitation; (c) initial photocurrent for picosccond excitation (with PHF) divided by sum of ion mobilities; (d) integrated photocurrent (with PFH).
condensed phase is problematical. From their work and that of Holroyd,20 we can estimate that the ionization potential for N,N,N!N’-tetramethyl- 1,4phenylenediamine(TMPD) in hexane is roughly 1.5 eV below TMPD’s gas-phase ionization potential. Because TMPD and durene have similar molar volumes, we assume that the ionization potential for durene in hexane is also 1.5 eV below its gas-phase ionization potential of 8.03 The energy of two 266-nm photons is 9.3 1 eV, and thus the maximum energy of the outgoing electron is 2.8 eV. If durene relaxes to the zero-point level of S1 before absorption of a second photon, the maximum energy would drop to about 2.4 eV. In the onephoton ionization of TMPD in hexane, Choi et al. estimate that the mean radius of an assumed ZEXP distribution function increases from 2.3 to 4.5 nm as the maximum photoelectron energy increases from about 0.9 to about 2.5 eVS2While those results are expected to be systematically perturbed by the large values of the electric field which were applied, the mean radius value of 5.7 nm, seen in the present experiments, is in reasonable accord with the 4.5-nm value found at similar maximum photoelectron energy in the earlier experiments. Figure 6 shows the temperature dependence of the photocurrent yield under four different sets of conditions. In each case the logarithm of the yield of ions (in arbitrary units) that escape
(17) Gillis, H. A.; Klassen, N. V.; Woods, R. J. Can. J . Chcm. 1977, 55,
+A++
LULL.
(18) Atherton, S.J.; Baxendale, J. H.; Bud, F.; Kovacs, A. Radiur. Phys. Chcm. 1%, 28, 183. (19) Hoffman, G. J.; Albrecht, A. C . J . Phys. Chcm. 1990, 91, 4455.
(20) Holroyd, R. A. J. Chem. Phys. 1972,57, 3007. (21) Birh, J. B. Phorophysics of Aromatic Molecules; John Wiley: London, 1970; p 457.
5532 The Journal of PhysicaI Chemistry, VoI. 95, No. 14, 1991 geminate recombination is plotted against the reciprocal of the product of the dielectric constant c and the absolute temperature T. Because of unresolved questions about the temperature dependence of photon absorption cross sections and ionization quantum efficiencies, the ion yields may not accurately reflect the temperature dependence of the average escape probability of the collection of geminate charge pairs. Still the ion yield measurements are important in assessing the possible perturbation of the initial geminate pair distribution by absorption of a UV photon by the geminate electron. The cross section of an electron in hexane for absorption of a 266-nm photon is apparently unknown. If the molar extinction coefficient were lo3, our calculations indicate that almost 50% of the geminate electrons would absorb a 266-nm photon. Results from the infrared stimulation of geminate pair escape indicate clearly that the effect of such photon absorption on the free ion yield becomes more and more pronounced as the temperature is reduced83 Thus, we expect that comparisons of photocurrents measured under high-intensity picosecond excitation conditions with those measured at lower intensities will reveal any pair distribution perturbations in the former case by a weakened dependence of the free ion yield on temperature. The ion yield data were measured at applied electric fields ranging from 1.2 X lo6 to 1.5 X lo6 V/m. The data have been corrected to zero applied field by division by the Onsager field dependence factor 1 e3E/(8mgk2P) where E is the applied field, ~0 the permittivity of vacuum, and k Boltzmann’s constant. Curve a of Figure 6 is for 3-ns, 266-nm excitation pulses intense enough to yield photocurrents comparable to those in the picosecond experiments. The initial current (see Experimental Section) is divided by measured values of the sum of ion mobilities in order to obtain the relative yield data which are shown. The positive ion (presumably the durene dimer cation) is found to have a mobility I.(+given by In I.C+= 1.07 - 0.69 In q, where is the viscosity of hexane in centipoise and the units of p+ are lo4 cm2(Vs. The negative current carrier (presumably Oz-) has a mobility given by In p- = 1.36 - 0.72 In q. Notice that in both cases the mobilities depend more weakly on viscosity than the 1/q dependence of Stokes’s law. Curve b (closed circles) is for very low intensity 3-ns excitation pulses such that second-order charge recombination is unimportant. In that case, the free ion yield is measured by integrating the ion current over the millisecond duration of the photocurrent pulse. The slope for curve a is -3.1 1 f 0.16 (95% confidence level) while that from the integrated current approach of curve b is -3.07 f 0.36. The good agreement means that the mobility data are accurate enough to yield reliable free ion yields from measured initial currents. If such slopes were detemined wholly by the temperature dependence of geminate pair escape and if the radius distribution were temperature independent, then the mean radius of an assumed 9EXP distribution would be about 1.5 nm. That value seem quite unreasonable and implies that either or both the quantum efficiency for ionization or the thermalization radius are temperature dependent. Curve c is for p i y d excitation conditions comparable to those used to obtain Figures 1-4. Initial currents were measured and then divided by the mobility sum as in curve a; the slope is -3.68 f 1.06 in reasonable agreement with those of curves a and b. Curve c was measured, though, with a hexane solution saturated with PFH whose presence is expected have a modest effect on the free ion yield.= For comparison, curve d gives low-intensity (nanosecond excitation) measurements of integrated currents for a solution that was similarly saturated with PFH; its slope is -2.56 f 0.30. Thus,
+
(22) Tweeten, D. W.; Lipsky, S. J. Phys. Chem. 1989, 93, 2683.
