14688
J. Phys. Chem. 1996, 100, 14688-14693
Solvent Reorganization Energy in Excited-State Electron-Transfer Reactions. Quenching and Geminate-Pair Back Electron Transfer Catherine D. Clark and Morton Z. Hoffman* Department of Chemistry, Boston UniVersity, Boston, Massachusetts 02215 ReceiVed: February 19, 1996; In Final Form: May 3, 1996X
The temperature dependencies of the quenching rate constants (kq) and cage escape yields of the redox products (ηce) from the electron-transfer reaction of *Ru(bpy)32+ (bpy ) 2,2′-bipyridine) with nine aromatic amines in deaerated 1:1 (v/v) CH3CN/H2O solutions have been determined. Values of λ, the solvent reorganization energy for electron-transfer quenching and back electron transfer within the solvent cage, have been extracted from plots of log(kqT1/2) Vs 1/T and log((ηce-1 - 1)T1/2) Vs 1/T, respectively. For the quenching process, λ is not a constant value for the series of quenchers; in general, higher values of λ are exhibited by primary amines and lower values by tertiary amines. The structure and size of the quenchers and the nature of the ring substituents contribute to the value of λ. For the back-electron-transfer reaction within the geminate redox pair formed in the quenching process, the more sterically hindered two-ring amines exhibit a higher value of λ (1.1 ( 0.08 eV) than do the majority of the one-ring amines (0.82 ( 0.04 eV). A Marcus plot of log(ηce-1 - 1) Vs ∆G°bt shows a correlation within only the inverted region for systems with the same λ; the earlier identification of the results for the same photosensitizer and quenchers as a bell-shaped curve is due to the coincidental overlap of two independent segments within the inverted region.
Introduction In recent years, light-induced electron-transfer reactions have been investigated extensively with a view toward the understanding of the primary mechanism of natural photosynthesis and the development of artificial systems for the conversion and storage of solar energy.1 Ru(II) complexes, especially those that possess diimine ligands, are readily synthesized with a range of charges, structures, redox potentials, and photochemical/ photophysical properties, making them useful as photosensitizers.2 Photoinduced electron transfer between excited Ru(II) complexes and aromatic amines (A) has been the subject of a number of studies, the principal aim of which being to test theories of electron transfer with particular emphasis on the Marcus model.3 Because of the magnitude of work done with Ru(bpy)32+ (bpy ) 2,2′-bipyridine), this complex still serves as the standard against which other complexes with different metal centers and/ or ligands are compared. The reductive quenching of *Ru(bpy)32+ by A can be described by reactions 1-3; the details of the release of Ru(bpy)3+ and A•+ into bulk solution is described by the conventional cage escape model (reactions 4-6).4 The cage escape yield (ηce) of the redox products is given as kce/(kce + kbt); (ηce-1 - 1) ) kbt/kce. hν
Ru(bpy)32+ 98 *Ru(bpy)32+
(1)
ko
*Ru(bpy)32+ 98 Ru(bpy)32+ + hν′
(2)
kq
*Ru(bpy)32+ + A 98 Ru(bpy)3+ + A•+
(3)
*Ru(bpy)32+ + A f [Ru(bpy)3+‚‚‚A•+]
(4)
kbt
[Ru(bpy)3+‚‚‚A•+] 98 [Ru(bpy)32+‚‚‚A]
(5)
kce
[Ru(bpy)3+‚‚‚A•+] 98 Ru(bpy)3+ + A•+ X
(6)
Abstract published in AdVance ACS Abstracts, August 1, 1996.
