J . Phys. Chem. 1988, 92, 4241-4245 would correspond to free rotation, but are extrapolated from high viscosity into the low-viscosity regime. Evans and Kivelson3' have proposed an explanation for nonzero intercepts in terms of cross-correlation functions of torquelike and kinetic terms. While this approach holds promise, it does not yield, as yet, a closed expression for the intercept. It is possible that T~ may be obtained from molecular dynamics simulation of the cross-correlation functions. ~
~~
(31) Evans, G.; Kivelson, D. J . Chem. Phys. 1986, 85, 385.
4241
The single particle relaxation times can also be interpreted in terms of an Arrhenius-type of temperature dependence
where E,,ra,is the activation barrier to reorientation. The Arrhenius plots of the experimental depolarized Rayleigh data are given in Figure 4 for m-cresol and p-cresol. The activation barriers for both compounds is E,,,, = 7.9 0.1 ( 5 ) kcal/mol, within the experimental error. This value suggests the motion involves the breaking of several hydrogen bonds.
Photocurrent Enhancement in Nonpolar Liquids by the Addition of Electron Scavengers Greg A. Howell, Kaidee Lee? David W. Tweeten, and Sanford Lipsky* Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455 (Received: October 27, 1987; In Final Form: February 2, 1988)
The photocurrent from anthracene, triphenylamine,and N,N,"'-tetramethyl-p-phenylenediamine excited above their ionization thresholds in liquid n-pentane or n-hexane is found to be enhanced by the addition of low concentrations (S0.02 M) of the electron scavengers perfluoromethylcyclohexane or perfluorodecalin. The enhancement is not observed in solvents of higher electron mobility (e.g., cyclohexane, isooctane, etc.) or for scavengers of lower electron affinity (e.g., n-perfluorohexane). For the solute naphthalene, no enhancement is observed under any conditions. The effects of excitation energy and applied electric field strength are reported.
Introduction It has been recently reported that the ionization current from TMPD (N,NJV,N'-tetramethyl-p-phenylenediamine) photoexcited above its ionization threshold is reduced by the addition of perfluorocarbon scavengers.' Depending upon the nature of the solvent and of the scavenger, the photocurrent was observed to decline by factors of about 1.5-3 over the range of perfluorocarbon concentrations studied (from -0.02 to 0.2 M). This reduction in photocurrent has been attributed to an effect of the scavenger to prethermalize the epithermal electron, thus reducing the radius of the geminate ion pair and making less probable its escape to free ions. The dependence of the photocurrent on electric field strength2 appears to be consistent with this view as does too the effect of the nature of the solvent-perfluorocarbon combination on the magnitude of the photocurrent quenching and its dependence on perfluorocarbon concentration.' In addition to this prethermalization of the epithermal electron, the simple effect of the perfluorocarbon to attach the thermalized electron might also be anticipated to have some influence on the observed photocurrent. Binding of the electron to the perfluorocarbon should tend to reduce the rate at which the geminate ion pair annihilates on "close encounter" and, to the extent that such encounters are significantly frequent configurations in the phase space of the pair, could conceivably increase the photocurrent by enhancing the escape probability. A recent analysis of this effect by Tachiya3 indicates that in nonpolar fluids, since the Onsager radius is so large (Rc 300 A), the effect may not be observable unless the annihilation rate of the scavenged pair is extraordinarily low. In the present investigation we report our observations of a very weak enhancement of the photocurrent by the addition of cyclic perfluorocarbon scavengers to solutions of TMPD, triphenylamine, or anthracene in n-pentane or n-hexane at scavenger concentrations less than 0.02 M . At higher scavenger concentrations, the photocurrent monotonically declines as has been previously reported.'
