New approximate analytical expressions for transient concentration profiles and current pertaining to a homogeneous chemical reaction at hemispherical microelectrodes

A mathematical model corresponding to homogeneous chemical reactions under transient chronoamperometry conditions at hemispherical microelectrodes has been developed. The analytical solutions for the concentration of species and current were obtained using Duhamel's theorem. This closed-form theoretical expression pertains to the transient concentration profiles and fluxes of chemical species involved in chemical and electrochemical reactions at hemispherical microelectrodes. As t → ∞, the analytical expressions corresponding to the concentration and current approach steady-state values. The solutions obtained are explicit only under limiting current conditions. The approximate expressions for concentrations and current as functions of time corresponding to the EC' and CE mechanisms at hemispherical microelectrodes are also reported.