1985
J. Phys. Chem. 1982, 86, 1985-1994
are dealing again with a “one-electron system” interacting with the Si atom. Table I1 presents absolute energies, equilibrium bond lengths, dissociation energies, and spectroscopic constants for both states. Figure 2 shows a series of potential curves and Figure 8 compares the potential curves and vibrational levels of Si-Li and C-Li at the MCSCF+l+S/ALIS+l+B level. Note that both the 42-and 211 states are bound (by 35 and 21 kcal mol-’, respectively) and the 42-is the ground state. Contours of the valence orbitals of Si-Li are shown in Figures 9 and 10 and are remarkably similar to the corresponding C-Li plots. In particular, the 42-contours indicate that the singlet coupled pair which in Si-H is a bond is a doubly occupied 3s orbital on Si in Si-Li. Further, while the L orbital in Si-H is a “lobe”, in Si-Li it is essentially a 3p, Si orbital. Similarly the contours for the 211 state shown in Figure 10 suggest that the bond is dominated by the 3p, orbital and that the lobes, ly and 4, show the effect of the interaction with Li, being bent away from the bond. Note that they are considerably less “bent” than in the 211 state of C-Li primarily because the Si-Li bond length is so much larger (5.075 vs. 4.026 au). In summary, while C-H and Si-H have 211ground states, both C-Li and Si-Li have 42-ground states. This inter-
esting feature suggests that the reactions in which two C-Li or Si-Li fragments couple, i.e. C-Li
+ C-Li
-
Li-C=C-Li
would proceed along the least-motion path with no activation energy. This is to be contrasted with the C-H situation where the least-motion pathway is characterized by a barrier estimatedmat 12 kcal mol-’. We suspect that the plethora of unconventional structures of organic molecules which are predicted to arise when one or more hydrogens are replaced by Li may be traced to the preference of C-Li for a 42-ground state. If so, the various mixed compounds of silicon, carbon, and lithium would seem to be a fruitful area for theoretical study. We are pursuing these ideas.
Acknowledgment. We thank Thom. Dunning, Jr., of the Theoretical Chemistry Group at the Argonne National Laboratory for his support and encouragement during the course of this work. Also, A.M. acknowledges the financial assistance of the Argonne Universities Association. (29) S. P. Walch, submitted to J. Chem. Phys.
Effect of Electron Scavengers To Reduce the Ionization Current of Photoexcited N,N,N’,N’-Tetramethyl-p-phenylenediamine in Nonpolar Organic Liquids Kaldee Lee and Sanford Llprky’ Depafiment of Chemistty, University of Minnesota, Minneapolis, Minnesota 55455 (Received:December 7, 198 I, I n Final Form: January 27, 1982)
The effects of perfluoro-n-hexane, perfluoro-n-heptane,perfluoromethylcyclohexane,and perfluorodecalin to reduce the ionization current of photoexcited N,IV,”JV’-tetramethyl-p-phenylenediamine (TMPD) have been studied in the solvents tetramethylsilane, 2,2-dimethylbutane(2,2-DMB),isooctane, cyclohexane, n-hexane, and n-pentane. Results are reported over a range of excitation energies from 5.2 to 6.7 eV and, for selected systems, over a temperature range from -78 to 25 “C. At quencher concentrations, cq I0.2 M, the ratio of the photocurrent without quencher, Jo,to that with quencher, J,is found to be concave upward, linear, or concave downward in its dependence on cq, depending on the system studied. At higher cq, Jo/J is always concave upward. Both Joand J increase to about the same extent as the excitation energy increases, thus maintaining JolJ constant. As the temperature increases, J increases somewhat more rapidly than does Joand increasingly so the larger is cy An atttempt is made to explain these results with a model based on interaction of the quencher with an epithermal electron.
