Robust interpretation of electrochemical impedance spectra using numerical complex analysis

TL;DR

This paper introduces a mathematical complex analysis approach to interpret electrochemical impedance spectra, enabling identification of circuit elements and model uniqueness without relying solely on traditional circuit fitting.

Contribution

It presents a novel complex analysis-based method for extracting features from EIS data, improving understanding of circuit components and model identifiability.

Findings

Able to detect inductors and constant phase elements in models

Enumerates all possible circuit families with resistors and capacitors

Successfully applied to lithium-ion battery impedance data

Abstract

Electrochemical Impedance Spectroscopy (EIS) is a non-invasive technique widely used for understanding charge transfer and charge transport processes in electrochemical systems and devices. Standard approaches for the interpretation of EIS data involve starting with a hypothetical circuit model for the physical processes in the device based on experience/intuition, and then fitting the EIS data to this circuit model. This work explores a mathematical approach for extracting key characteristic features from EIS data by relying on fundamental principles of complex analysis. These characteristic features can ascertain the presence of inductors and constant phase elements (non-ideal capacitors) in circuit models and enable us to answer questions about the identifiability and uniqueness of equivalent circuit models. In certain scenarios such as models with only resistors and capacitors, we are able to enumerate all possible families of circuit models. Finally, we apply the mathematical framework presented here to real-world electrochemical systems and highlight results using impedance measurements from a lithium-ion battery coin cell.