Extended Distribution of Relaxation Time Analysis for Electrochemical Impedance Spectroscopy

Abstract

The distribution of relaxation time (DRT) is increasingly investigated as a novel analytical method for electrochemical impedance spectroscopy. However, this method has not yet been generalized, as it cannot be applied to a spectrum influenced by an isolated capacitator and a resistor connected in parallel with an inductor. To generalize the DRT analysis, we propose a novel principal relation and actual calculation methods using an iterative elastic net regularization algorithm. The elastic net regularization was implemented using the Levenberg–Marquardt method. The proposed algorithm aids in analyzing the DRT for spectra that cannot be solved using conventional methods. We compared the DRT results in different regularization methods obtained from the proposed program with those obtained from other open-source programs. Additionally, the realistic problems of the DRT analysis are discussed considering the calculated results and their theoretical basis. Different DRT curves can be obtained depending on the particular program and regularization methods, even when the spectrum is the same. Moreover, overconfidence in the electrochemical DRT method can be avoided with a clear understanding of DRT basics.

Keywords

• extended distribution of relaxation time analysis
• impedance spectroscopy
• elastic net regularization
• spectrum analysis