Determination of the Reorganization Energy

Here a value of AG = 0.7 eV is found, which leads to A = 2.8 eV [66]. This rather large value is mainly due to an inner sphere reorganization (see Section 6.1.2). Much smaller values are obtained with pure outer sphere redox systems, for instance metallocenes. In the latter cases AG values in the order of 0.2-0.26 eV have been reported [67], i.e. values which correspond to A = 0.7-1 eV. There are other cases such [Fe(CN)6] where one would also expect an outer sphere reorganization but rather high values have been found (AG = 0.55 eV A = 2.2 eV) [67]. In this context it should also be mentioned that modern theories on electron transfer at electrodes have shown that the A values also depend on the distance of the electron acceptor or donor molecules from the electrode surface [65]. 

Investigations of reorganization energies at semiconductor electrodes have already been performed in the mid-1970s [27, 14]. In this case Sn02 electrodes of relatively 

7 Charge Transfer Processes at the Semiconductor-Liquid Interface 

Theoretical current-potential curves were determined by using Eqs. (7.102) to (7.105) as given by the solid curves in Fig. 7.53 which gave the best fit with experimental data. The theoretical curves, calculated for one redox system but with different dopings, were obtained with a single A value. 

Redox system redox (V) (SCE) Homogeneous solutions [65] A(eV) Modified Au electrodes [52] Heavily doped Sn02 electrodes 

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This argumenl is used in the electrochemistry literature, but it is only qualitative since it disregards the role of the reorganization energy in determining the free energy. Indeed, if we use the zero-temperature approximation forthe Fermi functions in (17.14) we find that the equality kb a = Ei— t-which must be satisfied at equilibrium, leads to Eab = only for 0. 

The profile itself is strongly determined by the reorganization energy A which is by definition the energy of the product with respect to its equilibrium state when its solvent coordinate is still the same as that of the reactant state. If the curvatures of the reactant and the product parabolas are identical, the reorganization energy can also be defined as the work required to distort the reactant (D,A) from its equilibrium coordinate (Fig. 6.1) to the equilibrium coordinate qp of the product without any electron transfer (Fig. 6.1). 

For n < 10 we were able to detect CT fluorescence accompanying the charge recombination24,26 prom that fluorescence was determined via a method that is discussed in the appendix. The results showed that displays a closely exponential distance dependence H y exp(-0.44 n). Thus, within Ae limits of experimental uncertainty, the distance dependence of k. j. and H y indeed obey the quadratic interdependence predicted by eqn (2) for a fixed value of FC. This appears a highly important result, but it should be stressed that, due to the iimit sensitivity of the CT-fluorescence based determination of H y, we were unable to test the interdependence for n > 10, and furthermore that even so the absence of CT fluorescence in polar solvents made it impossible to perform the test in such solvents where major changes of the reorganization energy as a function of D/A distance are likely to occur. 

Treatment of hopping conduction in terms of Marcus theory stresses the importance of the reorganization energy term as a major factor in determining the charge... 

In typical outer sphere electron transfer on metal electrodes, A is in the weakly adiabatic region and thus sufficiently large to ensure adiabaticity, but too small to lead to a noticeable reduction of the activation energy. In this case, the rate is determined by solvent reorganization, and is independent of the nature of the metal [Iwasita et al., 1985 Santos et al., 1986]. 

From a comparison of Eqs. (9) and (22) we see that H = F(0 ). To elucidate the physical meaning of the exponent in Eq. (22), we consider first the case when 0 = 1 (barrierless reaction). In this case Eq. (20) determines the change of the free energy of the system F(l) when it is polarized by the electric field AEU = E -E (only the free energy related to the inertial polarization is considered). It may be easily seen that the absolute value of F(l) is equal to the energy of the reorganization of the medium Es (>0). 

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