S0022-3654(96)00495-9 CCC: $12.00
Values of kq for the Ru(II)/A system increase with increasing driving force (more negative ∆G°) of reaction 3 in the normal Marcus region,5 reaching a plateau near the diffusion-controlled limit6 (Rehm-Weller behavior).7 The question of the adiabaticity of the quenching reaction has been addressed through the change in the stucture of the diimine ligands to alter the electronic coupling; Sandrini et al.,8 in a study with a complex with tert-butyl substitution on the bpy ligands, concluded that the quenching exhibits nonadiabatic behavior. On the other hand, Tazuke et al.9a found that the quenching reaction is adiabatic in highly exoergic regions, with nonadiabaticity becoming important for bulky ligands when the driving force is small; however, Maruyama and Kaizu9b recently reevaluated the same quenching data and concluded that the process is nonadiabatic. Most of these previous studies were carried out in CH3CN; Baggot determined kq and its activation parameters for the system in methanol.10 The importance of the solvent has been demonstrated by Garrera et al.11 for Ru(bpy)32+; the activation parameters showed that the quenching reaction follows Marcus behavior in protic solvents, but that the structure of the aromatic moiety is important in aprotic solvents. Tazuke et al.12 showed that kq varies with the nature of the amine (tertiary > primary, secondary) at the same value of ∆G°; the difference was attributed to differences in the solvent reorganization energy on the basis of estimates from the Marcus model. Marcus theory predicts that the rate constant of electron transfer will follow a bell-shaped energy gap dependence as a function of ∆G°et, initially increasing as ∆G°et becomes more negative in the normal region and decreasing with increasing driving force in the inverted region.5 This predicted behavior has been consistently observed for intramolecular electron transfer between covalently linked donor-acceptor moieties.13 For intermolecular electron-transfer reactions, the focus of studies on energy gap dependencies has been on two types of systems that can approximate the intramolecular case: contact ion pairs that are formed by the direct charge-transfer excitation © 1996 American Chemical Society
Geminate-Pair Back Electron Transfer
J. Phys. Chem., Vol. 100, No. 35, 1996 14689
Experimental Section
Laser Flash Photolysis. Transient absorption and emission measurements were performed with a Nd:YAG laser (Quantel YG581) with excitation at 532 nm and a constant laser power of 150 mJ/pulse; details of the apparatus have been described before.19 The output voltage of the photomultiplier (Hamamatsu R928) was controlled to produce a linear response. The data were averaged for 10 and 20 laser pulses for the absorption and emission measurements, respectively. Solution temperatures were controlled to within (0.1 °C in a thermostated cell holder. Experiments were performed on Ar-purged 1:1 (v/v) CH3CN/H2O solutions at ambient ionic strength with [Ru(bpy)32+] ) 25 µM and [A] ) 0.02-15 mM. Care was taken to remove oxygen from the solutions as they were being prepared inasmuch as some of the amines undergo rapid air oxidation, resulting in color changes. Values of kq were obtained from the slopes of the linear plots of the observed first-order rate constants (kobs) for the decay of *Ru(bpy)32+ at 605 nm Vs [A], using four different quencher concentrations. The quantum yield of formation of redox products (Φ) is given as ∆[A•+]/∆[*Ru(bpy)32+]. Values of ∆[*Ru(bpy)32+] were calculated from measured values of ∆A at 450 nm extrapolated to the midpoint of the 7 ns laser pulse, in the absence of quencher, by using Beer’s law (∆A ) ∆l∆c), where ∆ is the difference in the values at 450 nm of the ground and excited states of Ru(bpy)32+ (-1.0 × 104 M-1 cm-1),20 l ) 2 cm, and ∆c is the change in the concentration of the absorbing species. Values of ∆[A•+] were obtained 1-5 µs after the pulse from measurements of ∆A at a wavelength appropriate to the amine: 520 nm for pheno (∆ ) 0.93 × 104 M-1 cm-1);21 by electron transfer to TMPD at 610 nm (∆ ) 1.2 × 104 M-1 cm-1)22 for p-anis, PD, and TMB;15a from ∆A of Ru(bpy)3+ at 510 nm (∆ ) 1.34 × 104 M-1 cm-1)25 inasmuch as [Ru(bpy)3+] ) [A•+] for p-tol, DPA, DMA, and DMB.15a Values of ηce were determined from the relationship Φ ) ηqηce and averaged from 3-5 duplicate solutions; ηq, the efficiency of quenching, was calculated from (kobs - ko)/kobs, where ko and kobs are the observed first-order decay rate constants in the absence and presence of quencher, respectively. Electrochemistry. Cyclic voltammetry was carried out with an EG&G potentiostat (Model 273A) with computer interface and associated software. Experiments were performed on Arpurged CH3CN and 1:1 (v/v) CH3CN/H2O solutions containing 0.1 M [(C2H5)4N]ClO4 (GFS, electrochemical grade) and 2 mM amine at a scan rate of 0.2 V/s, using a glassy carbon working electrode, a Ag/AgCl reference electrode, and a Pt counter electrode. Ferrocene (Aldrich) was used as an internal standard. Fast scan (1000 V/s) experiments utilized a EG&G Parc Universal Programmer (Model 175) to generate the waveform, which was passed into the potentiostat with the same electrochemical cell configuration. The output from the cell was passed to a Tektronix TDS 320 oscilloscope, which was set to trigger upon the initiation of the potential sweep. The data were then acquired with a computer interface and Tektronix Docuwave software and analyzed with an Igor graphical program.