The dependence of the enhancement effect on the nature of the solvent, the nature of the scavenger, the excitation energy supplied to the solute, and the magnitude of an externally applied electric field is analyzed via the Tachiya t h e ~ r y . ~ Experimental Section Light from a 30-W D2 lamp fitted with MgF2 window (Hamamatsu L879) was passed through a 0.3-m vacuum monochromator (McPherson 218) operating at band-passes between 2.1 and 5.3 nm and focussed with LiF lens (f= 5.7 cm) onto the front face of the cell. The cell consisted of two stainless steel electrodes (with 2.20 X 1.27 cm2 polished surfaces), each attached to a Ceramiseal connector soldered to a flange and assembled to a stainless steel body through an indium O-ring. One of the electrodes was spring-loaded and insulated against the cell body by a Macor ring. The other electrode was rigidly mounted. An electrode spacing of 0.23 cm was obtained by insertion of a quartz plate between the electrodes. The leading edges of the electrodes were pressed against a 1.5-mm-thick Suprasil quartz window attached to the body via an indium O-ring. The electric field strengths employed were usually 3.5 kV/cm but sometimes ranged to 21.8 kV/cm. The photocurrent was monitored by a programmable electrometer (Keithley 617) that was interfaced with an IBM P.C. All solutions were air-equilibrated at 22 "C and utilized concentrations of solute (TMPD, triphenylamine, or anthracene) of -2 X M. Dark currents (obtained with shutter closed for 75 s) ranged from 15% to 50% of the total current but were always sufficiently stable to allow for reproducible and accurate subtraction. TMPD (Aldrich) was purified by vacuum sublimation followed by recrystallization. Aldrich triphenylamine (98%) and anthracene (99.9%) were used without further purification. Naphthalene (scintillation grade) was recrystallized from cyclohexane. Per-
-
~~
'
Present address: Chemistry Department, SUNY at Stony Brook, Stony Brook, NY 11794.
0022-365418812092-4241$01.50/0
(1) Lee, K.; Lipsky, S. J . Phys. Chem. 1982, 86, 1985. (2) Lee, K.; Lipsky, S. J . Phys. Chem. 1984, 88, 4251. (3) Tachiya, M. Chem. Phys. Lett. 1986, 127, 462.
0 1988 American Chemical Society
4242
1
.30
' /I
I
3'0
1 2 0
JOIJ
Howell et al.
The Journal of Physical Chemistry, Vol, 92, No. 14, 1988
1 10
Jo
21 0
0
L
j
/
I
i
j
1.00 O
1.20
I
L
'
10.0
5 0
'
1
15.0
'
'
20.0
1
E (KVIcm) JOIJ
Figure 2. Photocurrent, Jo, from TMPD (2 X M) in n-pentane excited at 5.30 eV as a function of the applied electric field strength, E.
1.10
1.00
I 0
1
0.025
0.050
I 0.075
I
0.100
JOIJ
Cq ( M I Figure 1. Ratio of the photocurrent, Jo, in the absence of a scavenger, Q , to the photocurrent, J , in the presence of a concentration, cqrof Q , plotted as a function of the scavenger concentration. System is TMPD (2 X M) in n-pentane excited at 5.80 eV with an applied field strength of 3.50 kV/cm. Scavengers are perfluorodecalin (A) and perfluoromethylcyclohexane (B).
fluorodecalin (PCR), perfluoromethylcyclohexane (PCR), npentane (Burdick and Jackson), and n-hexane (Burdick and Jackson) were additionally purified by percolation through activated silica gel and then stored over a 4-i% molecular sieve. Carbon tetrachloride (Fisher, Spectroanalyzed) was additionally distilled.
Results We define J and Joto be the magnitudes of the current from the photoexcited solute in the presence and absence, respectively, of a concentration, cq, of scavenger. In Figure 1 we show plots of J o / J v s cq for TMPD (2 X lo4 M) in n-pentane using either perfluorodecalin (A) or perfluoromethylcyclohexane (B) as scavengers. The excitation energy, text, is 5.8 eV, and the applied field strength, E , is 3.50 kV/cm. For both solutions a distinct minimum in Jo/Jis observed at cq 0.01 M. At higher cq, Jo/J becomes linearly dependent on cq with intercepts, for both scavengers, of 0.92-0.93 and slopes of 3.3 M-] for perfluorodecalin and 2.7 M-' for perfluoromethylcyclohexane. Under similar conditions but with n-perfluorohexane as scavenger, no minimum is observed. Jo/Jstarts out concave upward and then rapidly achieved a linear dependence on cq with slope of 4.0 M-'.I Also, no minima have been observed with either perfluorodecalin or perfluoromethylcyclohexane in the solvents tetramethylsilane, isooctane, or cyclohexane.] In all of these cases Jo/Jmonotonically increases from unity with increasing cq. At field strengths higher than 3.50 kV/cm, the value of J o / J at the minimum in the cyclic perfluorocarbon-n-pentane system was increased to o.975 at 6.56 kV/cm and to 1.0 at e 1 7 kV/cm. At higher field strengths there remained no evidence of a minimum. To confirm that our applied field strengths lie within the range of voltage-current characteristics that ensure the absence of volume recombination of charge carriers, we show in Figure 2 a plot of Jovs E for a 2 X lo4 M solution of TMPD in n-pentane. The slope-to-intercept ratio of the linear part of the characteristic cm/V. This compares very well with the Onsager is 5.9, X prediction4 (Le., e3/2ekZPwhere e is the electric charge, k is the Boltzmann constant, T is the temperature, and E = 1.844, the (4) Onsager, L. Phys. Rec. 1938,54, 554.
