A Bayesian Approach to Autonomous Analysis of Electrochemical Impedance Spectra

Abstract

Electrochemical impedance spectroscopy (EIS) is a valuable characterization tool for a wide variety of materials due to its ability to probe transport and reaction pathways over a broad range of timescales. Recently, developments in experimental techniques have increased the use of EIS in high-throughput materials characterization. However, extraction of meaningful insight from high-volume EIS data streams is often stymied by the complexity of processing and analyzing impedance spectra. To address this challenge, we present a framework for fully autonomous analysis of EIS data leveraging Bayesian methods to obtain both the distribution of relaxation times (DRT) and equivalent circuit fits.The predominant quantitative method for EIS analysis is equivalent circuit modeling, which requires careful selection of equivalent circuit elements to represent physical processes in the system under study. However, the last decade has seen increasing interest in the DRT, which enables detailed EIS analysis without a priori construction of equivalent circuits. Deconvoluting the DRT is an ill-posed problem which may be tamed by imposing constraints upon the solution (regularization), but the solution is highly sensitive to the nature and severity of such constraints, which are challenging to calibrate. We demonstrate the application of Bayesian inference to determine the optimal regularization level and accurately deconvolute the DRT. The Bayesian approach identifies both smooth features (e.g. dispersed ZARCs) and sharp features (e.g. RC and Gerischer elements) in the DRT, is highly robust to noise, and is self-calibrating. We also explore the connection between the DRT and equivalent circuit modeling, illustrating how well-calibrated estimates of the DRT can both enable empirical selection of equivalent circuit models and provide initial parameter estimates for complex non-linear least squares fitting of these models. We apply these methods to both synthetic spectra and experimental data from high-throughput characterization of fuel cells and batteries to demonstrate their validity and utility. The software is published in an open-source Python package to enable broad usage and further development.Acknowledgments:This work was supported by the Advanced Research Projects Agency-Energy (ARPA-E) through the REFUEL program (Award No. DE-AR0000808) and the Army Research Office under Grant No. W911NF-17-1-0051.