2ND-ORDER KINETICS FOR STEADY-STATE EC' REACTIONS AT A DISC MICROELECTRODE

A second-order (non-linear) model is derived for the steady state kinetics of an EC' reaction at a disc microelectrode in the case where the electron transfer process is followed by a homogeneous chemical reaction regenerating the electroactive species. It is assumed that the potential of the electrode is such that the surface concentration of the reacting reduced species is zero. The problem reduces to one with a pair of coupled non-linear reaction-diffusion equations which, in dimensionless terms, contains only two free parameters; the reaction rate and a parameter which is proportional to the ratio of the bulk concentrations of the reactants. A finite-difference scheme is derived for the governing equations, and a detailed study was performed to verify the accuracy and reliability of the numerical method. Details of solutions, including profiles of concentration and chemical activity, are presented for a number of characteristic cases at different points in the parameter space. The limiting current density at the electrode is calculated for a wide range of parameters and compared with that predicted by assuming equivalence with a spherical microelectrode. There is excellent agreement, and it is shown that an asymptotic formula, derived in a previous study, can be used to predict the current at a disc microelectrode in a wide range of practical situations.