Non-Linear First-Harmonic Balance to Compute the Electrochemical Impedance of Butler-Volmer Equation

Abstract

The Butler-Volmer equation is commonly used to describe heterogeneous reaction mechanisms (e.g., charge transfer) involved on electrochemical systems. Under the application of an oscillatory exciting potential, the frequency response (i.e., electrochemical impedance spectroscopy) of the net current on the electrode is extensively quantified to characterize the mechanisms involved in the reaction process. This work uses a first-harmonic balance method to compute the electrochemical impedance response of the Butler-Volmer equation under kinetic control and subjected to a simple mass transfer coefficient model. The proposed approach recovers some nonlinear aspects, such as the effects of sinusoidal potential amplitude in the electrochemical impedance. The results showed that the frequency response can be equivalently described by a series RC circuit, where the resistance is attributed to the charge transfer and the capacitance to the accumulation dynamics on the electrode surface. The effects of fractional-order kinetics and mass transport restrictions were also considered, leading to a behavior similar to a Randles equivalent circuit. A simple example with parameters of the electrochemical ferricyanide/ferrocyanide system was used to illustrate the findings.