A nonlinear Cole-Cole model for large-amplitude electrochemical impedance spectroscopy

Electrochemical impedance spectroscopy (EIS) is increasingly used to monitor the behavior of electrochemical processes. Commonly, EIS is driven by an input signal comprised of a small-amplitude sinusoidal wave superimposed on a constant dc potential (i.e., potentiostatic) to facilitate its analysis through a linearization methods. However, valuable information of electrochemical processes can be also collected at large-amplitude perturbation voltages, which can excite nonlinearities reflected as amplitude-dependent impedances. The aim of this work is to explore a tractable formalism to derive nonlinear transfer functions to describe the EIS response under large amplitude perturbation signals. Gelatinized starch suspension is used as simple case study to determine the parameters of the nonlinear elements. A nonlinear extension of the Cole-Cole equation is proposed to account for the EIS measurements recorded at different amplitudes, where its frequency response is computed by means of first-harmonic balance and Fourier approximation of nonlinearities. The nonlinear Cole-Cole model is comprised of nonlinear resistances and constant phase elements. Unlike linear behavior, the nonlinear response of EIS cannot be obtained explicitly, but through numerical analysis of a set of nonlinear equations. The resulting transfer function leads to a nonlinear fractional equation, where the frequency response depends on the signal amplitude under voltage excitation.