The Temperature and Potential Dependence of the Rate Constant for Electron Transfer at the Metal Redox Electrolyte Interface

Abstract

The Gurney-Gerischer-Marcus (GGM) model is used to investigate the potential and temperature dependence of the rate constant for electron transfer at the interface between a metal and a redox electrolyte. In this model electron transfer is described in terms of nuclear configuration-potential energy diagrams, electronic configuration-potential energy diagrams, state distribution functions and rate constant distribution functions. The model of identical parabolas, which leads to Gaussian electron distribution functions, g(E), for the redox electrolyte, is used for the nuclear configuration diagrams. The rate constant distribution, k(E), is obtained from the overlap between occupied and unoccupied state distribution functions of the metal and redox electrolyte. Integration of k(E) over the vertical transition (Franck-Condon) energies, E, gives the rate constant, k, which is calculated as a function of the electrode potential and temperature for various values of the reorganization energy, λ. Differentiation of k with respect to potential returns g(E) for the redox electrolyte except for a small deviation which is due to the weak dependence on energy of the distribution of states in the metal. For high λ the variation of symmetry factor with potential is small and the Tafel plots do not show a significant decrease in rate at high overpotentials. For small λ the Tafel plots are strongly curved but do not go through a maximum at high overpotential; the Tafel plots tend to a limiting value with only a small decrease in rate constant at high overpotential. This result is reflected in the temperature dependence of the rate constant and in the dependence of the Arrhenius activation energy, E_a, on potential; E_a does not increase at high overpotentials. These results are due to the weak dependence on energy of the distribution function for a metal compared to a redox electrolyte and emphasize the advantages of using distribution functions to describe the kinetics of electron transfer.