Numerical Simulation of the Diffusion Processes in Nanoelectrode Arrays Using an Axial Neighbor Symmetry Approximation

Abstract

Nanoelectrode arrays have introduced a complete new battery of devices with fascinating electrocatalytic, sensitivity, and selectivity properties. To understand and predict the electrochemical response of these arrays, a theoretical framework is needed. Cyclic voltammetry is a well-fitted experimental technique to understand the undergoing diffusion and kinetics processes. Previous works describing microelectrode arrays have exploited the interelectrode distance to simulate its behavior as the summation of individual electrodes. This approach becomes limited when the size of the electrodes decreases to the nanometer scale due to their strong radial effect with the consequent overlapping of the diffusional fields. In this work, we present a computational model able to simulate the electrochemical behavior of arrays working either as the summation of individual electrodes or being affected by the overlapping of the diffusional fields without previous considerations. Our computational model relays in dividing a regular electrode array in cells. In each of them, there is a central electrode surrounded by neighbor electrodes; these neighbor electrodes are transformed in a ring maintaining the same active electrode area than the summation of the closest neighbor electrodes. Using this axial neighbor symmetry approximation, the problem acquires a cylindrical symmetry, being applicable to any diffusion pattern. The model is validated against micro- and nanoelectrode arrays showing its ability to predict their behavior and therefore to be used as a designing tool.