The transient and stationary behaviour of first-order catalytic mechanisms at disc and hemisphere electrodes

Abstract

The voltammetric response of a first-order catalytic mechanism at disc electrodes has been studied under transient and stationary conditions and compared with that obtained at spherical electrodes. From the analytical solutions here presented we demonstrate that the expression for the current is given by the product of a potential-dependent function and a function of time, the electrode size, shape, and the chemical kinetics. This fact is physically insightful since it shows that the dimensionless current–potential curve is independent of time, the geometry of the electrode and the chemical kinetics, being identical to that corresponding to a reversible E mechanism both under transient and stationary conditions. Analytical equations for a catalytic mechanism at disc electrodes were only available under limiting current conditions. The steady state cyclic voltammetric response is also analyzed, describing three different situations where a time-independent response is attained in function of the electrode size and the kinetics of the regeneration reaction. Necessary and sufficient mathematical conditions to obtain constant equivalence relationships in voltammetric techniques at electrodes of any geometry are given and applied to the time-independent voltammetric curves obtained for a first-order catalytic mechanism at disc and hemispherical electrodes of any size.