AN ALTERNATING-CURRENT IMPEDANCE MODEL INCLUDING MIGRATION AND REDOX-SITE INTERACTIONS AT POLYMER-MODIFIED ELECTRODES

Electron hopping in redox polymer-modified electrodes requires coincident ion movement to maintain electroneutrality, and transport effects can arise due to either process. In this paper, the equation for diffusion/migration by electron hopping is used with the classical Nernst-Planck equation for mobile ionic species to rigorously model the ac impedance response of a redox-site-containing polymer attached to an electrode and by a binary aqueous electrolyte. The theory also includes the effect of polymer redox-site interactions. Donnan exclusion is assumed, permitting only one mobile ion in the film. This leads to an analytical solution to the problem because the polymer can be treated as a binary electrolyte. When ion movement is slow relative to electron hopping, the impedance spectrum contains a classical Warburg region just as when electron hopping controls the rate. Although these two types of rate control cannot be distinguished from a single ac impedance spectrum, one can determine the transport controlling process from the potential dependence of the data from a series of spectra.