Second-order kinetics for EC' reactions at a spherical microelectrode

A second-order (nonlinear) model is derived for steady-statekinetics of an EC' (catalytic electrochemical) reaction at aspherical microelectrode in the case where the electron transferprocess is followed by a homogeneous chemical reaction regeneratingthe electroactive species. An asymptotic analysis of the modelis performed, and the asymptotic results are compared with thosefrom a numerical solution of the full nonlinear model. It isshown that in the fast reaction limit, where the current atthe electrode takes its maximum possible value, the concentrationsof the reactants are controlled by diffusion both close to andfar from the electrode, with significant chemical activity occurringonly in a narrow zone standing off the electrode. Also, it isshown that an equation obtained from a different asymptoticlimit may be used to predict the limiting current at the microelectrodein all circumstances. The reasons for the surprising measureof agreement at the surface of the electrode are discussed,the predictions from the model of the limiting current are compared(favourably) with experimental results, and the model is comparedwith the standard pseudo-first-order model, which, althoughalso based on a linearization of the governing equations, hasa restricted range of validity.