Introduction All observations that have so far been made on the photoionization of TMPD in neat nonpolar liquids are consistent with the following view of the process. At the photoionization threshold there is generated a quasi-free electron which thermalizes at some distance from its sibling positive ion. This geminate pair then move stochastically in their mutual Coulomb field, either escaping each other, with low probability (to generate a photocurrent in the presence of a small external field), or, with much larger probability, recombining, without significant loss of spin polarization, to generate the fluorescing state of TMPD. The evidence for all of this is obtained from (i) the solvent dependence of the photocurrent energy threshold (which supports the quasi-free nature of the ejected electron), l p 2 0022-3654/82/2086-1985$01.25/0
(ii) the external field dependence of the photocurrent (which supports the stochastic nature of the motion of the geminate pair),’-4 and (iii) the dependence of the fluorescence quantum yield on both excitation energy“ and applied field strength6J (which support the retention of (1) Holroyd, R. A.; Russell, R. L. J. Phys. Chem. 1974, 78, 2128. (2) Peterson, S. H.; Yaffee, M.; Schultz, J. A,; Jarnagin, R. C. J . Chem. Phys. 1976,63, 2625. ( 3 ) Sethi, D. S.; Choi, H. T.; Braun, C. L. Chem. Phys. Lett. 1980, 74, 223. (4) (a) Choi, H. T. Ph.D. Dissertation, Dartmouth College, Hanover, NH, 1980. (b)Choi, H. T.; Sethi, D. S.; Braun, C. L. J . Chem. Phys., submitted. ( 5 ) Wu, K. C.; Lipsky, S. J. Chem. Phys. 1977, 66, 5614. (6) Bullot, J.; Cordier, P.; Gauthier, M. Chem. Phys. Lett. 1978, 54, 77.
0 1982 American Chemical Society
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The Journal of Physical Chemistry, Vo/. 86, No. 11, 1982
spin polarization and the conservation of the sum of fluorescence probability and escape probability). In the presence of a low concentration ( ~ 0 . M) 1 of an electron scavenger, the fluorescence of TMPD is quenched for excitation energies both below and above the photocurrent threshold but always more severely above the thre~hold.~ The energy at which this enhanced quenching onsets is sufficiently close to the energy threshold of photocurrent in the absence of quencher’ to indicate that the quencher is without significant influence on the primary light absorption process. Also one finds5 that the probability for this enhanced quenching (i.e., the quenching that is residual after correction for quenching of the fluorescing SI state) exhibits a dependence on solvent very similar to that observed for the rate constant of thermal electron attachment to these same solute^.^^^ To assume that the quencher scavenges the geminate electron (and thereby renders nonradiative the subsequent recombination) would be consistent with these results were it not for one variant observation. Whereas the probability, p(cq),for thermal geminate electron scavenging is expected to exhibit a dependence on the square root of the scavenger concentration, cq, i.e. p(cq) = (acq)”2/[1
+ (acq)1’2]
instead one finds an unequivocally better fit of this probability to a Stern-Volmer expression, i.e. P(cq) = KaCq/(l
+ Kacq)
Accordingly it has been suggested5that the scavenger acts not on the ion pair but rather on some neutral excited state of TMPD that either decays to the emitting state of TMPD (and exponentially in time to generate eq 2) or decays otherwise to the geminate ion pair. To account for the similarity between this state and that of a quasi-free electron vis-&vis the solvent dependence of their energy thresholds and of their reactivity with scavengers, the state was presumed to be a large-orbit, Rydberg-like state of TMPD. This suggestion of a metastable, neutral precursor state of the geminate pair was subsequently supported by evidence’O that the quencher, perfluoro-n-hexane, not only acted to reduce the “recombination” fluorescence with a Stern-Volmer form for p(c,) but also served to reduce the steady-state photocurrent, J(c,), with the same SternVolmer form (i.e., J(cq)= J(O)/(l+ K$,) and, within experimental error, the same Stern-Volmer constant (Le., K j = K,). This was demonstrated for TMPD in two M-l; KJ = 11 M-l) and tetsolvents, isooctane (K, = ramethylsilane (K, = 3.24 M-l; KJ = 3.5 M-l) at excitation wavelengths of 210 and 220 nm, respectively.’O The present investigation set out to extend this study of photocurrent quenching to other quenchers, to other solvents, and to excitation at other energies. As we will detail below, the results that were obtained with perfluoro-n-hexane in isooctane and in tetramethylsilane do not extrapolate to other quencher-solvent systems. Also we find that, even for perfluoro-n-hexane in isooctane and in tetramethylsilane, the difference K j - K, depends on the excitation wavelength employed and can be positive or negative with a zero occurring, by chance, very close to the excitation wavelengths chosen in the previous study.1° (7) Bullot, J.; Cordier, P.; Gauthier, M. J.Chem. Phys. 1978,69, 1374, 4908. (8) Allen, A. 0.;Holroyd, R. A. J. Phys. Chem. 1974, 78, 796. (9) Allen, A. 0.;Gangwer, T. E.; Holroyd, R. A. J. Phys. Chem. 1975, 79, 25. (10) Lee, K.; Lipsky, S . Radiat. Phys. Chem. 1980, 15, 305.