Materials. [Ru(bpy)3]Cl2 (GFS Chemicals) was recrystallized from water and dried over silica gel. N,N,N′,N′-tetramethyl-1,4-phenylenediamine (TMPD), p-toluidine (p-tol), phenothiazine (pheno), p-anisidine (p-anis), 3,3′,5,5′-tetramethylbenzidine (TMB), dimethylbenzidine (DMB), 1,4-phenylenediamine (PD), diphenylamine (DPA), and N,N-dimethylaniline (DMA) were obtained from Aldrich and were purified by vacuum distillation; the structures of the amines are shown in Figure 1. Distilled water was further purified by passage through a Millipore purification train. Acetonitrile (Baker HPLC grade) was used without further purification.
Results and Discussion Electrochemical Potentials. Cyclic voltammetry of Ru(bpy)32+ shows reversible waves corresponding to one-electron oxidations and reductions. A value of the reduction potential of *Ru(bpy)32+ [E°(*Ru2+/Ru+)] can be estimated from E°(Ru2+/Ru+) + Eem, where E°(Ru2+/Ru+) is the reduction potential of the ground state and Eem is the excitation energy estimated from the maximum wavelength of emission.24 Inasmuch as Eem ) 2.01 eV25 and E°(Ru2+/Ru+) ) -1.13 V (Vs NHE) in 1:1 (v/v) CH3CN/H2O, E°(*Ru2+/Ru+) ) 0.88 V (Vs NHE).
Figure 1. Structures of the aromatic amine quenchers.
of the paired ground-state reactants14 and geminate redox pairs that are formed by diffusive quenching of excited reactants.4,15-17 For excited-state redox quenching, both weak and strong Marcus dependencies of the electron-transfer rate constants within geminate redox pairs on the driving force have been recorded, generally within the inverted region; occasionally, however, bell-shaped curves have been observed. Ohno and co-workers15 found a well-defined bell-shaped curve for the rate constants of back electron transfer (kbt) between the geminate redox pairs formed in the bimolecular reductive quenching of a series of excited Ru(II)-diimine complexes [Ru(bpy)32+, Ru(bpz)32+, Ru(phen)32+, Ru(Ph2phen)32+]18 by aromatic amines in mixed CH3CN/H2O solutions. On the other hand, the reductive quenching of excited Ru(II) homo- and heteroleptic bpz and bpm18 complexes by different quenchers has shown only a weak or no energy gap dependence of kbt.16 Weak or no energy gap dependencies of kbt have also been seen for the intermolecular oxidative quenching of Ru(II) complexes by methylviologen.13b,c,17 These seemingly disparate observations raise the question of the generality of the bell-shaped energy gap dependence for kbt in the geminate redox pair generated in excited-state quenching reactions, which, in the past, have been studied only at a single temperature. To explore this question, we have measured the temperature dependence of the efficiency of cage escape of the redox products released into solution (ηce) and of kq for the quenching of *Ru(bpy)32+ by the same aromatic amines that were used previously;15 in addition, two other amines were included to extend the series.
