Allowance for Force Constant Changes in the Theory of Electron Transfer at the Metal-Redox Electrolyte Interface

Abstract

The Gurney-Gerischer-Marcus (GGM) model for electron transfer¹ is used to investigate the effects of force constant changes between initial and final states for electron transfer at the interface between a metal and a redox electrolyte. The effects on the symmetry factor, β, and on the determination of the redox electrolyte distribution of states are investigated and compared to the predictions of the GGM model using no change in force constant. Comparisons are also made between the Marcus^2,3 and GGM models. The GGM model with non-identical parabolas for the potential energy-nuclear configuration diagrams is used to numerically calculate the distribution of states in the redox electrolyte from which data the rate constant distribution for reduction is obtained from the overlap between occupied states of the metal and the unoccupied states of the redox electrolyte. Numerical integration of the rate constant distribution gives the rate constant which is calculated as a function of the electrode potential. The calculated Tafel plots are found to be non-linear but do not go through a maximum. The Marcus and GGM models predict markedly different dependences of the symmetry factor on potential. Differentiation of the calculated rate constant with respect to potential gives the distribution of states 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. Anomalous results reported in the literature are shown to be qualitatively consistent with a difference in force constant between initial and final states for electron transfer.