Simple hierarchical impedance functions for asymmetric cells: Thin-layer cells and modified electrodes

Abstract

The main result is a closed-form solution for concentration profiles, currents, potential distributions and impedances when electrons (polarons) and counter-ions have different transference numbers. Two cases are treated in detail and illustrated with the new Laplace inversion program: a single uni-univalent salt asymmetric cell and the related modified electrode with fixed positive sites, mobile electrons and counter-ions. The first case is a model of redox polymers with counter-anions. The second case is the metal redox center as the fixed site with mobile counter-ions, which illustrates a more complex stoichiometry. Methods for adding the isolated processes of bulk (geometric, high frequency) charging, interfacial kinetics, adsorption/reaction and ion pair or complex formation/dissociation to the total impedance function are emphasized. The nonlinearities of the continuity equation can be written in ways that cover both electron diffusion and electron hopping. The nonlinear effects can be minimized because certain time-dependent terms occur as ratios in the canonical single-species flux equations. In this proposal, based on extensive examples in the literature, the total impedance can be understood without generating the large complicated equations which occur when all processes are written into a single theory.