Shape-dependency of current through non-linear irregular electrodes

Abstract

We describe a simple way to understand the non-linear response of an irregular resistive electrode in d=2. It is based on the concept of an active zone in the Laplacian transfer to and across irregular interfaces. It applies to arbitrary electrode geometry and permits to compute the flux across an irregular electrode from its geometry without solving the Laplace problem. The simplifying arguments that are used are tested numerically on prefractal models of the geometrical irregularity. One finds that, for electrodes following a local Butler–Volmer response, the Tafel slope depends on the geometry. It is shown that the measure of the cell impedance leads to the determination of the actual active potential. It also gives the mean size of a part of the electrode with a surface impedance equal to the electrolyte bulk resistivity.