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CHAPTER 4
Theory of Electrochemical Electron Transfer
The first and fundamental formulation of Marcus theory for homogeneous ET reactions (redox reactions) was summarized in Chapter 2. In this chapter, an abridged version is presented of its extension to electrode systems from Refs. [1, 2, and 2a]. The two Office of Naval Research reports were written by Marcus in 1957 but were published in 1977 in a book edited by Peter A. Rock. In the following, the symbol M. is for Marcus.
4.1.Electrostatic Free Energy and Nonequilibrium Dielectric Polarization for Electrode Systems
In ET at electrodes, the total dielectric polarization P(r) is, like in the homogeneous case, the sum of two terms:
We remind the reader that the electronic polarization Pe(r) is the portion of the electric polarization which is in electrostatic equilibrium with the electric field strength E(r), that is, the polarization is determined by the field through the electronic polarizability αe:
The E-type polarization is related to Dop, the square of the refractive index:
An important point is that E(r) depends on the charge distribution and on Pu(r). On the other hand, Pu is the portion of dielectric polarization which is in general not in equilibrium with E. When it is in equilibrium, it can be expressed in terms of E and of the atomic–orientational polarizability αu:
When it is not, it appears as a solution of a variational equation.
The U-type polarization depends on both Dop and Ds:
4.2.The Electrochemical System
After having briefly reminded the reader of the properties of the polarization vector function, I describe now the simple model of electrode system considered by Marcus.
An oriented, thin, and nonpolarizable solvent layer is supposed to exist at the electrode–solution interface (“inner layer” of the electrical double layer, see, e.g., Ref. [3]). The adsorbed layer produces a fixed potential difference χ across the interface. The magnitude of χ depends on the solvent, on the nature of the electrode and on the temperature.χ is first supposed to be independent of the average electrode charge density. The ions taking part in ET are designated as “central ions.” When the solution is not infinitely diluted, the central ions will be surrounded by an ionic atmosphere of other ions. If a salt is present in solution whose ions do not exchange electrons with the electrode (inert electrolyte), the ionic atmosphere will be made up also from ions of the inert electrolyte.
The picture of the system is now complete: metal electrode, solvent layer, central ions taking part in the ET process, ionic atmospheres surrounding them [1, p. 211].
4.3.Electrostatic Potential
As in the case of homogeneous ET, “each central ion is treated as a sphere having a surface charge density σ(r) equal to the ionic charge divided by its area. The