Robust Interpretation of Electrochemical Impedance Spectra Using Numerical Complex Analysis

Electrochemical Impedance Spectroscopy (EIS) is a noninvasive 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 suggest the presence of inductors and constant phase elements (nonideal capacitors) from impedance data and enable us to answer questions about the identifiability and nonuniqueness 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.