What Complex Analysis Can Tell Us About Electrochemical Impedance Spectroscopy

Electrochemical Impedance Spectroscopy (EIS) is a standard non-invasive technique widely used to understand electronic and ionic transport mechanisms in diverse material systems. There have been several approaches, particularly using machine learning, to classify and categorize the complex-valued data that is produced through EIS. Existing approaches typically have been optimized to specific materials systems, thus lacking general applicability of the classification framework. In this work, we describe a novel mathematical framework that allows us to discover key features within the EIS data.
This framework builds on the fundamental principles of complex analysis and recent advances in numerical rational function approximation, to extract key mathematical properties of material systems directly from their EIS data, without relying on the knowledge of equivalent circuit models. We look at ways to ascertain the presence of imperfect capacitors or constant phase elements and Warburg elements. We explore questions about the identifiability and uniqueness of equivalent circuit models that can produce the EIS impedance data.
We highlight results using both synthetic data and experimental data. Some of the analyzed experimental data is obtained from organic mixed electronic ionic conductors, organic electrochemical transistors, and thin films of molybdenum disulfide (MoS2). We also compare our results with those obtained by standard machine learning approaches and discuss the complementary insights that our mathematical framework can provide.