New method for graphing impedance values as an analytical tool suitable for electrochemical impedance spectroscopy

Abstract

A new method for graphing electrical impedance values named a “differentiation-based Bode plot” is proposed. This method facilitates the analysis procedure and reduces the arbitrariness of the interpretation of electrochemical impedance spectroscopy (EIS) data. Among the various methods for graphing impedance values, Nyquist plots are commonly adopted (primarily in the field of EIS) because of the apparent correlation between their shape and the corresponding equivalent circuit. However, because Nyquist plots do not contain frequency information, Bode phase and magnitude plots are frequently utilized. Although such plots are suitable for determining the absolute magnitude and phase of the impedance, they are not always useful for selecting the structure of an equivalent circuit, which is a hypothetical model for electrochemical cells. In the proposed method, instead of the real (Z’) and imaginary (Z’’) parts, two functions of the impedance derivatives with respect to frequency, i.e., dZ’/d(log f) and dZ’’/d(log f), are plotted. As substitutions for the Bode phase and magnitude plots, arctan{dZ’’/d(log f) ÷ dZ’/d(log f)} and log[sqrt{(dZ’/d(log f))² + (dZ’’/d(log f))²}] are plotted against log f. Unlike the classical Bode plot, the differentiation-based Bode plot is independent of the lateral shift in the Nyquist plot, which is advantageous for determining an equivalent circuit. To demonstrate this advantage, the impedance values of typical equivalent circuits used in electrochemistry are calculated and plotted to compare differentiation-based Bode plots with Nyquist and classical Bode plots.