STEADY-STATE MULTICOMPONENT DIFFUSION AND MIGRATION TO A PLANAR ELECTRODE .1. ANALYTICAL SOLUTION FOR THE CASE OF A SINGLE REACTING SPECIES

An analytical solution has been obtained for the steady-state diffusion and migration to a planar electrode by a multicomponent system that consists of one reacting species and any number of indifferent species. It takes the implicit form of a set of non-linear algebraic equations which must be solved numerically for the current density, electrode potential and solution potential. The solution is more general than the obtained previously in that it is applicable to conditions of mixed transport-kinetic control as well as of limiting mass transport, does not depend on the particular form of the kinetic rate law and can easily accommodate effects such as concentration overpotential and ohmic drop. These results have been used to compute polarization curves and concentration profiles for the well-characterized system of CuSO4 + H2SO4 electrolytes in the vicinity of a copper electrode. The effects of H+ and Cu2+ concentrations, migration and ion-ion interactions on the polarization curves and limiting currents are discussed. At low and high overpotentials, simplifications allow one to derive explicit expressions for the current-potential behaviour that can be used directly for the estimation of kinetic parameters from experimental data. The relationship at high overpotential, which has the same mathematical form as the Tafel equations, is particularly useful since it applies to cases where there is little or no supporting electrolyte and migration cannot be ignored.