The Journal of
PhysicaIChemistcy
0 Copyright, 1986, by the American Chemical Society
VOLUME 90, NUMBER 12 JUNE 5, 1986
LETTERS How Do Solvent Relaxation Dynamics Affect Electron-Transfer Rates? A Study in Rigid Solution Mark McGuire and George McLendon* Department of Chemistry, University of Rochester, Rochester, New York 14627 (Received: October 7. 1985; In Final Form: April 14, 1986)
Nonadiabatic electron transfer has been studied in glycerol in which the solvent relaxation time ( T ~ is) varied (by temperature) from IO-* to IO-' s. A strong dependence of rate on T is observed with k 0: ( T ~ ) - ( " . ~A. qualitative rationale suggests that ~ on whether the electronic coupling the actual dependence for a nonadiabatic process can range from (TL)' to ( T ~ ) -depending strength or solvent polarization determines the frequency factor for reaction. Such intermediate cases may be significant in a variety of condensed-phase electron-transfer processes.
Introduction Several recent reports have raised fundamental questions about how electron-transfer reaction rates' are affected by solvent relaxation times and nonequilibrium solvation. For example, Miller2 observed a time-dependent shift of the optimum AG for nonadiabatic electron transfer and assigned this shift to a time-dependent solvent reorganization energy, A,. Kosower recent suggested that solvent motion controls the lifetime of charge-transfer excited states for arylaminonaphthalenesulfonate derivatives3 and has suggested theoretical models for the dynamics of solvent rearrangement. Weaver, in electrochemical studies: and K o s ~ w e rin , ~photochemical studies, have applied theoretical models like those developed by Hynes (1) Recent detailed reviews of electron transfer theory and (a) Newton, M. D.; Sutin, N. Annu. Rev. Phys. Chem. 1984,35,437-480. (b) Guarr, T.; McLendon, G. Coord. Chem. Rev. 1985, 68, 1-57. (2) Miller, J. R.; Beitz, J. V.;Huddleston, R. K. J . Am. Chem. SOC.1984, 106, 5057-5068. (3) Kosower, E. M. Acc. Chem. Res. 1982, 15, 259-266. (4) Weaver, M. J.; Gennett, T. Chem. Phys. Lett. 1985, 113, 213-218. ( 5 ) Kosower, E. M . J . Am. Chem.Soc. 1985, 207, 1114-1118.
and Wolynes6s7to explain an observed correlation between the overall observed electron-transfer rate and the solvent longitudinal relaxation time, rL. A similar effect has recently been noted by Bard.9 These t h e ~ r i e ssuggest ~ , ~ that when a reaction is strongly coupled to the medium (as for electron transfer), then the appropriate (nuclear) frequency factor, vN, is not, kT/h, as suggested by transition-state theory, but rather vN i= To date these theories have been minimally tested, since, in the cited work, TL varies less than tenfold. We now report studies'& (6) Calef, D. F.; Wolynes, P. G. J . Chem. Phys. 1983, 78, 470-482. (7) Recent treatments include: (a) Van der Zwan, G.; Hynes, J. T. J. Chem. Phys. 1982, 76,2993-3001. (b) Zusmar,L. D. Chem. Phys. 1980,49, 295-304. (c) Calef, D. F.; Wolynes, P. G. J . Phys. Chem. 1983, 87, 3387-3400. (d) Efrima, S.; Bixon, M. J. Chem. Phys. 1979,70, 3531-3535. (e) Van Duyne, R. P.; Fischer, S. F. Chem. Phys. 1974, 5, 183-197. (8) McGuire, M. E. Ph.D. Thesis, University of Rochester, 1985. (9) Zhang, X.;Leddy, J.; Bard, A. J. J. Am. Chem. SOC.1985,107,3719. Note: The critical dielectric parameters are not fully defined in this work, so comparison to theory is difficult. (10) (a) This work was presented at Pac Chem '84, Honolulu, Hawaii, Dec, 1984. (b) Strauch, S.; McGuire, M.; McLendon, G.; Guarr, T. J. Phys. Chem. 1983,87, 3579. (c) Guarr, T.; McGuire, M.; Strauch, S.; McLendon, G. J. Am. Chem.Soc. 1983, 105, 616-618.
0022-3654/86/2090-2549$01.50/00 1986 American Chemical Society
2550 The Journal of Physical Chemistry, Vol. 90, No. 12, 1986
Letters
TABLE I reaction (1) R u ( M e 4 ~ h e n ) 3 2 + + l ~ ~ v 2 + (2) Ru(4,7Me,phen), / (3) Ru( bpy) 32+/ MV2+ (4) R ~ ( M e , p h e n ) ~ ~ + / M V ~ +
medium (temp,
K)"
G (253-183) G (258-195) G (263-203) EG/W ( 193-153)d
AE,b eV 0.64 0.54 0.37 0.64
~ET,,I~'
4ETobadc
2.2 x 103 1.7x 103 398 X lo2 82
7.5 8.5 13.5 7.5
"Medium: G = glycerol (neat); EG/W = 2:1 ethylene glycol/water. Temp, range of temperature (K) studied. bReaction exothermicity (ref 8). cobserved change in rate at 15 A. dTemperature range for 2:1 EG/W over which Perrin behavior observed. ePredicted change in rate at 15 A, from eq 4 ref 2, hw = 1200 cm-I; X, = 1.5 eV, A, = 0.15 eV
of a series of collisionless (nonadiabatic) electron-transfer reactions between R ~ ( p h e n ) ~homologues ~+ ( R U ( L L ) ~ ~and + ) methylviologen (MV2+)dispersed in rigid glyceroliOb*c in which the solvent dielectric relaxation time varies by > lo7 over a temperature range 253-180 K. These studies provide a stringent test of the relationship between T~ and k,,. We sought to address the following questions: 1. How does k,, vary over a wide temperature range, and does this variance depend on the nature of the solvent? 2. Do observed changes in k, mirror changes in T ~and , if so, how do such changes compare with theoretical predictions?
Experimental Section The preparation and/or purification of the R u ( L L ) ~ ~com+ plexes and MV2+has been described previously.s~iOb~c Glycerol (Aldrich, Spectral Grade) was used as received and stored tightly sealed in a desiccator. Ethylene glycol (Eastman) was used as received. Solvent purity was checked by viscosity and refractive index measurements, suggesting an H 2 0 content of
21 (In 13 0 I
1'
I
7
3.5
I
I
I
1
I
R ~ C L L > , ' ~ / ~ GV I*y~c e r o I
4
t +0
1
C
0
A
Io/I = ex~W"/,[Ql) Io is the static emission intensity in the absence of quencher; I is the static emission in the presence of quencher concentration [Q]; N 6.02 X loz3;V, is the "critical quenching volume" around each Ru; (V, = (R,)34"/3), such that if RRuQ.C R, emission is totally quenched (Le., k,, >> k,, = 1 / ~ ~while ) , if R R u 4> R, emission is unperturbed (i.e., k,,
