Current and Optimal Dimensions Predictions for a Porous Micro‐Electrode

Abstract

AbstractThe expression of the current delivered by a cylindrical porous micro‐electrode operating a single heterogeneous reaction and mass diffusion of the reagent is analytically derived in this work from a complete solution of the diffusion/reaction macroscopic problem. This solution is valid regardless of the aspect (thickness to inner radius) ratio. It encompasses the hybrid solution reported elsewhere, valid only when this ratio remains small compared to unity, and, consequently, the case of a planar electrode as well. The asymptotic form of the solution in this latter case is also provided. The complete solution is used to predict the optimal thickness of the electrode and its optimal inner radius (i. e. the supporting wire radius) corresponding to the best compromise between a minimum electrode volume and a maximum current per unit volume. This work hence provides a complete optimization procedure that can be used as predictive tools for the design of porous electrodes.