Lee and Lipsky
Accordingly, the photocurrent quenching, although not necessarily at variance with the existence of a metastable, precursor state of the geminate pair, can no longer be considered to support this view, and other explanations that might account for these observations are now examined.
Experimental Section The equipment used for both photocurrent and fluorescence measurements has been previously de~cribed.~JO Exciting band-passes were usually of the order of 3 nm for fluorescence measurements and between 0.8 and 5.3 nm for photocurrent measurements depending upon the system studied. Photocurrents were always kept sufficiently low to avoid volume recombination of charge carriers. Two photocurrent cells were employed, one of which was temperature controlled. Room-temperaturemeasurements were sometimes performed in both cells to ensure that cell geometry and nature of the electrode surface were not significant factors. The temperature-controlled cell employed stainless-steel electrodes (1 X 2 cm) separated by 0.533 cm. The edge closest to the cell window was separated from it by ca. 0.01 cm. The cell consisted of three concentric quartz cylinders to each of which was fused a Suprasil window. The outer cylinder was evacuated and the central one was maintained at the desired temperature by circulation of precooled gaseous nitrogen. The solution temperature was monitored by several thermocouples and is considered accurate to f l OC. The second cell was of Pyrex construction with a Suprasil window attached via Pt/AgCl. The electrodes (0.9 X 2 cm) were of copper and separated by 0.572 cm. The electrode edge closest to the Suprasil window was separated from it by less than 0.01 cm. The exciting monochromator projected an image of the entrance slit onto the front window of each cell, parallel to the electrode planes. Dark currents contributed ca. 0.5% to the total photocurrent for solvents like tetramethylsilane which have large free-ion yields but were ~ 5 0 %for solvents such as nhexane containing high concentrations of quencher. The steadiness of these currents, however, permitted reliable subtraction of the dark current from the total current in most cases. Photogenerated background current, as determined by exciting the neat solvents (i.e., without TMPD) were found always to be negligible (i.e., 0, P1 vs. a"" starts out concave downward and then reverses this concavity at some large a (which value increases with increasing n). From this it can be concluded that plots of Jo/J vs. cq (over a limited range of cq) will be concave downward, linear, or concave upward depending upon the magnitudes of yo and y1 (see eq 4). To develop this somewhat more quantitatively, consider a solvent for which we know the escape probability at cq = 0 (i.e., Po = +Jo/&) and thus also Po via eq 5, for some particular n. Now consider a plot of P1 vs. CY"+' (=yo + ylcq) and shift the origin of this plot from an+' = 0 to an+' = yowith yochosen equal to (P2/4r0)"+'. Thus, at our new origin P' = Po-1.If we now rescale the ordinate so that Pf' = 1, the resulting plot is simply Po/P (=J o / J )vs. ylc,. Clearly if yo is small (Le., Po is large as, for example, for tetramethylsilane), then our plot will start out concave downward, become linear, and finally, if the range of ylcq is sufficiently great, develop an upward concavity. On the other hand, for large yo (i.e., small Po,as, for example, for n-hexane), J o / J will always be concave upward. At intermediate yo,Jo/J will start out linear (and will remain linear for an extended range of ylcq) and finally sweep upward at high ylcq. Of course, since the plots in Figures 1-5 have cq (and not ylcq) as abscissa, it is clear that, for two systems with the same yo (i.e., different quenchers in the same solvent), the smaller is y1 the more linear will the experimental plot appear for the same range in cq, Most of the results summarized in Table I with regard to the classification of the Jo/J plot can, with an appropriate choice of n, be rationalized at least semiquantitatively in this way. We consider some examples below. Choi, Sethi, and Braun4 report that, of the distribution functions which they have investigated of the form of eq
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The Journal of Physical Chemistty, Vol. 86,No. 11, 1982