'
0.951
I
I
6 0
6 5
&
exc
1
7 0
(ev)
Figure 3. J o / J at cq = 0.01 M perfluorodecalin (see caption to Figure 1) as a function of excitation energy. 1.301
I
0.90
I
I
I
,
I
1
1.20
JoIJ
1.10
1.00
1 0
I
0.025
0.050
0.075
0.100
Cq (MI Figure 4. Same as caption to Figure 1A except with TMPD replaced by triphenylamine and excited at 6.36 eV (A) or replaced by anthracene and excited at 6.53 eV (B).
dielectric constant of n-pentane at 20 OC5) of 6.0, X cm/V. The effect of excitation energy, csxs, on the magnitude of J o / J at cq = 0.01 M (Le., at the minimum) is shown in Figure 3 for the TMPD-n-pentane-perfluorodecalin system at E = 3.50 kV/cm. As can be seen, the depth of the minimum decreases as ( 5 ) Riddick, J. A,; Bunger, W. B. Techniques of Chemistry; Wiley-Interscience: New York, 1970; Vol. 11, p 72.
-
Photocurrent Enhancement in Nonpolar Liquids
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988 4243
increases, finally disappearing at eexc 6.4 eV. At energies below 5.8 eV, the photocurrent was too small for reliable measurement. In addition to TMPD, three other solutes were also briefly investigated in n-pentane with perfluordecalin as scavenger. For naphthalene, no photocurrent enhancement was observed, but for both triphenylamine and anthracene J o / J again exhibited a minimum at cq 0.01 M. These results are shown in Figure 4. The excitation energy has been shifted to 6.36 eV for triphenylamine (A) and to 6.53 eV for anthracene (B) in order to accommodate their higher ionization energy thresholds in npentane. The linear portions of the J o / J vs cq plots in Figure 4 have intercepts of -0.91 and 0.95 and slopes of 3.4 and 3.0 M-’ for triphenylamine and anthracene, respectively. Returning to the TMPD system, we have found that the photocurrent enhancement effect is essentially unaffected when O2 is removed from the system and slightly intensified when n-pentane is replaced by n-hexane. On the other hand, no photocurrent enhancement could be observed when perfluorodecalin was replaced with CCl,. In this latter experiment the TMPD concentration was increased to 1.5 X M in order to more favorably compete with CCl, for absorption of light. However, under these same conditions, photocurrent enhancement was still observed with perfluorodecalin as scavenger. Finally, it is important to note the irradiation of the TMPDperfluorodecalin (0.01 M)-pentane system at 4.51 eV, which is just below the photoionization threshold (4.89 eV at cq = 0), showed no observable photocurrent (i.e., less than 2 fA which is ca. 0.05% of the -4-pA current obtained at 5.8 eV). eexc
-
Discussion All electron plus solute positive ion geminate pairs [e-$] that are initially generated by photoionization of s will, in the presence of an electron-attaching scavenger, Q, either recombine or be scavenged to form [Q-,s+]. Of the population scavenged, some fraction will themselves recombine. The remainder will escape recombination (Le., be unrecombined at infinite time) and, in the presence of an electric field, act as the charge carriers of the photocurrent. If we ignore, for the moment, the effect of the scavenger to prethermalize the epithermal electron, then, as Tachiya has recently derived,) the total yield of free ions, & can be expressed as 4t = 41°
