Toward a better characterization of constant-phase element behavior on disk electrodes from direct impedance analysis: Methodological considerations and mass transport effects

Complex nonlinear-least-squares fitting of impedance data to an equivalent circuit is probably the most intuitive method used to represent the whole electrode impedance from experimental electrochemical impedance spectroscopy data. However, among other questions it has the primary problem of identifying a physically significant model representing the system under examination. In that context it then becomes very suitable the study of other analysis procedures to complement this approach. With regard to constant-phase element (CPE) behavior characterization, direct impedance analysis seems to be a good choice since CPE behavior is explicitly revealed in the high frequency decay of the imaginary component of the impedance. For that reason it is becoming popular among electrochemists who can get the CPE exponent from a simple fit of the imaginary part of the impedance to a frequency power law. There are, however, important limitations to the frequency range employed in this analysis that are commonly ignored. In the case of disk electrodes, geometrical constraints related to the insulating-metal boundary induce current and potential distributions that screen the real underlying CPE behavior in the high frequency domain. On the other hand, for lower frequencies, CPE behavior can also be masked by the effects of diffusion. In this paper we present some methodological considerations taking these effects into account in order to get a more reliable characterization of the CPE behavior from direct impedance analysis. We illustrate these issues with different experimental conditions and show that in many cases deviations can be remedied thanks to a convenient theoretical treatment that allows correct values of CPE parameters to be retrieved.