3, the one with n = 2 generates the most reasonable compromise between (i) a fit of the Onsager theoretical prediction of the field dependence of the free-ion yield to their experimental data and (ii) the physical requirement that & not exceed unity. In the particular case of excitation at 5.90 eV, they report for +Jo (ref 4b) and & (ref 4a) values of 0.0946 and 0.66 (tetramethylsilane), 0.0205 and 0.39 (isooctane), and 0.000 232 and 0.56 ( n - h e ~ a n e )Accord.~ ingly, Po(=+Jo/&) and Po (from eq 5 , with n = 2) are 0.14 and 4.9 (tetramethylsilane), 0.053 and 6.3 (isooctane), and 0.00041 and 12.6 (n-hexane). Using these, we plot in Figure 12 the theoretical predictions of J o / J (=Po/P)vs. ylcq ( = a 3- aO3= (P6 - Po6)/(64r,3))for the three aforementioned liquids. To make an absolute comparison with experimental results, we determine ylcq so that the experimental ratio Jo/J and the theoretical ratio Po/P are equal at the highest cq experimentally studied for a given solvent-solute system. For example, from Figure lA, we note that for tetramethylsilane + perfluoro-n-hexane, J o / J = 1.64 at cq = 0.20 M and that a linear regression from 0.20 to 0.02 M fits the data well with intercept =1.00. Accordingly, Figure 12A should predict this system if we identify ylcq = 295ro-3(at which value Po/P = 1.64) with cq = 0.2 M (Le., rO3yl= 1.48 X lo3 M-’). Indeed, we find that application of a linear regression to the theoretical points from ylcq = 295ro-3to ylcq = 29.5r0-3(Le., cq = 0.02 M) gives an excellent fit (with a linear correlation coefficient p = 0.9997) with intercept of 1.01. On the other hand, since Figure 12A is generally concave downward, we would expect for more effective quenchers in this solvent (i.e., those for which J o / J is larger a t the same cq) that intercepts somewhat greater than 1.00 should obtain. This is generally borne out, as,for example, in Figures 4A and 5A for tetramethylsilane containing perfluoromethylcyclohexane and perfluorodecalin, respectively, for both of which intercepts of 1.1are observed. In a semiquantitative way both the “linearity” of these plots and the magnitude of the intercepts are predicted from Figure 12A. Thus, a linear regression of P o / P over the range ylcq = 665r0-3 (corresponding to J o / J = 2.35 a t cq = 0.1 M in Figure 4A) to ylcq = 133r0-3(corresponding to cq = 0.02 M) fits well ( p = 0.9997) with intercept of 1.05. In a similar way can Figure 12C be used to predict the concave-upward behavior of quenchers in n-hexane (and n-pentane in which solvent, too, the geminate pair escape probability is very small; see Figure 2). Thus, a linear regression of Po/P from ylcq = (1.89 X 104)ro-3(corresponding to J o / J = 1.60 at cq = 0.19 M in Figure 2C) to (cq = 0.10 M) gives acceptable linylcq = (9.93 x 103)~0-3 earity ( p = 0.9996) and intercept of 0.95. Figure 12B suggests that, for quenchers in isooctance, Jo/J should remain linear up to high cq and then become concave upward. For example, good linearity with intercept of 0.98 can be achieved for linear regression from ylcq e (3.55 x 103)r0-3 to ylc = 0 and this indeed mimics the behavior of perfluoro-n-kexane (see Figure 1B) and perfluoro-n-heptane (see Figure 3B). However, for more effective quenchers than these, the prediction of upward concavity is not confirmed (at least not until very high concentrations are achieved; see Figure 10). Thus, for both perfluoromethylcyclohexane (Figure 4B) and perfluorodecalin (Figure 5B), intercepts which exceed unity are experimentally observed for linear regressions with cy 5 0.1 M. The discrepancy in isooctane can be removed (without substantially altering the predicted behavior in the other solvents) by changing the distribution function index from n = 2 to n = 3. This follows from a property of eq 5 that,
-
Lee and Lipsky
as n increases, Po/Pvs. ylcq develops its upward concavity at higher values of Po/P. Thus, for example, using Po = 7.2 (corresponding to Po= 0.053 for isooctane with n = 3), a linear regression of Po/P from ylc, = (2.2 x 105)ro-4 (corresponding to + j o / + j = 4.60 at cq = 0.20 M) to ylcq = (4.4 X 104)ro-4(cq = 0.04 M) gives a good fit ( p = 0.9999) with an intercept, now greater than zero, of 1.13. Of course, by changing the index from n = 2 to n = 3, the data of Choi, Sethi, and Braun4 fit somewhat less well the Onsager prediction of the field dependence. Nevertheless, the modification is not great (and, anyhow, it remains unclear how closely one should expect agreement with the Onsager prediction). Certainly in view of the uncertainties in the nature of the distribution function (as well as in the determination of both #Jo and &), it is fruitless to seek here any quantitative confirmation of the epithermal scavenging model. Suffice it to say that the model provides a rather consistent explanation of the curvature of the + j o / $ j vs. cq plots for tetramethylsilane, isooctane, and n-hexane (and for other solvents, too, appears to work about as well using Table I11 to generate $Jo and assuming & to lie in the range 0.3-0.6). According to Choi, Sethi, and B r a ~ nboth , ~ $Jo and & are dependent on excitation energy in such a fashion that their ratio Po = +Jo/& increases monotonically by about a factor of 5-10 as, , ,e increases from 5.2 to 6.5 eV. Nevertheless, over this range we observe essentially no change in +$/I)~(see Figure 6). To explain this on the basis of the epithermal