14690 J. Phys. Chem., Vol. 100, No. 35, 1996
Clark and Hoffman
TABLE 1: Values of E°(A•+/A), ∆G°q, ∆G°bt, and λ for Quenching and Back Electron Transfera
a
amine
E°(A•+/A)b (V) Vs NHE
-∆G°q (eV)
-∆G°bt (eV)
λ (quenching) (eV)
λ (back electron transfer) (eV)
1 TMPD 2 PD 3 TMB 4 DMB 5 pheno 6 p-anis 7 p-tol 8 DPA 9 DMA
0.21 0.34 0.48 0.63 0.64 0.68 0.87c 0.93c 0.92c
0.67 0.54 0.40 0.25 0.24 0.20 0.01 -0.03 -0.04
1.34 1.47 1.61 1.76 1.77 1.81 2.00 2.06 2.05
1.8 1.5 0.97 1.8 0.47 1.5 1.0 1.4 0.61
0.85 0.78 1.1 1.2 1.0 0.84 1.1 1.0 1.1
In 1:1 (v/v) CH3CN/H2O. b 0.2 V/s scan rate. c 1000 V/s scan rate.
In very many cases, the reduced or oxidized forms of organic quenchers are unstable, especially in the presence of H2O, making it difficult, if not impossible, to obtain reversible cyclic voltammograms.26 Often, half-wave potentials, especially for aromatic amines, have been used as a measure of the redox potential, but this can lead to very poor estimates. If very fast scan rates are used to compete with the secondary reactions, reversible behavior can be obtained.27 Quasi-reversible cyclic voltammograms were obtained for the six amines with E°(A•+/ A) potentials 1. Values of ket as a function of temperature calculated with this model are given in the supporting information.
kd )
(
)
rA rB 1 2kTN 2+ + 3000η rB rA a ∞r-2 exp[w(r,µ)/kT] dr ∫a
k-d )
(
)
exp[w(a,µ)/kT] 1 kT 1 + ∞ -2 2 r r 2πηa B A a∫ r exp[w(r,µ)/kT] dr a
(
(14)
(15)
)
zAzBe2 exp(βσARxµ) exp(βσBxµ) × + w(r,µ) ) 2r 1 + βσAxµ 1 + βσBxµ
shaped curve obtained by Ohno et al.;15a our measured value of E° (and thus ∆G°bt) for p-anis is different from that reported, thereby somewhat worsening the bell-shaped correlation. The maximum of the bell-shaped curve, according to Marcus theory, occurs when the reorganization energy (λ) equals -∆G°et. However, the value of λ of 1.7 eV obtained from these data and those of Ohno et al.15a is high in comparison to recently obtained values: ∼1 eV for intramolecular electron-transfer reactions in CH3CN13b,30 and ∼0.8 eV for intermolecular reductive quenching of *Ru(bpy)32+ by aromatic amines in protic solvents.11 This analysis of the dependence of kbt on the energy gap is only as good as its two important assumptions: that λ and kce are the same for all of the systems. With regard to λ, this quantity is a measure of the free energy required to activate the motions of all the atoms of the initial state, including those in the solvent shell, from their equilibrium positions to those of the final state. The value of λ has two contributions: λin from the motion of the atoms of the reactants (exclusive of the solvent shell), which is insignificant for the species under consideration here,38 and λout from the reorganization of the solvent molecules and the ions that surround the reacting species in the solvent cage. It is certainly expected that λ would be sensitive to the nature, size, and steric restrictions of the species involved; whether λ is truly a constant value for all of the components of homologous series cannot be tacitly assumed. That λ is sensitive to relatively minor changes in the solution medium has been demonstrated in a recent paper;39 we showed that λ for quenching and back electron transfer in the same chemical system [Ru(bpy)32+ and methylviologen] in aqueous solution was even a function of the nature of the supporting electrolyte used to control ionic strength. With regard to kce, its values can be calculated with eq 15; the assumption can be made that the sizes of the photosensitizer and quenchers remain virtually unchanged when they undergo electron transfer. At 20 °C, the calculated values of kce range from 1.4 × 109 s-1 for DMB to 4.0 × 109 s-1 for PD, indicating that any presumed constancy of