Theory of unsupported, steady-state, Nernstian, three-ion, twin-electrode, voltammetry: the special case of dual concentration polarization

Steady-state voltammetry is easily attained in narrow cells. Here we develop an exact mathematical description of one of the simplest instances, in which a redox pair is present, but without supporting electrolyte. The Nernstian oxidation that depolarizes the anode is partnered at the nearby cathode by the converse reduction. The resulting voltammogram is sigmoidal in overall shape but, generally, no explicit analytic expression describes the current-potential relationship, or even the height of the limiting-current plateau. Such limiting currents arise either by exhaustive oxidation of one member of the redox pair at the anode or by exhaustive cathodic reduction of the other member. For a critical composition, which this study identifies, both exhaustions occur concurrently. The ionic strength plays a paramount role in unravelling the conditions during the experiment. Although no direct analytical application of this “closed” experiment suggests itself, there are implications of the theory for microgap cells and electroanalytical methods in “open” configurations, as well as separatory possibilities.