model requires that, as eexC increases, the parameter y1 must decline. This is required to maintain d+J/dcq independent of ,,,t while, a t the same time, allowing the electron range, ( r)o, to increase (as evidenced by the increase in Po). A somewhat more quantitative statement of this derives from the relation KJ N Porld(p’)/d(ylc,) (11) The derivative, d(P1)/d(ylcq).,can be taken as approximately independent of , , ,e since, for the values of P spanned by the liquids studied here, the curvature of P’ is slowly changing its sign. Therefore, to maintain K J independent of texcit is necessary that y1vary as Pcl. The parameter y1 must, of course, be proportional to an electron-quencher interaction cross section and therefore, from dimensional arguments, must also be inversely proportional to a parameter, L”, with the dimension of a length to the nth power. For the case n = 1,L is interpreted by Mozumder and Tachiya13 as the mean free path for elastic scattering. If L is independent of excitation energy (or varies slowly), then clearly we must require, within the framework of the epithermal model, that the interaction cross section decrease with increase in text. As the temperature is lowered, $J is observed to decline (see Figure 7 ) . In large part this can be attributed to an increase in the Onsager radius (ro = e 2 / ( e k T ) ) .Using eq 5 with n = 2 and taking for isooctane Po = 6.30 at 298 K (from Choi, Sethi, and Braun’s value of Po = 0.053)4predicts reasonably well the decline at cy = 0. Thus, for example, the prediction of the ratio 1ciJo(298K):$,’(255 K):1,b~~(195 K) is 1.0:0.75:0.42whereas the experimental ratio is 1.0:0.65:0.33 (with a larger value of n in eq 5 , somewhat better agreement can be achieved). Equations 4 and 5 also predict that, as the concentration of quencher increases, GJ will become increasingly sensitive to temperature (assuming again that all of the temperature dependence resides in ro). Thus, for example, from the data of Figure 4B, which shows at 298 K that $$/#J = 2.30 at 0.06 M of perfluoromethylcyclohexane, it follows from eq 5 (with n = 2) that /3 = 7.46. From here it is simply calculated that $A298 K):$A255 K):$J(195 K) is 1.00:0.70:0.34
The Journal of Physical Chemistry, Vol. 86, No. 17, 1982 1993
Effect of Electron Scavengers
at 0.06 M whereas the experimental ratio (see Figure 7) is 1.00:0.640.29. A similar calculation works about as well for perfluoro-n-heptane in isooctane. Whereas the magnitude of the quenching of the photocurrent is independent of eexc (at least from 6 5 - 6 . 5 eV), the quenching of the fluorescence excited above the photoionization threshold is strongly influenced by eexc. This behavior is illustrated in Figure 9. As a consequence of this difference, we find that above some excitation energy, t , the fluorescence is more strongly reduced by quencher than is the photocurrent (Le., K, > K j ) whereas for terC < t the reverse obtains (i.e., K, < Kj). The cross-over energy, t , is a function of the system studied. For example, for cyclohexane 1 5.4 eV for perfluoro-n-heptane and t 5.2 eV for perfluoromethylcyclohexane, whereas for isooctane 1 6.2 eV for perfluoro-n-heptane and t N 5.9 eV for perfluoro-n-hexane. That KJ should be less than K , is not difficult to rationalize for almost any model of the quenching action so long as we demand that recombination of a scavenged electron (i.e., the negative solute ion) with its sibling positive ion be nonradiative. Thus, for example, since the scavenging of epithermal and thermal electrons can give no fluorescence whereas just a fraction of only the epithermally scavenged electrons will give no photocurrent, it is clear that any combination of contributions from the epithermal and thermal processes will cause KJ to be inferior to K,. The problem lies with a rationalization for the reverse inequality. Somehow a process is required which can reduce the ion current without necessarily quenching the fluorescence. Two possibilities suggest themselves, namely, (i) some fraction of epithermally scavenged electrons do, in fact, ultimately generate S1in their recombination with TMPD and (ii) some fraction of the epithermal electron-quencher “encounters”do not lead to capture. For process i to be energetically feasible for the slow approach of two molecular ions in solution, it is required that et - c, - EA > 0 where et and ,,c are the TMPD ionization energy threshold in solution and the So S1 absorption threshold, respectively, and E A is the solution adiabatic electron affinity of the quencher. But this is unlikely to be satisfied. In the solvents that we have studied, et - eo ranges from -1.0 to 1.7 eV whereas EA, at least for the cyclic perfluorocarbons, is most plausibly in excess of this (using a polarization energy of above 1.0 eV19 and a gas-phase electron affinity estimated to be greater than 1 eV).20p21 