kce can also be brought into question. The calculated values of kce as a function of temperature lead to the evaluation of kbt as a function of temperature for the nine quenchers; kce and kbt are given in the supporting information. Reorganization Energy. In the classical formulation of Marcus theory, the rate constant of an electron-transfer reaction is given by eq 18, where V is the electronic coupling coefficient. Electron-transfer reactions can be described as adiabatic (strong donor-acceptor coupling, V . kT) or nonadiabatic (poor coupling, V , kT).24 For typical transition metal redox reactions at 25 °C, the point of deviation between adiabatic and nonadiabatic behavior occurs at V ∼ 0.025 eV.40
exp(-βrRxµ) (16) β)
(
)
8πNe2 1000kT
k)
1/2
(17)
Cage Escape Yields. Values of ηce as a function of temperature are given in the supporting information;37 in general, ηce increases with increasing temperature. Inasmuch as (ηce-1 - 1) ) kbt/kce according to the conventional model,4 a plot of log(ηce-1 - 1) Vs ∆G°bt is predicted to give a bell-shaped dependence if kce is the same for all of the [Ru(bpy)3+‚‚‚A•+] systems. If this assumption were at least approximated, the observed dependence would be solely due to the variation of kbt with ∆G°bt. Figure 3 shows a plot of log(ηce-1 - 1) Vs ∆G°bt at 20 °C, which resembles the bell-
[
]
-(λ + ∆G°)2 4π2V2 exp 4λkT h(4πλkT)1/2
(18)
This formulation has been extended41 for nonadiabatic reactions to include the simultaneous contribution of lowfrequency classical modes and high-frequency quantum modes. The effects of the high-frequency modes are observed in the inverted region, with higher rate constants than those predicted by the classical theory. The temperature dependence that is predicted by eq 18 is an inverse bell-shaped curve, with the activation energy decreasing through the normal region, becoming zero where λ ) -∆G°, and increasing as the inverted region is traversed. When the quantum effects are considered, the
14692 J. Phys. Chem., Vol. 100, No. 35, 1996
Clark and Hoffman
Figure 4. Plot of log[(ηce-1 - 1)T1/2] Vs 1/T: PD (O), TMB (b), p-anis (2).
Figure 5. Plot of log(ηce-1 - 1) Vs ∆G°bt at 20 °C for quenchers with λ ) 1.1 ( 0.08 eV (O) and λ ) 0.82 ( 0.04 eV (b).
temperature dependence follows the classical prediction in the normal region, but is practically activationless in the inverted region.41 This lack of a temperature dependence in the inverted region has been observed by Liang et al. for intramolecular back-electron-transfer reactions.42 The temperature dependencies of ket and kbt (supporting information) indicate that they have activation energies throughout the entire range of ∆G° studied, suggesting that both quenching and back electron transfer behave classically to a first approximation and can be treated by eq 18. In that case, values of λ and V can be determined from the slopes and intercepts of linear plots of ln(kT1/2) Vs 1/T.13b,30,43 This treatment was applied to the quenching and backelectron-transfer reactions; values of V, which are obtained from a long extrapolation and must be viewed with caution, are generally the same for both processes. V ranges from 0.03 eV for DMB to 0.005 eV for pheno, which is not very large nor significantly different from 0.025 eV (∼kT). Thus, the demarcation between adiabatic and nonadiabatic for these reactions is not clear-cut, which is consistent with the conflicting conclusions reached by others9 for the same photosensitizer and quenchers. Values of λ for quenching (Table 1) were the same whether they were obtained from plots of log(ketT1/2) or log(kqT1/2) Vs 1/T. The values of λ for the different quenchers certainly are not constant, but appear to exist within four groups: (1) pheno, DMA; (2) TMB, p-tol; (3) PD, p-anis, DPA; and (4) TMPD, DMB. To a very rough approximation, the higher values of λ are exhibited by primary amines and the lower values by tertiary amines, although this trend does not hold for TMPD and DMA, which are both tertiary amines. It should be noted that Tazuke et al.12 found ket for the reaction of *Ru(bpy)32+ with an extensive series of amines in neat CH3CN to be higher for tertiary amines than for primary and secondary amines; this observation was attributed to the variation in λout with the nature of the quencher. Gould et al.44 also observed that λ increases with an increase in the number of methyl substituents on organic donors. Thus, both the structure, size, and steric restrictions of the quenchers will contribute to the observed values of λ. There is no doubt that the nature of substituents will also affect the value of λ, making it difficult to draw further conclusions on the basis of this particular set of quenchers. The values of λ for back electron transfer within the geminate redox pair (Table 1) were found to be the same whether plots of log(kbtT1/2) or log [(ηce-1 - 1)T1/2] Vs 1/T (Figure 4) were used. The significant result here is that the more sterically hindered two-ring systems exhibit a higher value of λ (1.1 (
0.08 eV) than do the majority of the one-ring systems (0.82 ( 0.04 eV); similar steric effects on λ have recently been reported.45 The one-ring amines, p-tol and DMA, are atypical with λ values of 1.0 eV, which could arise from variations in λ with the nature of the amine.12 The plot of log(ηce-1 - 1) Vs ∆G°bt can now be redrawn, grouping together the systems with the same values of λ (Figure 5). The result is a correlation within only the inverted region, as observed recently with other systems.13b,c,44,45a,b We are forced to conclude that the earlier identification of the results for this system15a as a bell-shaped curve is due to the coincidental overlap of two independent segments within the inverted region; the earlier analysis of the data was based on the premise that λ for all of the quenchers is the same, a situation that clearly is not the case. A similar explanation was used recently by Doolen et al.46 to explain their results for the values of kbt in contact ion pairs; the relationship between kbt and ∆G°bt showed normal Marcus behavior, whereas the temperature independence of kbt indicated that the reaction was in the inverted region. The discrepancy was attributed to differences in the solvent reorganization energies among the systems that were being compared; in the context of the work reported here, this explanation means that each donor-acceptor pair lies on a different Marcus curve, which overlap and intersect. We emphasize that it is imperative in studies of inter- and intramolecular electron transfer that reaction rates be measured as a function of temperature. Investigations of the dependence of rate constants of electron transfer on the driving force must include the careful choice of a truly homologous series of reactants, since differences in the structure and nature of the reactants can result in different values of λ, resulting in data that lie on different Marcus curves. Acknowledgment. This research was supported by the Office of Basic Energy Sciences, Division of Chemical Sciences, U.S. Department of Energy. The authors thank Dr. J. R. Miller for important discussions. Supporting Information Available: Values of kq, kd, k-d, ket, ηce, kce, and kbt as a function of temperature in 1:1 (v/v) CH3CN/H2O (7 pages). Ordering information is available on any current masthead page. References and Notes (1) Juris, A.; Balzani, V.; Barigelletti, F.; Campagna, S.; Belser, P.; von Zelewsky, A. Coord. Chem. ReV. 1988, 84, 85.
