The Absence of a Marcus Inversion Region for Electron Transfer at the Metal-Redox Electrolyte Interface

Abstract

The theory of electron transfer at the metal- redox electrolyte interface is described by starting with the work of Gurney and incorporating that of Gerischer and Marcus. This GGM model brings together diverse approaches to the description of electron transfer at electrodes. The electron transfer is described in terms of nuclear configuration potential energy diagrams, electronic configuration potential energy diagrams, electron distribution functions and rate distribution functions. The distinction between microscopic energies and macroscopic (thermodynamic) energies is made and the concept of the Fermi level of the redox electrolyte is clarified.

The model of identical parabolas is used for the nuclear configuration diagrams and this is shown to lead to Gaussian electron distribution functions for the redox electrolyte. The rate distribution is obtained from the overlap between occupied and unoccupied states of the metal and redox electrolyte. Integration of the rate distribution gives the rate which is calculated as a function of the electrode potential for various values of the reorganization energy λ.

It is shown that the variation of symmetry factor β is small for high λ and that the Tafel plots do not show significant decrease in rate at high overpotentials in the anomalous or inversion region. The Tafel plots for charge transfer (mass transfer is assumed to be fast at all potentials) tend to a limiting value with only a small decrease at high overpotential. This contrasts with the prediction based on nuclear configuration potential energy curves and is attributed to the fact that the overlap is between a Gaussian and a Fermi function rather than between two Gaussians, the latter being the case for homogeneous reactions.