Simulating cyclic voltammetry at rough electrodes by the digital-simulation–deconvolution–convolution algorithm

Abstract

The influence of electrode roughness on diffusional cyclic voltammetry (CV) is investigated from a theoretical perspective. For this purpose, the digital-simulation-deconvolution-convolution (DSDC) algorithm, initially developed for the simulation of CV at porous electrodes, is subjected to three substantial modifications. First, by employing adaptive numerical resolution and sample volumina, the computational demand of the digital simulation (DS) step is reduced significantly. Second, by modifying the Douglas-Gunn algorithm of the DS-step to operate on an arbitrarily incremented spatial grid perpendicular to the macroscopically planar electrode surface, the bulk of the fluid can be treated with an exponentially increasing spatial discretization which uses computational power even more efficiently. The third modification is an optimization of the computationally demanding deconvolution step which is used to extract the mass-transfer function from the data computed in the DS-step. This, initially recursive procedure, is replaced by a three-step sequence consisting of (I) a numerical Laplace transformation (NLT) on an exponentially expanding time-grid, (II) a Laplace-domain integration (LDI) and finally (III) a numerical inversion of Laplace transformation (NILT) using the Gaver-Stehfest (GS) inversion formula. Based on this novel strategy for CV simulation, the effects of electrode roughness are thoroughly investigated. It is demonstrated that for an ideally reversible reaction the effects of electrode roughness on the CV response are insignificant at common experimental timescales. In contrast, for scenarios with electrochemically quasi-reversible (or irreversible) kinetics, the apparent rate constants are allegedly upscaled by the area ratio Psi = A rough / A planar . This manifests in a lower peak-to-peak separation without a distortion of the shape of the voltammetric profile. This behavior is finally explained in a quantitative manner in terms of convolution-sums and mass-transfer functions which ultimately puts the parameter electrode roughness into the semianalytical framework of convolutive modeling.