Theory of Coupled Electron−Proton Transfer with Potential-Dependent Transfer Coefficients for Redox Couples Attached to Electrodes†

Abstract

A theoretical study of coupled electron−proton transfer is presented for heterogeneous electron transfer to redox centers attached to electrodes. Proton transfer steps are assumed to be at equilibrium and the transfer coefficients are assumed to exhibit the potential dependence predicted by Marcus Density-of-States theory. Five cases are considered: 1e1H, 1e2H, 2e, 2e1H, and 2e2H. Procedures are given for calculating the apparent standard rate constant, the apparent transfer coefficient, and the path of electron transfer as a function of overpotential and pH. The behavior of these parameters are compared with a previous theoretical treatment in which the transfer coefficient for each electron transfer step was assumed to be 0.5 independent of overpotential. The predictions of the two treatments are qualitatively similar but quantitatively different. In particular, when the transfer coefficient depends on the electrode potential, apparent standard rate constants are smaller, asymmetrical Tafel plots appea...