Analytical formulae for chronoamperometry of a charge neutralisation process under conditions of linear migration and diffusion

The electrochemical reaction of the charge neutralisation of a binary electrolyte ion, at a planar electrode, is a rare example for which analytical formulae for potential step chronoamperometry can be obtained, under conditions of migration-diffusion transport in semi-infinite, one-dimensional space domain. This has been previously shown by Myland and Oldham [Electrochem. Commun. 1 (1999) 467], assuming equal diffusion coefficients. In the present work, a more general analytical solution is obtained, for the case of unequal diffusion coefficients. The effect of the diffusion coefficient ratio D_R/D_C, of the electroactive ion R and the counter-ion C, on the limiting chronoamperometric current, is examined. The effect increases with the growing ratio |z_R/z_C| of the electric charges of these ions, and becomes nonnegligible for |z_R| greater than or equal about 2, and for typical departures of D_R/D_C from unity. Among other things, the formulae obtained can be useful for testing digital simulation methods for the Nernst–Planck equations.