Assessing Nonlinear Polarization in Electrochemical Cells Using AC Impedance Spectroscopy

Electrochemical energy storage and conversion devices are used to power a range of electrical loads including portable electronics, electric vehicles, and utility grids. The energy efficiency of these systems decreases with increasing current load due to energy losses (in the form of heat) associated with different processes. Electrochemical impedance spectroscopy (EIS) is a nondestructive technique commonly used to assess rate-limiting steps in electrochemical devices. Most EIS measurements for energy storage devices are only performed around open-circuit and do not probe system behavior under non-zero biases where these devices operate. Despite its widespread use, this approach does not provide information about the relative overpotentials associated with coupled nonlinear processes (e.g., diffusion limited redox reactions) commonly encountered in these systems. Furthermore, ambiguous terms such as equivalent series resistance and interfacial resistance can lead to confusion and data misinterpretation. For example, Ohm’s law cannot be applied to calculate nonlinear overpotentials using a resistance that was measured from a locally linear response. To determine overpotentials in nonlinear systems using EIS, one must integrate the individual resistive elements of the equivalent circuit as a function of steady state current. Recent experimental work has used this method to decouple ohmic, kinetic, and transport overpotentials in redox flow batteries. In these prior studies, impedance elements were derived, but analytical expressions for the corresponding overpotentials were not presented. While integrated resistance measurements are a powerful experimental tool, a more rigorous mathematical framework describing the approach is needed. The present work bridges this gap by: (i) deriving a general impedance expression for coupled charge transfer and diffusion processes and (ii) integrating the individual resistive elements as a function of steady-state current to obtain global polarization relationships. Analytical expressions for diffusion overpotentials are obtained for special cases, and numerical methods are applied when closed-form expressions do not exist. The work considers three model electrode geometries (planar, cylindrical, and spherical) and two diffusion boundary types (reflective and transmission). Finally, this treatment is extended to macroscopically homogenous porous electrodes which are relevant for describing practical devices. This presentation will highlight how measuring impedance at different steady-state biases provides critical insights on the rate-limiting processes in energy storage devices. While this work focuses on a simple Faradaic charge transfer process, the method can be used to evaluate other nonlinear phenomena in electrochemical power supplies. For example, the resistance of passive films (e.g., solid electrolyte interphase layer) in Li-ion batteries is typically only probed near open-circuit. Similarly, literature on solid-state batteries commonly uses ambiguous terms such as interfacial resistance to describe rate-limiting processes. For these more complex systems, integrating the resistive elements can provide insights on how these phenomena influence device efficiency. Overall, combining these experimental observations with physical models derived using the approach illustrated herein represents a powerful tool to guide component/system design and improve device performance. Acknowledgements This research was conducted at Oak Ridge National Laboratory, managed by UT Battelle, LLC, for the U.S. Department of Energy (DOE). This work is sponsored by the U.S. Department of Energy in the Office of Electricity through the Energy Storage Research Program and the Office of Energy Efficiency and Renewable Energy (EERE) in the Vehicle Technologies Office (VTO) through the Advanced Battery Materials Research (BMR) Program.