title: Generalized theory of steady-state voltammetry without a supporting electrolyte. Effect of product and substrate diffusion coefficient diversity.
abstract: A generalized theory of the steady-state voltammetric response of a microelectrode in the absence of supporting electrolyte and for any values of diffusion coefficients of the substrate and the product of an electrode process is presented. The treatment applies to any reasonable combination of the charge numbers of the substrate, its counterion, and the product. A way to incorporate the activation polarization into the model is also demonstrated. It has been shown that the height, position, and shape of the migrational voltammogram are affected by the ratio of the product to substrate diffusivity (theta). In particular, for the electrode processes with sign retention, unequal diffusivities of electroactive species influence both characteristic points of the voltammogram (the limiting current and the half-wave potential). For charge neutralization processes (uncharged product), the changes in theta parameter are accompanied only by a shift in the half-wave potential. The most dramatic changes in the I-E relation can be observed for the charge reversal processes. In this case, a consecutive increase in theta results in the transition of the voltammogram shape from rapid exponential growth (theta < 1), through ramp shape (theta = 1), to common wave shape (theta > 1). On the basis of the expressions derived for the limiting current (exact and linearized), a possibility of the determination of the diffusion coefficient of the electrode reaction product is demonstrated. In addition, the ranges of theta where the assumption of equal diffusivities of the substrate and the product is obeyed within an insignificant error have been determined quantitatively. The theory has been experimentally verified using voltammetric oxidation of hexacyanoferrate(II).