Electrochemical impedance spectroscopy (EIS) is a powerful nondestructive tool that is widely used to identify physical parameters and health diagnostics in lithium-ion batteries.¹ By applying a small perturbation of either current or voltage and subsequently analyzing the electrochemical responses over a range of frequencies, information can be revealed about the charge-transfer kinetics, transport phenomena, and thermodynamics of the cell.² Small amplitude perturbations are used to ensure the battery operates in its linear-response regime. The frequency-dependent cell impedance Z(ω) is most commonly analyzed by fitting an equivalent circuit model and extracting parameters from these fits. However, equivalent circuit models limit the amount of physically insightful information that can be extracted from battery EIS data.^3,4 Moreover, operating in the linear response regime also imposes a fundamental limitation on the total quantity of information contained in an impedance spectrum, since many of the physicochemical processes in a battery are inherently nonlinear in character.

Nonlinear electrochemical impedance spectroscopy (NLEIS) is an adjunct to EIS where larger amplitude sinusoidal current or potential perturbations are applied, and the nonlinear response of the battery is measured by the presence of higher harmonics in the output. Through a fairly straightforward analysis, a purely frequency-dependent second harmonic “impedance” Z₂(ω) can be defined. Higher harmonic, or nonlinear, electrochemical impedance spectra can provide deep insights into processes occurring in the electrochemical device under test, including insights into physicochemical processes that are invisible to standard (linearized) EIS approach.⁵

Here, Samsung 18650 LiNMC | C batteries (capacity = 1500 mAh) were cycled under various rates and conditions, with NLEIS data acquired throughout the duration of its cycle time, for different states of charge. For this particular battery capacity and chemistry, a typical “moderate” current perturbation was 300 to 500 mA. The experimentally measured nonlinear electrochemical impedance spectrum Z₂(ω) can be compared to results derived from the psuedo-2D model of a Li-ion battery⁶. Our physics-based approach for computing the nonlinear electrochemical impedance is a natural extension of the linearized EIS analysis that has been done previously.⁴

We show that NLEIS experiments have all the information of EIS, plus additional information on the electrode thermodynamics (low frequencies) and charge transfer kinetics. We show that aggressive cycling increases the kinetic impedance of the positive electrode, with little impact on the negative electrode. NLEIS shows a correlated effect, but it is possible to use Z₂(ω) to discern more about the nature of the interfacial degradation occurring on the positive electrode. In short, using nonlinear impedance in coordination with the linear impedance can provide further insight into more sensitive physicochemical phenomena that can be used to diagnose the state of health of Li-ion batteries during aging.

[1] N. Lohmann, P. Weßkamp, P. Haußmann, J. Melbert, and T. Musch, J. Power Sources, 273, 613-623 (2015)

[2] C. Chen and P.P. Mukherjee, Phys. Chem. Chem. Phys., 17, 9812-9827 (2015)

[3] T. Osaka, D. Mukoyama, and H. Nara, J. Electrochem. Soc. 162, 2529-2537 (2015)

[4] M. Doyle, J. P. Meyers, and J. Newman, J. Electrochem. Soc. 147, 99-110 (2000)

[5] J.R. Wilson, D. T. Schwartz, and S. B. Adler, Electrochimica Acta, 51, 1389-1402 (2006)

[6] T.F. Fuller, M. Doyle, and J. Newman, J. Electrochem. Soc. 141, 1-10 (1994)