+ (420 - 41O)
[
1 - K1(0) ““cq’]
(4) where
with rc equal to the Onsager radius (Le., e2/ckT E 307 %, in n-pentane at 22 “C) and Diequal to the mutual diffusion coefficient of the ion pair and where it is assumed that annihilation of the recombining geminate pair occurs on the surface of a sphere of radius Ri with “velocity” pi. For the recombination of [e-,s+] in n-pentane, the parameter S1is extremely small and, therefore, to good approximation, from eq 4 and 5, C#J~O = e-‘c/‘O (Le., the Onsager escape probability)., This derives from the following considerations. Since Rl is unlikely to exceed = 5 %, and 6 X 104,9,10it follows from eq 4 and 5 that Si will be negligible (Le., make a less than 1% contribution to the right-hand side of eq 4) unless Dir,/piR: exceeds -3 X lo2, or, with D, = 4.1 X cm2/s,ii,12unlessp, 5 2 X cm/s. But the velocity, pi, represents the proportionality constant in the “radiation” boundary condition that links the probability density of particles on the surface of the spherical boundary of radius R , (i.e., w(Rl)) to the radial flux of particles that pass through this surface (Le., react) and, as such, can be expressed as the equilibrium flux of particles of average velocity, ( u , ) , that strike the surface (i.e., (v,)w(Rl)/4) multiplied by the probability, al,that a particle that strikes will pass through. Accordingly, the velocity, p , , can be expressed as a ( ~ , ) / 4 and , ’ ~ with ( u l ) = lo7 cm/s it follows that SIwill be negligible unless cr, 5 But were a , this small, the homogeneous recombination rate constant e- s+ would be negligibly ~ m a 1 1 , ~whereas, *’~ in fact, such rate constants are generally observed to be quite close to their Debye limit.l5 Substituting Si = 0 into eq 2 and 4 and ignoring (-6 X 10-4)9$10 with respect to unity gives
-
+
(1)
where dIois the free-ion yield in the absence of scavenger (Le., the yield of escaped e- s+), +20 is what the free-ion yield of the scavenged pair (Le., [Q-,s+]) would be were their distribution of initial geminate pair separation distances the same as that of [e-$], K ~ ( c ~is) the recombination probability of [e-,s+] in the presence of a concentration, cq, of the scavenger, and ~ ~ ( is0 this ) recombination probability at cq = 0. Since 1 - K ~ ( cis~simply ) the total scavenging probability, hereafter referred to as hsc(cq), and since h,,(O) must be the escape probability of [e-,s+] at cq = 0,6*7it follows that eq 1 can be recast into the form
+
where J , the photocurrent, is taken to be simply proportional to 4t and
(3) is the scavenging probability conditional on nonescape of the ions.’ From eq 2 it is clear that there will be photocurrent enhancement (Le., J > Jo) when I$; exceeds (Le., when [Q-,s+] (6) Hong, K. M.; Noolandi, J. J . Chem. Phys. 1978,68, 5613. Friauf, R. M.J . Chem. Phys. 1979, 71, 143. (7) Choi, H. T.; Haglund, J. A,; Lipsky, S.J . Phys. Chem. 1983,87, 1583.
J.; Noolandi, J.; Hong, K.
