Modelling diffusion at random arrays of electrodes: Revisiting the Voronoi tessellation concept

Abstract

In order to assess the precision of simulations of diffusion at arrays based on the Voronoi tessellation approach we investigated two representative types of random arrays involving bands or disk electroactive sites [J. Electroanal. Chem. 147 (1983) 39] and modelled their diffusional patterns when the solution contains only one electroactive species undergoing a simple electron transfer reaction at the active sites under chronoamperometric conditions. On the one hand, the ensuing results establish that in both cases the Voronoi approach produces reasonably good predictions of the total currents flowing through the elementary cells of each array. Indeed, the relative error introduced by the Voronoi-based approach, being less than 5% in each case, is acceptable from an experimental point of view owing to many other sources of uncertainties involved for random arrays. On the other hand, this work demonstrates that the currents predicted for the individual sites within an elementary cell based on simulations using Voronoi approaches are excessively wrong since they totally neglect significant ыш redistributions of flux lines that happen when the diffusion layers expand with time. This hints to possible severe complication when Voronoi approaches are applied to encompass complex kinetics or to predict the outcome of electroanalytical methods that rely on a fine coupling between local concentrations and local fluxes.