Application of Measurement Models to Impedance Spectroscopy II. Determination of the Stochastic Contribution to the Error Structure

Development of appropriate models for the interpretation of impedance spectra in terms of physical properties requires, in addition to insight into the chemistry and physics of the system, an understanding of the measurement error structure. The time-varying character of electrochemical systems has prevented experimental determination of the stochastic contribution to the error structure. A method is presented by which the stochastic contribution to the error structure can be determined, even for systems for which successive measurements are not replicate. Although impedance measurements are known to be heteroskedastic in frequency (i.e., have standard deviations that are functions of frequency) and time varying over the duration of the experiment, the analysis conducted in the impedance plane suggests that the standard deviations for the real and imaginary parts of the impedance have the same magnitude, even at frequencies at which the imaginary part of the impedance asymptotically approaches zero. On this basis, a general model for the error structure was developed which shows good agreement for a broad variety of experimental measurements. This paper is part of a series intended to present the foundation for the application of measurement models to impedance spectroscopy. The basic premise behind this work is that determination of measurement characteristics is an essential aspect of the interpretation of impedance spectra in terms of physical parameters. The influence of the error structure on interpretation of impedance spectra is discussed elsewhere for various electrochemical and electronic systems. 1-7 In the previous paper of this series, it was shown that a measurement model based on Voigt circuit elements can provide a statistically significant fit to typical electrochemical impedance spectra. B Here a method is demonstrated in which the measurement model is used to * Electrochemical Society Student Member. ** Electrochemical Society Active Member. Present address: Department of Materials, Swiss Federal Institute of Technology (Lausanne), Lausanne, Switzerland. identify the stochastic component of the frequency-dependent error structure of impedance data. A preliminary model for the stochastic component of the error is proposed. The third paper of this series addresses the use of the measurement model for identification of the bias component of the error structure. ~