Electrochemical electron transfer: An Analytically Solvable Model

TL;DR

This paper introduces an analytical model for electrochemical electron transfer reactions, explicitly considering the potentials of both ions, and provides a general solution based on diffusion-reaction equations.

Contribution

It presents the first model explicitly incorporating both ion potentials and offers an analytical solution using Laplace transforms of Green's functions.

Findings

Model is more general than previous models

Explicitly considers potentials of both ions

Provides analytical solutions for electron transfer rates

Abstract

We propose an analytical model based on diffusion-reaction equation approach for electrochemical electron transfer reaction, where the rate is limited by the electron transfer process. The electron transfer from an ion in solution to the metal electrode would occur as soon as the energy of the orbital on the ion matches the Fermi energy of the metal and a new ion with more positive charge is formed. Obviously the ion before electron transfer and the new ion, which is formed after electron has transferred, moves under the influence of different potentials. The coupling between these two potentials is assumed to be represented by a Dirac Delta function. The diffusive motion in this paper is described by the Smoluchowski equation. Our solution requires only the knowledge of the Laplace transform of the Green's function for the motion in both the uncoupled potentials. Our model is more general than all the earlier models, because we are the first one to consider the potential of both the ions explicitly.