Effect of ion pairing on steady-state voltammetric limiting currents at microelectrodes part I. Theoretical principles

Voltammetric studies in solutions of high resistivity are facilitated by the use of microelectrodes under steady-state conditions. Such solutions are encountered with solvents of low permittivity because of the very sparing solubility of electrolytes. Moreover, in such media the supporting electrolyte, as well as the electroactive ionic species, is usually extensively ion paired. Here we predict the limiting current that will flow in these circumstances, when a monovalent ion undergoes a one-electron transfer at a hemispherical microelectrode to form a neutral product. The ion pairing equilibria are assumed to be fast but all diffusion coefficients are treated as distinct. An analytical solution is elusive in the general case, but a simple numerical procedure allows the limiting current to be predicted for any combination of the system parameters. Several special cases are also discussed, some of which yield explicit formulae for the limiting current. In a companion paper, experimental data are compared with the theoretical predictions.