Optimal Thickness of a Porous Micro-Electrode Operating a Single Redox Reaction

This article reports on a procedure to predict the optimal thickness of cylindrical porous electrodes operating a single redox reaction. This is obtained from a macroscopic model for the coupled diffusion-reaction process that is first validated with voltammetry experiments of the H2O2/H2O reduction reaction carried out with a series of porous electrodes elaborated in this work. An analytical solution to this model is developed in the steady regime and for electrodes featuring a thickness to mean radius ratio small enough compared to unity. An analytical expression of the optimal electrode thickness is derived corresponding to the crossover value of two asymptotic regimes characterizing the dependence of the volume current density produced by the electrode upon its thickness. The predictive tool of the optimal thickness is general, regardless of the porous microstructure. The case of the electrodes used in the reported experiments illustrates that the optimal thickness is not intrinsic to the microsctructure characterized by the size of the representative volume, its specific area and effective diffusion coefficient. It also depends on the operating conditions reflected in the kinetic number, Ki, and the thickness of the diffusion layer surrounding the electrode. The dependence of the optimal thickness on these two parameters is quite significant in a range of very small values of Ki but remains quasi constant beyond a threshold value.