Theory of electrode processes

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Abstract
The transfer of an electron from a metal electrode to an electroactive species in the interface is central to electrochemical equilibrium and kinetic analyses. The purpose of this paper is to present a discussion of the theory of electron transfer based on a linear response analysis. We base our theoretical considerations on the Yamamoto reaction rate theory; Yamamoto's theory is an outgrowth of the Kubo linear response theory. The rate constant and ultimately the exchange current expressions we obtain are derived from a model representation of the electrode interface. This model is a generalization of one considered by Dogonadze and Chizmadzhev. In particular, we examine an outer sphere type transfer mechanism, but we allow for the following effects: (1) the effect of reactant center of mass motions and transport to a most favorable electron exchange configuration, (2) the effect of internal vibronic interactions within the electroactive species, and (3) the effect of strong electron exchange interactions. This last effect precludes the direct use of quantum mechanical perturbation theory to obtain the rate constant expressions. For our model system we obtain general rate expressions valid for adiabatic to nonadiabatic transfers. This follows from the generality of the Yamamoto theory. We find particularly that the effects of reactant transport and internal vibronic contributions can be cast into a virial form for the rate constant. Moreover, the activation energy, in the Arrhenius sense, contains new terms relating specifically to the new effects we consider, namely, transport and vibronic effects.