Deconvolution of immittance data: Some old and new methods

The background and history of various deconvolution approaches are briefly summarized; different methods are compared; and available computational resources are described. These underutilized data analysis methods are valuable in both electrochemistry and immittance spectroscopy areas, and freely available computer programs are cited that provide an automatic test of the appropriateness of Kronig–Kramers transforms, a powerful non-linear-least-squares inversion method, and a new Monte Carlo inversion method. The important distinction, usually ignored, between discrete-point distributions and continuous ones is emphasized, and both recent parametric and non-parametric deconvolution/inversion procedures for frequency-response data are discussed and compared. Information missing in a recent parametric measurement-model deconvolution approach is pointed out and remedied, and its priority evaluated. Comparisons are presented between the standard parametric least squares inversion method and a new non-parametric Monte Carlo one that allows complicated composite distributions of relaxation times (DRT) to be accurately estimated without the uncertainty present with regularization methods. Also, detailed Monte Carlo DRT estimates for the supercooled liquid 0.4Ca(NO3)2 · 0.6KNO3 (CKN) at 350 K are compared with appropriate frequency-response-model fit results. These composite models were derived from stretched-exponential Kohlrausch temporal response with the inclusion of either of two different series electrode-polarization functions.