Electroactive concentrations at the surface of a spherical electrode

Abstract

Though they are rarely determined as such, the concentrations of the electroactive oxidant and reductant at the surface of a voltammetric working electrode are valuable parameters in kinetic, thermodynamic and analytical studies. Semiintegration of the current yields these surface concentrations under conditions of semiinfinite planar diffusive transport, uncomplicated by chemical reaction. At spherical electrodes, however, semiintegration may produce only a crude approximation to the true surface concentrations, especially in cases of amalgam formation, or when the diffusion coefficients of the oxidized and reduced species differ significantly. In this article we derive mathematical procedures that perform for spherical electrodes the operation equivalent to that performed by semiintegration for planar electrodes: the conversion of current data into surface concentration data. These procedures, which we term “spherical convolutions”, are applied to experimental cyclic voltammograms for the reductions of Fe(C 2O 4) 3− 3 and Cd 2+ at a static mercury drop electrode. Their accuracy is demonstrated by testing the obedience of the generated concentration data to the Nernst equation. General purpose algorithms to carry out spherical convolutions are presented.