Some new directions in impedance spectroscopy data analysis

Abstract

New developments in two main data analysis areas are discussed: (a) complex nonlinear least squares (CNLS) fitting of data and (b) data-transforming and optimizing integral transforms. In the first category, a Monte Carlo study is used to answer the question of which of several different parameterizations of an ambiguous equivalent circuit model lead to minimum correlation between fitting parameters, a desirable condition. In addition, results are briefly discussed which address the questions of (1) what should be minimized in CNLS fitting? (2) how well can one discriminate between exact small-signal binary electrolyte response and conventional finite-length diffusion response? and (3) what is the ultimate precision of parameter estimates obtained in a CNLS fit? In the second area, new forms of the Kronig-Kramers relations (KKR) are discussed; the accuracy of several different ways of carrying out the numerical quadratures needed in such transforms is compared; and it is shown how random errors present in complex data are transformed by the KKR. Then, new transforms are described and illustrated that can replace exponential Fourier and KK transforms and, at the same time, can greatly reduce random error and some kinds of systematic errors in real, imaginary, or complex frequency response data or transient response data without the need for smoothing or filtering parameter choices.