Dynamic Impedance Spectroscopy: Fitting Multivariate Impedance Spectra using B-Spline Basis

Classical approaches to modelling dynamic or multivariate impedance spectroscopy data rely on either fitting individual spectra using an iterative procedure or using a joint least-squares analysis combined with partial prior knowledge of the model as a function of parameters which show a dependence on a control variable such as voltage or time. However, these approaches often fail to provide accurate results due to their sensitivity to the initial guess of the model parameters and the lack of an adaptive modelling approach. We address these limitations by introducing an approach that combines the parametric modelling of single spectra and use cubic B-splines to introduce the dependence of such parameters on the control variable. We illustrate our method by analyzing a set of 50 spectra obtained from dynamic impedance studies of electron transfer involving a redox couple in solution. We further demonstrate that the spline-based method is less sensitive to initial guesses, outperforms classical fitting methods in preserving the model parameters’ dependence on the control variable and yields a significantly lower weighted residual mean square value compared to classical approaches.