Characterising Fickian diffusion on the surface of a sphere

Abstract

• Two-dimensional Fickian charge diffusion over a sphere located on an electrode. • Charge is injected at the sphere-electrode contact. • Modelling relates to single entity impact experiments. • Log-log flux-time transient reveals the changes in the diffusion regime. • Diffusion regimes embrace: convergent, divergent, linear and thin layer. Single-entity electrochemical analysis involving Fickian charge diffusion over the surface of a (truncated) sphere is explored via numerical simulation, mimicking the case where an insulating particle covered with an electroactive adsorbed layer impinges on an electrode. The ever-changing shape of the flux-time transient as the diffusion regimes change over the surface of the sphere from the point of charge injection are characterised with the use of the recently introduced diffusion indicator, α , [Haonan et. al., J. Electroanal. Chem. 855, 113602]. The indicator is shown to illuminate, with clarity, the change of diffusion from divergent near the point of injection through linear at the sphere circumference to convergent before being limited by the thin-layer effect as the surface of the sphere is fully oxidised or reduced. Truncated spheres are also examined and characterised along with diffusion under model ‘thin layer’ conditions.