Simulation of diffusion at microring electrodes through conformal mapping

Predicting diffusion at ring electrodes of any thickness poses a specific series of difficulties owing to the fact that on the one hand, ring electrodes resemble disk electrodes (thick rings) and on the other hand, they resemble band electrodes (thin rings). These difficulties are imposed onto any simulation program designed to determine accurately the concentration profiles and henceforth chronoamperometric or voltammetric currents at ring electrodes. In this article, we show that all these intrinsic difficulties are de facto resolved simply by employing a new conformal mapping approach for simulation of the diffusional problems at a ring electrode. This method affords precise and effective solutions, though the computation time remains extremely modest. The speed of the numerical solutions may be even boosted by using a non-uniform exponentially expanding time grid, which is also described in this article.