Combined effects of Tafel kinetics and Ohmic potential drop on the nonlinear responses of electrochemical systems to low-frequency sinusoidal perturbation of electrode potential – New approach using the Lambert W-function

Nonlinearity effects of electrochemical systems kinetics on impedance measurements are re-examined in the low-frequency (LF) domain through symbolic manipulation and numerical computation performed with Mathematica. It is a new approach to some problems not yet completely resolved in electrochemical impedance spectroscopy despite a number of publications on this subject in the specialized literature. This article is focused on electrochemical systems governed by Tafel kinetics under steady-state conditions, so-called Tafelian systems below, and perturbed by a sinusoidal variation of electrode potential vs. time, at low frequency. First, harmonic analysis of the system response to sinusoidal perturbation of potential with negligible Ohmic drop effects is dealt with. Next, the combined effects of Tafel kinetics and Ohmic drop are thoroughly examined. The current–potential response at low frequency is modelled using the Lambert W-function. New formulations are derived for the nonlinear polarization resistance of Tafelian systems in the presence of Ohmic drop. Closed-form or infinite-series formulations are derived for the amplitudes of fundamental and harmonic components of periodic current. Finally, the validity condition for impedance measurements carried out in the LF domain is derived for Tafelian systems.