Accounting for Unsteady-State Behavior during Electrochemical Impedance Spectroscopy

Abstract

Electrochemical Impedance Spectroscopy (EIS) is one of the most effective methods to characterize an electrochemical system. Most of the common mathematical tools available for the correct interpretation of EIS data assumes a steady-state system. So, the system should have a constant voltage at a given current or vice versa during the duration of experiment. However, the system can deviate from a steady-state because of the perturbation applied during EIS measurement or because of the intrinsic chemistry of the system. For example, during charging or discharging of a battery at a constant current, voltage is drifting due to the changes in chemistry of the materials inside the battery. This drift in voltage can be significant especially during lower frequency scans that can lasts hours (<0.3 mHz). In such a case, extracting meaningful data from EIS can be challenging due to violation of the steady state condition. Here we show a reliable method to correct for the drift that might occur during such a low frequency measurement. This method takes advantage of the fact that phase angles in many systems are not affected by such an unsteady state behavior. Therefore, drift-free impedance modulus data is reconstructed from the phase angle spectrum with the help of a Z-HIT algorithm that applies the logarithmic form of the Hilbert transform to systems exhibiting ‘two-pole’ behavior. From this drift-free EIS data, the severity of drift can be analyzed. In addition, a better-fitted equivalent circuit model can be simulated. Furthermore, this method removes inaccuracy during multi-sine excitation combined with other tools. Applicability of this method in characterizing different electrochemical devices such as batteries, fuel cells and supercapacitors is presented. Keywords: EIS, Z-HIT, Battery, Supercapacitor, Fuel cells,