For process ii we consider the formation of a metastable negative quencher ion which either decays to neutral quencher and thermalized electron or relaxes to the stable negative quencher ion. Clearly for both decay channels will the photocurrent be reduced but only for the second channel will there be fluorescence quenching. No modification is required in eq 3-5 since y1 only measures a solute-dependent range-reduction process and therefore encompasses both decay channels of the metastable ion. To explain the increase in K , with increasing excitation energy, it is sufficient to invoke the aforementioned decline in both yo and y1 and the concomitant increase in the probability of thermal electron scavenging. We make no attempt here to quantify this model since clearly too much remains speculative. The linearity of the R vs. cq-l plots can, however, be forced from the model by ignoring the processes that quench the fluorescence, other than that
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(19) Holroyd, R. A.; Gangwer, T. E. Radiat. Phys. Chem. 1980,15,283. (20) Liebman, J. F. J.Fluorine Chem. 1973, 3, 27. (21) Lifshitz, C.; Tiernan, T. 0.;Hughes, B. M. J. Chem. Phys. 1973, 59, 3182.
due to capture of the epithermal electron followed by stable negative ion formation, and adopting, for the probability p of such capture, y12cq/(y0+ ylcq)where y1 = yI1 y12is the sum of the aforementioned two decay channels of the metastable negative ion. On this basis it is simple to show that the reciprocal of the intercept of R vs. cq-l is K = &y12/y1 (which would explain why the K values of Wu and Lipsky5 are always less than the & values of Choi, Sethi, and B r a ~ nand ) ~ the ratio of intercept to slope K, = yl/yo. The most serious problem with this approach, however, is its neglect of scavenging of thermal electrons. Were this included, linearity of R vs. cq-’ could only be preserved by appropriately complicating the expression for p . In Figures 10 and 11 we display the results for three systems for which J / j o / J /has j been studied over the entire composition range of the solutions. As is predicted from eq 5, we find always, at sufficiently high c , strong concave-upward behavior. However, in no caselave we been able to predict quantitatively the data exhibited here. In the attempt to do so, we have used eq 5 with n = 0 to n = 3 and have modified eq 4 to (Y = (ToXa + ylXb)l/(n+l) (12)
+
where X, and Xb are the component mole fractions and yo and y1 are determined from the experimental escape probabilities at X, = 1 and Xb= 1, respectively. We have also tried the Mozumder and Tachiya13technique (which also predicts concave-upward behavior), but this too fails when applied over the entire composition range (in the examples used by Mozumder and Tachiya,13G,(O)/G,(c,) did not exceed 3.9 whereas we are here attempting fits up to + J o / J / J as high as 500). In part, the difficulty is already apparent from a comparison of Figures 1B and 5B with Figure 10. It will be noted that, whereas at low c perfluorodecalin is a more effective quencher of the pkotocurrent than is perfluoro-n-hexane, at high cq this difference is reversed. Clearly eq 5 and 12 are incapable of accounting for this reversal. Indeed, from Table 111, it is apparent that even in pure perfluorodecalin a small residual photocurrent is observed which is absent in perfluoro-n-hexane. The most plausible explanation for these effects derives from the relatively large electron affinity of a perfluorocycloalkane (vis-&vis the perfluoro-n-alkane),1zi~i21 which could facilitate ion formation either via a direct contact charge-transfer absorption (Le., TMPD + Q + hu TMPD+ + Q-)or via interaction of the perfluorocarbon with some excited state of TMPD (i.e., TMPD* + Q TMPD+ + Q-). In either case the effect would only manifest itself at perfluorocycloalkane concentrations sufficiently high to make negligible the contribution to the ion current from direct photoionization. By comparison with tetramethylsilane (for which Po = 0.14): the geminate pair escape probability for perfluorodecalin is Po E 1 X (from Table I11 and assuming & = 0.61). Using this with an n = 2 distribution, eq 5 predicts aro = 51.1 and therefore that the average geminate pair separation in pure perfluorodecalin is ( r ) O 19 A. Such a large value is difficult to rationalize for a contact charge-transfer absorption but is not too disparate from the values of 14-15 A that have recently been reported for charge transfer from excited alkanes to perfluorocycloalkanes.1z~2z Finally, we wish to comment briefly on the solvent dependence of KJ for various solutes. Figure 13 shows K j for each solute plotted vs. the vertical electron affinity of
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(22) Luthjens, L. H.; Codee, H. D. K.; DeLeng, H. C.; Hummel, A. Chem. Phys. Lett. 1981, 79, 444.
