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

A second-order (nonlinear) model is derived for steady-state kinetics of an EC' (catalytic electrochemical) reaction at a spherical microelectrode in the case where the electron transfer process is followed by a homogeneous chemical reaction regenerating the electroactive species. An asymptotic analysis of the model is performed, and the asymptotic results are compared with those from a numerical solution of the full nonlinear model. It is shown that in the fast reaction limit, where the current at the electrode takes its maximum possible value, the concentrations of the reactants are controlled by diffusion both close to and far from the electrode, with significant chemical activity occurring only in a narrow zone standing off the electrode. Also, it is shown that an equation obtained from a different asymptotic limit may be used to predict the limiting current at the microelectrode in all circumstances. The reasons for the surprising measure of 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 compared with the standard pseudo-first-order model, which, although also based on a linearization of the governing equations, has a restricted range of validity