has a larger escape probability than [e-,?]) for the same radial probability density of initial geminate pair distance^.^ For an initial separation distance of ro, Sano and Tachiyas have derived that
The function pt(cq) can be obtained from the theoretical treatment of NoolandL6 Definingflr,) to be the radial probability density of initial separation distances, ro, and gSc(ro,cq)to be the scavenging probability when ro2f(ro)is the Dirac delta function, 6(pr0),it follows that the scavenging probability for the function f ( r o ) is simply (7)
Values of g,(ro,cq) are obtained from the Noolandi calculation6 in terms of a dimensionless concentration parameter (k,r2/4D)cq, where k , is the bimolecular rate constant for reaction of the scavenger to attach e- and D is the e- diffusion constant. Thus, with an assumed form forf(ro) and values for k, and D, eq 7 (8) Sano, H.; Tachiya, M. J . Chem. Phys. 1979, 71, 1276. (9) At 5.90 eV Choi et al. report the photocurrent quantum yield and photoionization quantum yield for TMPD in n-hexane to be 2.32 X lo4 and 0.56, respectively (see ref 10). In this stud we have found Jo(in n-pentane)/Jo(in n-hexane) N 1.5. Therefore, q+ in pentane is -6 X ( I O ) Choi, H. T. Ph.D. Dissertation, Dartmouth College, Hanover, NH, 1980. Choi, H. T.; Sethi, D. S.; Braun, C. L. J . Chem. Phys. 1982, 77, 6027. (1 1) From the mobility of the electron in n-pentane at 23 OC,p = 0.16 cm2/(V s) (see ref 12) via the Einstein relation D = k T p / e . (12) Schmidt, W. F.; Allen, A. 0. J . Chem. Phys. 1970, 52, 4788. (13) Monchick, L. J . Chem. Phys. 1975, 62, 1907. Nagvi, K. R.; Waldenstrom, S.; Mork, K. J . J . Phys. Chem. 1982, 86, 4750. (14) Rice, S. A,; Baird, J. K. J . Chem. Phys. 1978, 69, 1989. (15) Allen, A. 0.;Holroyd, R. A. J . Phys. Chem. 1974, 78, 796.
8.
4244
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988
provides h,,(c,) and, with this, is obtained pt(cq)via eq 3.7 For f ( r o ) we have chosen
f ( r o ) = (P3/2)e-Oro
(8)
Such a function has been demonstrated to account well both for the quantum yield of escaped electrons from TMPD and for the dependence of this yield on electric field strength.2,10*16The parameter, /3, is obtained from the experimental escape probability in the absence of scavenger. This is accomplished by substituting eq 8 into eq 7 with gsc(ro,O)= e-rc/roto give
h,,(O) =
(/+,I
3’2K3[ 2 (PrJ
(9)
-
where K 3 is the modified Bessel function of order 3.’ As previously discussed, for TMPD in n-pentane, h,,(O) 6 X (at 5.9 eV). Substitution into eq 9 gives Pr, = 36.91. For the scavenging of thermal electrons by perfluorodecalin, kSr,2/4D 3.57 X lo3 M-I,’ and accordingly, at cq = 0.01 M (where Jo/J has its minimum), the parameter (k,r,2/4D)cq = 35.7. Using tabulated values of g,(r0,s)I7 in eq 7 and numerically integrating, we obtain h,,(cq) = 0.0687 and therefore pt(cq) = 0.0682 at cq = 0.01 M. At cq = 0.01 M , ( J - J o ) / J o reaches its maximum value of -0.03 (see Figure 1). Substituting this into eq 6 together with To =6 X and pt = 0.068 gives S, = -2.6 X estimate now a value for p 2 , we take D, N 1 X cm2/s18-20 and estimate R, not to exceed 10 A.21 Thus from eq 5, p 2 cannot exceed 5 X and with ( u ) N 2 X lo4 cm/s, we then compute that a cannot exceed Granting the validity of this treatment, and, as we will develop later, our other data appear to support it, there appears to be a very strong prohibition on the collapse of s+ and Q-.What is the origin of this prohibition? The gas-phase adiabatic ionization potentials of TMPD, triphenylamine, anthracene, and naphthalene are 6.2, 6.8, 7.4, and 8.2 eV, respectively,22 and the solvation energies of their positive ions are ca. 1.3,23l.0,24 l.0,24 and 1.0 eV,Z5respectively. The electron affinity of perfluorodecalin (PFD) is not yet known but is unlikely to exceed that of F (Le., 3.34 eV).26 The solvation energy of PFD- in n-pentane as estimated from the Born equation27is -0.6 eV. Thus, if we assume that TMPD* and PFD- are fully solvated in their encounter complex, then their collapse to TMPD + PFD could only be endoergic (and, therefore, likely to exhibit prohibition) if the TMPD+-PFDbinding energy exceeded 1 eV. Although this value is not unreasonable (as we will develop later), it must be kept in mind that it is based on rather generous assumption of the electron affinity of PFD. On the other hand, for perfluoromethylcyclohexane, with an electron affinity of 1.06 eV,28an endoergic collapse would require much too large a lower bound on the binding energy of ca. 3.3 eV. Similarly, for the case of s = anthracene and Q = PFD, in which case photocurrent enhancement is also observed
