Electrochemical random-walk theory: Probing voltammetry with small numbers of molecules: Stochastic versus statistical (Fickian) diffusion

Electrochemical simulation is employed to investigate voltammetry in solutions of very low concentrations. Using Monte Carlo random-walk simulations, potential-step chronoamperometry is considered from the perspective of individual species under Brownian motion in solution interacting with an electroactive surface for electron transfer. This allows the exploration of stochastic versus statistical diffusion, where the latter is described by continuous theory (Fick’s laws of diffusion). This approach details individual electron transfer events, and the stochastic nature of voltammetry under ultra-low concentration conditions. An optimisation in this work over previous random-walk simulations is the realisation of true spherical diffusion, rather than the bipyramidal diffusion approximation. Graphic Processors are used for the simulations, due to the independence of the particles in the system, resulting in a ∼1000× speed increase over conventional computer processors.