Probing Nonlinear Dynamics to Unlock New Insights into Battery Systems
Authors: Murbach Matthew D , Schwartz Daniel T. 
Published: February 2020

Electrochemical impedance spectroscopy (EIS) is a powerful technique for the analysis of lithium-ion batteries and is widely used for both characterizing new materials as well as for diagnostics.1Small perturbations are purposefully used in order to linearize the highly nonlinear battery system, enabling simpler mathematical descriptions of the physical processes. Linearization enables the use of relatively simple equivalent circuit models, but it filters out potentially useful physical and chemical information contained in the nonlinear physics of the system. Conversely, by probing an electrochemical system with moderate amplitude current perturbations and measuring the voltage response, nonlinearities in the system can be measured through higher harmonics in the voltage spectrum (Figure 1). In fact, with advances in digital signal processing, today's potentiostats and frequency response analyzers can make collecting nonlinear impedance measurements comparable in time and difficulty to a traditional EIS measurement (in which the harmonics are often measured, but discarded).
Nonlinear (higher) harmonic analysis has been shown to be a powerful tool for characterizing complex electrochemical systems such as corrosion,2 hydrodynamic voltammetry,3 and solid oxide fuel cells4by providing rich information difficult or impossible to measure using typical linear impedance alone. Here we apply this extension of EIS, known as nonlinear EIS (NLEIS), to the study of lithium-ion batteries.
The price one pays for the greater information content of NLEIS experiments is the additional analysis required to interpret details of the harmonic response from the battery system. We address this analysis challenge by extending the impedance modeling work of Doyle, Meyers, and Newman5 into the nonlinear domain. We solve the frequency domain formulation of the pseudo 2-D battery model to efficiently compute the physics of the harmonic spectrum of the battery. The experimental results and modeling work are described in detail over the mHz to kHz frequency range needed to probe the full set of battery physicochemical processes. The results show the power of nonlinear impedance techniques for the analysis of lithium-ion batteries with an emphasis on the new physics revealed when one moves from the linear to the nonlinear regime.
References:
1. Osaka, T., Mukoyama, D. & Nara, H. Review—Development of Diagnostic Process for Commercially Available Batteries, Especially Lithium Ion Battery, by Electrochemical Impedance Spectroscopy. J. Electrochem. Soc.
162, A2529–A2537 (2015).
2. Darowicki, K. & Majewska, J. Harmonic Analysis Of Electrochemical and Corrosion Systems-A Review. Corros. Rev.
17, 383–400 (1999).
3. Medina, J. A. & Schwartz, D. T. Nonlinear Dynamics of Limiting Current in the Flow-Modulated Uniform-Injection Cell. J. Electrochem. Soc.
144, 155–164 (1997).
4. Wilson, J. R., Schwartz, D. T. & Adler, S. B. Nonlinear electrochemical impedance spectroscopy for solid oxide fuel cell cathode materials. Electrochimica Acta
51, 1389–1402 (2006).
5. Doyle, M., Meyers, J. P. & Newman, J. Computer simulations of the impedance response of lithium rechargeable batteries. J. Electrochem. Soc.
147, 99–110 (2000).

Figure 1