-
--
(16) Lee, K.; Lipsky, S. Can. J . Chem. 1985, 63, 1374. (17) Kindly supplied to us by Dr. Noolandi. (18) The self-diffusion coefficient of n-pentane is 5.54 X cm2/s at 25 “ C (see ref 19). The diffusion coefficients of TMPD and perfluorodecalin in n-pentane were crudely estimated by assuming they scaled inversely as their molecular radii as determined from molar volumes or from van der Waals volumes as estimated from atomic increments (see ref 20). (19) Fishman, E. J . Phys. Chem. 1955, 59, 469. (20) Edward, J. T. J . Chem. Educ. 1970, 47, 261. (21) The sum of the molecular radii is estimated (see footnote 18) to be 8.0 A. (22) Levin, R. D.; Lias, S. G. Ionization and Appearance Potenfial Measurements, 1971-2981; US.National Bureau of Standards: Washington, DC, 1982; NSRDS-NBS 71. (23) Holroyd, R. A,; Russell, R. L. J . Phys. Chem. 1974, 78, 2128. (24) Holroyd, R. A,; Preses, J. M.; Zevos, N . J . Chem. Phys. 1983, 79, 483. (25) Holroyd, R. A,; Preses, J. M.; Battcher, E. H.; Schmidt, W. F. J . Phys. Chem. 1984, 88, 744. (26) Chen, E. C. M.; Wentworth, W. E. J . Chem. Educ. 1975, 52, 489. (27) Estimated from the Born equation as suggested in ref 24. (28) Grimsrud, E. P.; Chowdhury, S.; Kebarle, P. J . Chem. Phys. 1985, 83. 1059.
Howell et al. (see Figure 4), the complex would still require an unreasonably large binding energy of ca. 2.5 eV, even with the assumption of a 3.34-eV electron affinity of PFD. An alternative possibility is that F has replaced PFD- in the encounter complex most plausibly via dissociative capture by PFD of the thermal electron (to generate R’ + F). The collapse to neutrals would now be further prohibited by the much larger solvation energy of F (Le., 22.5 eV in n-~entane)~~JO and, too, by its larger electron affinity (3.34 eV).26 Thus, for s = TMPD, this collapse to neutrals would be endoergic by at least ca. 1 eV and for s = anthracene would be endoergic if the Fs’binding energy exceeded ca. 0.6 eV.31-33On the other hand, for naphthalene, in which case no photocurrent enhancement was observed, we would accordingly (assuming again that exoergicity is the crucial factor) require that the binding energy not exceed ca. 1.4 eV. That thse bounds are not unreasonable can be demonstrated as follows. From the point of view of the ionic dissociation of a “stable” ion pair, the escape probability can be represented as the product of the dissociation rate constant, kd, and the lifetime, T , of the ion pair.34 The rate constant is estimated to have a preexponential factor, A , of ca. 1 0 ~ ~ - 1s-I 0 and ~ ~ a Boltzmann factor of exp[B / k T ] where B is the ion-pair binding energy.34 Since the escape in the absence of scavenger, and this is probability is 6 X slightly enhanced in the presence of scavenger, an upper bound estimate of B is obtained as -kT In (6 X 10-4/A~). Recent measurements on TMPD irradiated in isooctane in the presence of PFD provide evidence for a TMPD’ electronic absorption which lingers after the illumination has ceased and slowly decays with a ca. 0.018 s-I unimolecular rate constant.35 Estimating from this a T N 56 s provides an upper bound estimate of B N 1.2 eV. Whether or not PFD dissociatively captures the electron remains uncertain. Taking the C-F bond strength as 4.3 eV,32s36it can be estimated that the free energy change for PFDF + R’ in n-pentane would indeed be favorable unless PFD has an electron affinity exceeding N 1.4 eV.37 For perfluoromethylcyclohexane (PFM), a similar calculation but using 1.06 eV for the electron affinity of PFM2s gives a favorable AG of ca. -0.36 eV. From a rather qualitative point of view, all of our other observations appear to be consistent with the predictions of eq 2. Clearly, as dIoincreases, J will approach Jo and the photocurrent enhancement effect should decline. Since already in n-pentane the effect is a rather small one, the substantial increases in by factors of ca. 4 in cyclohexane, 84 in isooctane, and 440 in tetramethylsilane’ make virtually impossible its observation in these solvents at the 1% reliability level of our experiments. On the other hand, in n-hexane with decreased by ~ 1 . 5the , enhancement should have been increased and, indeed, was, in fact, so observed, although the rather small predicted change in Jo/J at the minimum from -0.97 (in n-pentane) to 0.95, (in n-hexane) was somewhat obscured by experimental uncertainties. The effect of increasing photon energy and increasing applied electric field strength to reduce the extent of photocurrent enhancement can also be attributed to their effects to increase C$’O.
