Digital simulation of migrational voltammetry.: The effect of difference in diffusion coefficients of the reactant and the product of an electrode reaction

Abstract

A simulation scheme, based on the fast implicit finite difference algorithm has been proposed for the modeling of steady-state voltammograms under conditions of mixed diffusion–migration transport in multi-ion systems. The scheme assumes the single-step reversible process taking place at a hemispherical electrode, and does not impose any limitations on the diffusion coefficients of the species present in the solution. Using this simulation tool the theoretical voltammograms for the charge neutralization-, charge decrease-, and charge increase systems were obtained for a broad range of diffusion coefficients of the reactant and the product, and for different concentrations of supporting electrolyte. For the charge decrease- and charge increase systems, the normalized limiting current plotted versus log( D R/ D P) gives a sigmoidal curve. The migrational component in the transport of the electroactive species varies significantly with log( D R/ D P), the largest variation being observed for log( D R/ D P) close to zero. A decrease in D P decreases the limiting current, while for a large D P the limiting current increases asymptotically to a limiting value. This value is identical to the limiting current observed in the analogous systems with a charge neutralization reaction, which shows that the charge of the product plays no role if the diffusion coefficient of the product approaches infinity. Approximate functions have been constructed to calculate the normalized limiting current (relative error <2%) and the shift of the normalized halfwave potential (error <2 mV) in the range of the D R/ D P ratio found in real experimental situations.