Unified Model for Transient Faradaic Impedance Spectroscopy: Theory and Prediction

Abstract

We describe a unified model for transient faradaic impedance spectroscopy developed by obtaining a rigorous expression for the current for a potential step to an electrochemical system containing an oxidant and/or a reductant with no assumptions on the reversibility for redox reactions. Effects of electrode reaction kinetic and other parameters such as the exchange rate constant (k(0)), potential step period (t(p)), diffusion coefficient (D), transfer coefficient (alpha), the number of electrons transferred (n), and overpotential (eta) on observed impedance parameters have been evaluated using the model. We obtained both polarization resistances (R-p's) and Warburg impedances (Z(w)'s) to characterize the nature of the charge-transfer reaction by showing the evolution trend in terms of their admittances employing kinetic parameters such as eta, k(0), t(p), a, n, and D. The peak shift and the half-peak width of Warburg admittance voltammograms were also studied as a function of k(0). We finally discuss ranges of step periods, which allow meaningful transient impedance measurements to monitor faradaic processes in real-time by staircase cyclic voltammetric-Fourier transform electrochemical impedance spectroscopy (SCV-FTEIS) experiments, for a given step height.