Transport to rough electrode surfaces: Part 2: Perturbation solution for two-dimensional steady state transport to an arbitrary surface under mixed diffusion-kinetic control

Abstract

A perturbation approach presented previously to investigate systematically the electrode response of a rough surface with arbitrary, small features has been extended to include the combined effects of diffusion and first-order reversible kinetics. The non-uniformity of the electrode response can be characterized in terms of two quantities—lateral shifts in the locations of current maxima and minima from corresponding peak and valley positions on the surface, and the difference in the current density at the highest and lowest points. It has been shown that for the reaction mechanism considered in this study, a dimensionless number expressing the ratio of diffusional resistance to kinetic resistance, which is similar to the inverse of the Wagner number, can parameterize completely both the current density difference, if it is normalized with respect to the mean, and the lateral shift. The results indicate that diffusion tends to enhance these effects, whereas kinetics suppresses them. However, if the current density difference is not normalized and its absolute magnitude is considered, the situation is less clear-cut and affected by the specific details of the reaction mechanism.