Geminate-Pair Back Electron Transfer (2) Kalyanasundarum, K. Photochemistry of Polypyridine and Porphyrin Complexes; Academic Press: New York, 1992. (3) Roundhill, D. M. Photochemistry and Photophysics of Metal Complexes; Plenum Press: New York, 1994. (4) Balzani, V.; Scandola, F. In Energy Resources Through Photochemistry and Catalysis; Gra¨tzel, M., Ed.; Academic Press: New York, 1983; pp 1-48. (5) Suppan, P. Top. Curr. Chem. 1992, 163, 97. (6) (a) Bock, C. R.; Conner, J. A.; Gutierrez, A. R.; Meyer, T. J.; Whitten, D. G.; Sullivan, B. P.; Nagel, J. K. J. Am. Chem. Soc. 1979, 101, 4815. (b) Ballardini, R.; Varani, G.; Indelli, M. T.; Scandola, F.; Balzani, V. J. Am. Chem. Soc. 1978, 100, 7219. (7) Rehm, D.; Weller, A. Isr/ J. Chem. 1970, 8, 259. (8) Sandrini, D.; Maestri, M.; Belser, P.; von Zelewsky, A. J. Phys. Chem. 1985, 89, 3675. (9) (a) Kitamura, N.; Rajagopal, S.; Tazuke, S. J. Phys. Chem. 1987 91, 3767. (b) Maruyama, M.; Kaizu, Y. J. Phys. Chem. 1995, 99, 6152. (10) Baggot, J. E. J. Phys. Chem. 1983 87, 5223. (11) Garrera, H. A.; Cosa, J. J.; Previtali, C. M. J. Photochem. Photobiol. A: Chem. 1989, 47, 143. (12) Kitamura, N.; Kim, H.-B.; Okano, S.; Tazuke, S. J. Phys. Chem. 1989, 93, 5750. (13) (a) Closs, G. L.; Miller, J. R. Science 1988, 240, 440. (b) Yonemoto, E. H.; Saupe, G. B.; Schmehl, R.; Hubig, S.; Riley, R. L.; Iverson, B. L.; Mallouk, T. E. J. Am. Chem. Soc. 1994, 116, 4786. (c) Kelly, L. A.; Rodgers, M. A. J. J. Phys. Chem. 1995, 99, 13132. (14) Asahi, T.; Ohkohch, M.; Mataga, N. J. Phys. Chem. 1993, 97, 13132. (15) (a) Ohno, T.; Yoshimura, A.; Mataga, N. J. Phys. Chem. 1990, 94, 4871. (b) Ohno, T.; Yoshimura, A.; Mataga, N.; Tazuke, S.; Kawanishi, Y.; Kitamura, N. J. Phys. Chem. 1989, 93, 3546. (c) Ohno, T.; Yoshimura, A.; Shioyama, H.; Mataga, N. J. Phys. Chem. 1987, 91, 4365. (d) Ohno, T.; Yoshimura, A.; Mataga, J. Phys. Chem. 1986, 90, 3295. (16) Sun, H.; Hoffman, M. Z. J. Phys. Chem. 1994, 98, 11719. (17) Ohno, T.; Yoshimura, A.; Prasad, D.; Hoffman, M. Z. J. Phys. Chem. 1991, 95, 4723. (18) phen ) 1,10-phenanthroline; Ph2phen ) 4,7-diphenyl-1,10-phenanthroline; bpz ) 2,2′-bipyrazine; bpm ) 2,2′-bipyrimidine. (19) Jones, G.; Oh, C. J. Phys. Chem. 1994, 98, 2367. (20) Yoshimura, A.; Sun, H.; Hoffman, M. Z. J. Phys. Chem. 1994, 98, 5058. (21) Alkaitis, S. A.; Beck, G.; Gra¨tzel, M. J. Am. Chem. Soc. 1975, 97, 5723. (22) Rao, P. S.; Hayon, E. J. Phys. Chem. 1975, 79, 1063. (23) Yoshimura, A.; Hoffman, M. Z.; Sun, H. J. Photochem. Photobiol. A: Chem. 1993, 70, 29. (24) Bolton, J. R.; Archer, M. D. AdV. Chem. Ser. 1991, 228, 7. (25) Eem is invariant of solvent, with λmax being 617 and 618 nm in H2O and CH3CN, respectively. (26) Amatore, C.; Kochi, J. K. In AdVances in Electron Transfer Chemistry; Mariano, P. S., Ed.; Jai Press: Greenwich, CT, 1991; Vol. 1, pp 55-65. (27) Andrieux, C. P.; Saveant, J. M. In InVestigation of Rates and Mechanisms of Reactions, Part II, Techniques of Chemistry, 4th ed.; Bernasconi, C. F., Ed.; Wiley: New York, 1986; Vol. VI, pp 305-388.