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Lee and Lipsky
electron or, at least, with some entity which closely mimics the behavior of such an electron.
Concluding Remarks We have attempted to explain the effects of various perfluorocarbons to quench the TMPD photocurrent and recombination fluorescence using a model which involves exclusively interactions of both thermal and epithermal electrons with the quencher. The rather peculiar solvent dependence of the shape of the photocurrent quenching curves at low quencher concentration (10.2M) and the temperature dependence of this quenching are predicted 5. L reasonably well by the model. The absence of any effect of excitation energy to alter the sensitivity of the photocurrent to the presence of solute, although unexpected, is \ t not inconsistent with the model. The quenching of the A&.--. recombination fluorescence can also be accommodated by OL -.SO ' -.25 0 the model by allowing for quencher-epithermal electron Vo ( e V 1 interactions which facilitate electron thermalization Flgure 13. Dependence of TMPD photocurrent quenching constant, without capture. The increased sensitivity of the K,, on solvent V , value for the quenchers perRuoromethyicyclne fluorescence intensity to the presence of quencher at higher (U), perfluorodecalin(e),perfluoro-n-heptane (A),and perfluoro-nexcitation energies is explained in terms of the effect of hexane (0). excitation energy to increase the geminate pair separation the liquid (i.e., -V0).23 The shape of this dependence of distance and thereby enhance the probability of thermal K j on V , (i.e., smoothly concave with a single maximum) scavenging. In view of contributions from both epithermal is very similar to what obtains when the reaction cross and thermal electron-quencher interactions to the section for thermal electron attachment to some solute is fluorescence intensity, the observed linearity of R vs. c;l However, any similarly plotted vs. the solvent V, must now be considered as an accident of a more complex quantitative connection must be considered with some functional dependence of fluorescence intensity on caution. As is apparent from eq 11 and the discussion quencher concentration. However, no quantitative apfollowing it, KJis proportional to an electron-solute cross plication of the model has yet been successful in generating section, u, but with a proportionality constant that may the appropriate functional form. At higher quencher or may not depend importantly on the nature of the solconcentrations, we are unable to account satisfactorily for vent. For example, were the parameter L2independent the magnitude of the photocurrent quenching, but this of solvent (or only very slightly dependent), then u would may be a defect not of the basic model but rather of the exhibit the solvent dependence of KjIPO and accordingly approximate formulation that we have utilized. Some over the range of solvents studied here would not maximize features of the results at high quencher concentration but rather would monotonically increase with increase in suggest some small contribution to the observed photoV,. Additionalto this, the interpretation of Figure 13 must current from charge-transfer reactions between excited also be constrained by considering that the electron does TMPD and quencher. not maintain a constant energy over its entire range. Acknowledgment. This research was supported in part Nevertheless, the qualitative correlation between K j and by the US Department of Energy, Division of Chemical Vo certainly lends support to the view that the solute Sciences, Office of Basic Energy Sciences. We are also very reduces the photocurrent by interaction with a quasi-free grateful to Dr. Hae Tak Choi for his helpful comments during numerous discussions of this work and to Mr. D. (23) Allen, A. 0.Natl. Stand. Ref. Data Ser. (U.S., Natl. Bur. Stand.) B. Johnston for his technical assistance. 1976. No. 58. '
