Pekar factor

It is to be emphasized that the simple Pekar factor [40] (the dielectric prefactor in Equation (3.88) appears only when the image effects are absent (e.g., as in the case of a point charge at the center of a spherical cavity) or suppressed. In this limiting case, D may be taken as the solute vacuum field. On the other hand, both Equation (3.88) and (3.89) manifest the same assumption of additivity, whereby the nonequilibrium inertial free energy reflected in As is cast as the difference between two equilibrium solvation free energies (Gs) i.e., the optical (sx term) and the total (e0 term) solvation free energies... 

In equations used in the analysis there appear the Pekar factor, y, and the second factor of the Marcus expression for the electrode kinetics, which we denote by g ... 

When one uses Eq. (43) the analysis may not be straightforward because, as shown above, rf is dependent on y in polar solvents therefore when /cv depends on Tf the plot of In against y may increase with an increase of the Pekar factor, contrary to the prediction of Eq. (43). Such positive slopes of the In versus y dependence point to the significant influence of solvent friction in the reaction dynamics [1,157]. 

Fig. 12. Rubrene ECL efficiency (i ed) as a function of the solvent polarity parameter (Pekar factor (1/n — le)) in ( ) single and (o) mixed 1 1 solvents. Solvent name abbreviations ACN. acetonitrile BL, 7-butyrolactone BN, butyronitrile DME, 1,2-dimethoxyethane DMF, N,N-dimethylformamide NMP, Al-methylpyr-rolidone THE, tetrahydrofuran benzene CH3 toluene f>CN, benzonitrile. Adapted from [123].

Note-. The factor Cpekar = (1 / e) — (1is often referred to as the Pekar factor. 

Attempts have been made to test the Marcus estimate of Gxo experimentally. One way of doing this is to study the variation in electron transfer rate constant with solvent nature. This results in a change in the Pekar factor and thus in Gxo-More will be said about these experiments in section 7.10. 

An example of a diabatic reaction is the oxidation of tetramethyl-p-diamino-benzene (TMDAB) to its cation radical. Kinetic data were obtained in seven solvents with Pekar factors ranging from 0.27 (chloroform) to 0.53 (acetonitrile). The Pekar factor yp is defined as... 

For the TMDAB, the logarithm of the electron transfer rate constant In ket is clearly a linear function of the Pekar factor yp (fig. 7.22). On the other hand, a plot of In ket against In xp for the same data yields a weak linear correlation with a positive slope (fig. 7.23). This correlation is the opposite to that expected in other words, the rate constant should decrease with increase in xp if the reactions were adiabatic. The estimate of A G((, for this reaction is 6.4kJmol the value of A Gos depends on the nature of the solvent but it is close to in most solvents considered. The reason that the reaction is diabatic is clearly due to the weak... 

Fig. 7.22 Plots of the logarithm of the electron transfer rate constant for oxidation of TMDAB ( ) and TTF (o) against yp, the Pekar factor of the solvent [36].

Quite different behavior is found for the electron transfer reaction between tetrathiofulvalene (TTF) and its cation radical. For this system, there is no correlation between In et and the Pekar factor y (fig. 7.22). However, there is a strong correlation between Inkgt and IniL. These results are consistant with an adiabatic reaction with a dynamic solvent effect. The estimate of A G[s for this... 

Figure 9.19. Solvent dependence of In and versus the Pekar factor...

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