J. Phys. Chem., Vol. 100, No. 35, 1996 14693 (28) Mann, C. K.; Barnes, K. K. Electrochemical Reactions in Nonaqueous Systems; Marcel Dekker: New York, 1970. (29) Heitele, H.; Finckh, P.; Weeren, S.; Po¨llinger, F.; Michel-Beyerle, M. E. J. Phys. Chem. 1989, 93, 5173. (30) Zeng, Y.; Zimmt, M. B. J. Phys. Chem. 1992, 96, 8395. (31) Debye, P. Trans. Electrochem. Soc. 1942, 82, 265. (32) Smoluchowski, M. Z. Phys. Chem. 1917, 92, 129. (33) Melendar, G.; Eigen, M. Z. Phys. Chem. (Munich) 1954, 1, 176. (34) Sutin, N. Prog. Inorg. Chem. 1983, 30, 441. (35) The radii of the amines were calculated with the Hyperchem Molecular Modeling system, assuming a “mean spherical approximation” with freely rotating reactants; the longest radius for each amine was taken as the best approximation of the steric size of the quenchers (in angstroms): TMPD, 4.96; PD, 3.66; TMB, 7.12; DMB, 5.89; pheno, 5.00; p-anis, 4.48; p-tol, 3.76; DPA, 5.56; DMA, 4.06. (36) (a) Akhsdow, Y. Y. Dielectric Properties of Aqueous Solutions; Pergamon Press: New York, 1981; p 459. (b) Mato, F.; Hernandez, J. L. An. Quim. 1969, 65, 9. (37) Our values of ηce are consistently ∼40% lower than those reported15a for the same chemical systems under the same temperature (20 °C) and solution medium [1:1 (v/v) CH3CN/H2O] conditions. The reason for this apparent discrepancy is not known, although the same experimental and calculational procedures were used. If our values of ηce were increased by this same discrepant factor, assuming that it holds across the entire temperature range, some of the new calculated values would be greater than unity, which is clearly an unacceptable result. Interestingly, the evaluation of λ from plots of log((ηce-1 - 1)T1/2) Vs 1/T yields the same results, regardless of whether our experimental values of ηce or values corrected upward by a factor of 40% are used. (38) Mauzerall, D. C. In Photoinduced Electron Transfer, Part A: Conceptual Basis; Fox, M. A., Chanon, M., Eds.; Elsevier: New York, 1988; Chapter 6. (39) Clark, C. D.; Hoffman, M. Z. J. Phys. Chem. 1996, 100, 7526. (40) Newton, M. D.; Sutin, N. Annu. ReV. Phys. Chem. 1984, 35, 437. (41) Bixon, M.; Jortner, J. J. Phys. Chem. 1991, 95, 1941. (42) (a) Liang, N.; Miller, J. R.; Closs, G. L. J. Am. Chem. Soc. 1989, 111, 8740. (b) Liang, N.; Miller, J. R.; Closs, G. L. J. Am. Chem. Soc. 1990, 112, 5353. (43) For examples of calculations of λ from temperature dependence measurements: (a) Harriman, A.; Odobel, F.; Sauvage, J.-P. J. Am. Chem. Soc. 1995, 117, 9461. (b) Yoshimura, A.; Nozaki, K.; Ikeda, N.; Ohno, T. J. Am. Chem. Soc. 1993, 115, 7521. (c) Finckh, P.; Heitele, H.; Volk, M.; Michel-Beyerle, M. E. J. Phys. Chem. 1988, 92, 6584. (44) Gould, I. R.; Noukakis, D.; Gomez-Jahn, L.; Goodman, J. L.; Farid, S. J. Am. Chem. Soc. 1993, 115, 4405. (45) (a) Gould, I. R.; Farid, S. J. Phys. Chem. 1993, 97, 13067. (b) Gould, I. R.; Ege, D.; Moser, J. E.; Farid, S. J. Am. Chem. Soc. 1990, 112, 4290. (c) Murphy, S.; Schuster, G. B. J. Phys. Chem. 1995, 99, 511. (46) Doolen, R.; Simon, J. D.; Baldrige, K. K. J. Phys. Chem. 1995, 99, 13938.
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