-
-
(29) This is estimated via the Born equation using for the radius of F its crystallographic value of 1.33 A (see ref 30). (30) Ketelaar, J. A. A. Chemical Constiturion; Elsevier: New York, 1958; p 28. (3 1) The dissociative capture of an electron by R F to form R- + F is not considered here although in the gas phase this reaction often appears with a lower threshold energy than capture to R F (see ref 32 and 33). In the liquid phase, the much larger solvation energy of F ( e 2 . 5 eV) vis-i-vis R( Y 1 e v ) is expected to dominate the electron affinity differences between F and the pertinent perfluoro radicals (e.g., the electron affinity of perfluoromethylcyclohexyl is only about 0.6 eV greater than that of F; see ref 32). (32) Lifshitz, C.; Peers, A. M.; Grajower, R.; Weiss, M. J . Chem. Phys. 1970, 53, 4605. (33) Spyrou, S. M.; Sauers, I.; Christophorou, L. G . J . Chem. Phys. 1983, 78, 7200. (34) Braun, C. L. J . Chem. Phys. 1984, 80, 4157. (35) Cooper, W. F. M.S. Dissertation, University of Minnesota, 1985. (36) Heicklen, J. Adu. Photochem. 1969, 7 , 57. (37) In making this estimate, we have used solvation energies of 0.6 and 2.5 eV for perfluorodecalin and F, respectively (see ref 27 and 29), and an entropy change of 1.5 X 10-j eV/K reflecting simply the translational contribution.
+
Photocurrent Enhancement in Nonpolar Liquids With regard to excitation energy, the photocurrent from TMPD in n-pentane increases by a factor of -6.5 over the energy interval from eeXc = 5.8 to 6.4 eV at which latter energy essentially no photocurrent enhancement is observed (see Figure 3). Since much of this increase appears attributable to increase in the average range of the e l e ~ t r o n , ' ~it~reflects, ~* in liquids such as n-pentane, or n-hexane, a very substantial change in dl0. For example, in n-hexane, Choi and Brawlo have shown that with the distribution function of eq 8 the average electron range changes from -22 A at texc= 5.90 eV to 28 A at e,, = 6.2 eV, and via eq 9, it can be shown that this represents a change in dl0(=hsc(0))of about a factor of 2.8. With regard to change in field strength, it can be seen from Figure 2 that at E = 17 kV/cm (at which field there appears no enhancement) the photocurrent (which is proportional to dl0)has increased by a factor (-2.5) sufficient again to bury any enhancement in the 1% uncertainty. We attribute the disappearance of the enhancement effect by replacement of the cyclic perfluorocarbons with n-perfluorohexane (PFH), in major part, to its smaller efficiency for scavenging thermal electrons. Thus, in cyclohexane, previous studies have indicated that, at cq = 0.01 M, pt(PFD) N 1.5pt(PFH).7,39 From this it can be derived that the dimensionless concentration variable of the Noolandi theory6 (Le., k,cqr?/4D) equals 11.7 at 0.01 M PFH.40 This is about one-third its value for PFD. Accordingly, we can compute via eq 7 for n-pentane as solvent (with prc = 36.9) that h,,(cq) = 0.031 at 0.01 M PFH and pt(c,) = 0.030. This is lower by about a factor of 2.3 from its value for PFD, and accordingly, Jo/J would now be predicted to be only 0.99 at the minimum. Some additional obscuration of the minimum would also be predicted from the slightly greater effect of PFH to prethermalize the epithermal electron. This is indicated by the difference in slopes of the linear regressions of Jo/J on cq of 4.0 M-' for PFH' as compared to 3.3 M-' for PFD and 2.7 M-' for perfluoromethylcyclohexane (see Figure 1 ) . Finally, we comment briefly on the absence of photocurrent enhancement when CC14 is used as scavenger. Dissociative electron capture by CC14 to generate CC13 + C1- in saturated hydrocarbon liquids has been indicated by radiation chemical ~ t u d i e s , and ~'
