Determination of the distribution of relaxation times through Loewner framework: A direct and versatile approach

Abstract

In this work, a direct data-driven approach is employed to extract the distribution of relaxation times (DRT) from impedance data. The proposed procedure is based on the Loewner framework, that is a data driven methodology with theoretical basis in the linear system theory. One of the main advantages is that the DRT can be computed without need of regularization procedures or iterative optimization algorithms. We test the Loewner framework based algorithm on synthetic impedance data generated through equivalent circuit models widely used for modeling electrochemical systems. Impedance data set including noise are also processed. In addition, experimental electrochemical impedance spectroscopy (EIS) data are analyzed. The study shows a significant improvement in the accuracy and a high versatility of the methodology. However, the presence of significant amount of noise compromises the reliability of the obtained DRT due to the occurrence of artifact peaks. Some recommendations how to deal with noisy data are discussed.