Analysis of Electrochemical Impedance Spectra Using Phase Angle Symmetry Across Log Frequency

Abstract

A new method for analysis of the impedance behavior of electrochemical impedance circuits (or, in general, the Transfer Function for input-output systems) has been developed which utilizes the symmetry of the phase angle response and its derivative with the Log of the frequency to determine the value of the equivalent circuit elements. In addition, because of this symmetry, the lower frequency half of the impedance response over Log frequency can be calculated based only on information from the upper-half frequency response. The underlying analytical basis for the symmetry of the phase angle and the methods for applying this analysis are presented. Analysis of simple R-C circuits, Randle circuits and Constant Phase Element (CPE)-Randles are presented to derive the symmetric functions for these commonly used circuits. Experimental Electrochemical Impedance Spectroscopy (EIS) data focused on CoCrMo alloy performance in physiologically representative solutions were collected, analyzed using the described method and compared to standard non-linear least squares fitting. Excellent correlation between the analytical equations and experimental data was obtained. A substantial advantage of this approach is that it only requires knowledge of the high frequency-based response to predict the behavior in the low frequency range. Thus, determining the low frequency behavior requires capturing the high frequency impedance in a few seconds rather than in what had, until now, required up to many hours of experimental effort to obtain. Although the mathematical approach presented here is focused on corrosion parameters, it is applicable to other Transfer Function analyses that include dielectric constants, complex modulus and others.