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988 4245 indeed, the energetics for this reaction appear somewhat more favorable than for the corresponding reaction with perfluorocarbon^.^^^^^ Also, Warman and V i ~ s e have r ~ ~ reported on the existence of relatively long lived complexes of TMPD+Cl- in CC1444 (and in c y c l o h e ~ a n e ) . ~Thus, ~ the situation here is not too different from what we have suggested to be responsible for photocurrent enhancement in TMPD-PFD systems, and therefore the absence of such effect for CC14 is,somewhat surprising. However, the Tachiya model3 assumes diffusion in a purely Coulombic field with a fixed dielectric constant, t. Accordingly, at the encounter radius, R 2 , so long as the [s+,Q-] interaction potential remains as e2/cR2,the encounter complex will either annihilate or escape with the probability, $20. Any contribution to the binding energy that derives from non-Coulombic terms should accordingly decrease the escape probability from its value predicted by eq 4. Thus, one possible cause for the disparity between CC14 and PFD may lie with the greater polarizability of C1- vis-&vis F and its corresponding effect to additionally bind the complex. To confirm this, it would be useful to accommodate the basic Onsager theory4 to non-Coulombic interactions at short distances. Of course, too, a more refined theory must additionally accommodate the effect of the scavenger not only on the thermalized electron but also on its epithermal precursor. Such theoretical developments remain to be explored.
Acknowledgment. This research was supported in part by the U S . Department of Energy, Division of Chemical Science, Office of Basic Energy Sciences. We are also grateful to Mr. David B. Johnston for his technical assistance. Registry No. PFD, 306-94-5; TMPD, 141 18-16-2; anthracene, 12012-7; triphenylamine, 603-34-9; n-pentane, 109-66-0 n-hexane, 110-54-3;
perfluoromethylcyclohexane, 355-02-2.
(41) Cramer, W. A. In Aspects ofHydrocarbon Radiolysis; Gaiimann, T., Hoignt, J., Eds.; Academic: New York, 1968; p 191. Gyorgy, I.; Wojnlrovits, L. In Radiation Chemistry of Hydrocarbons; Foldiak, G., Ed.; Elsevier: New York, 1981; p 41. Gremlich, H. V.; Buhler, R. E. J . Phys. Chem. 1983,87, 3267. ( 4 2 ) The electron affinity of CC14 is 2.1 eV, and the C-C1 bond strength is 3.0 eV (see ref 43). The electron affinity of C1 is 3.61 eV (see ref 26), and the solvation energies of Cl- and CCI4- in n-pentane, as estimated from the Born equation, with r = 1.81 8, for CI- (see ref 30) and r = 3.84 8, for CC14(estimated from the molar volume; see ref 24), are 1.8 and 0.75 eV, respec( 3 8 ) Lee, K.; Lipsky, S. J . Chem. Phys. 1985, 82, 3650. tively. ( 3 9 ) Choi, H. T.; Wu, K. C.; Lipsky, S . Radiat. Phys. Chem. 1983, 21, 9s. ( 4 3 ) Gaines, A. F.; Kay, J.; Page, F. M. Trans. Faraday Soc. 1965, 61, ( 4 0 ) This value is derived from the equation = 1 + 0 . 0 9 [ k , ~ ~ r , 2 / 4 D ] ~ . ' 874. (44) Warman, J. M.; Visser, R. J. Chem. Phys. Lett. 1983, 98,49. where Q = 1 / ( 1 - p') (see ref 7 ) . Thus, with p (PFH) N 0.335 at 0.01 M (see ref 39), we obtain k,cqr2/4D = 11.7. (45) Warman, J. M., private communication.
e
