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.
@article{arxiv.2510.17835,
title = {Robust interpretation of electrochemical impedance spectra using numerical complex analysis},
author = {Jithin D. George and Willa Brenneis and Vinod K. Sangwan and Dilara Meli and Heather Kurtz and Jeffrey Richards and Lincoln J. Lauhon and Jonathan Rivnay and Mark C. Hersam and Jeffrey Lopez and Maria K. Y. Chan and Valerie Taylor},
journal= {arXiv preprint arXiv:2510.17835},
year = {2025}
}