Braun et al. within the accuracy of the measurements, there is no systematic difference between the slope of curve c and those of curves a, b, and d. Most importantly,the slope of curve c is not less negative than those of the other curves. This indicates that significant perturbation of the geminate electron-cation radius distribution by 266-nm electron excitation was not observed. Approaches other than transient absorption have been used recently to gain insight into characteristics of geminate cationelectron pairs. Brearley et al. recorded the time evolution of the delayed fluorescence arising from recombination of the geminate cation-electron pairs produced by photoionization of several solutes in tr~ns-decalin.~~ They showed that the fluorescence risetime kinetics could be fit by the empirical WAS function derived for geminate pair recombination kinetics in the work of Warman, Asmus, and S c h ~ l e r . ~The ~ work did not systematically test whether separation distributions like 9EXP allowed a fit to o b s e r v a t i o n ~ .Schmidt ~~ et al. used time-resolved dc conductivity studies of photoionized geminate pairs to show that the ?GAUSS and 9EXP distributions allowed fits to their data.zs They also used detailed computer simulations of their experiments to show that any experiment, such as theirs, which relies on electron scavenging will have difficulty in distinguishing between initial separation distributions. They find that the distribution of s e p arations between cations and scavenged electrons depends only weakly on the initial cation-electron separation distribution.2s All steady-state measurements, whether relying on temperat ~ r e electric ,~ field,zJ6 or scavenger concentration dependencez7 to provide information on the initial separation distribution, are expected to perturb that distribution. Nonetheless, several recent papersZxJ7 have indicated that the 9EXP distribution provides a satisfactory fit to a variety of experiments.
Conclusion Transient absorption of 1064-nm picosecond probe pulses by electrons in hexane was used to monitor the population decay of geminate electron-cation pairs produced by two-photon 266-nm ionization of the solute durene. After correction for a relatively weak background absorption which appears to arise from durene first excited singlet states, the geminate pair decay kinetics at 208 K were fit by the time-dependent diffusion theory of Hong and Noolandi. An excellent fit was achieved by assuming that the distribution function for initial geminate pair radii was of the form 9 / ( 2 L 3 )exp(-r/L) with a mean radius 3L = 5.7 nm. Photocurrents arising from geminate electrons that escape the Coulomb well were measured under both the high UV intensity conditions of the picosecond experiments and much lower intensity nanosecond laser excitation. Reasonable agreement of the temperature dependence of the ion yield indicates that the geminate charge pairs were not seriously perturbed by the high intensity excitation conditions of the picosecond experiments. Acknowledgment. We thank Fuxing Hou for making the ion mobility measurements. Grant DE-5G02-86ER13592 from the office of Basic Energy Sciences, United States Department of Energy, provided support for this work. (23) Brearley, A. M.; McDonald, D. B. Chem. Phys. Lett. 1989,155,83. Brearley, A. M.; Patel, R. C.; McDonald, D. B. Chem. Phys. Lerr. 1987,140, 270. (24) Warman, J. M.; Asmus, K. D.; Schuler, R. H. J. Phys. Chem. 1969, 73, 931. Rzad, S. J.; Infelta, P. P.; Warman, J. M.; Schuler, R. H. J. Chem. Phys. 1970,52, 3911. (25) Schmidt, K. H.; S a w , M. C., Jr.; Lu Y.; Liu, A. J. Phys. Chem. 1990, 94, 244. (26) Casanovas, J.; Guelfucci, J. P.; Terrisrol, M. Radiut. Phys. Chem. 1988, 32, 361. (27) Lee, K.; Lipky, S. J. Phys. Chem. 1984,88,4251; 1982,86, 1985.
