Leveraging the Discriminating Power of Second-Harmonic Nonlinear Electrochemical Impedance Spectroscopy with Nonlinear Transmission Line Model
Authors: Ji Yuefan , Schwartz Daniel T. 
Published: December 2024

Transmission line models (TLMs) are a powerful and adaptable modeling strategy for capturing complex electrochemical processes occurring in porous electrodes. [1,2] In practice, TLMs are less widely used than constant phase elements (CPEs) to model mid- to high-frequencies features in electrochemical impedance spectroscopy (EIS) data from porous electrodes; this can obscure the physical interpretation of interfacial processes. [3] We have recently shown how to convert physics-based models of the electrochemical double layer and charge transfer rates into well-established EIS and novel 2nd Harmonic Nonlinear EIS (2nd-NLEIS) circuit elements, extending a wide array of circuit structures into the weakly nonlinear regime. [4] The benefit of parameter estimation using both EIS and 2nd-NLEIS data is especially evident in two electrode cells, where simultaneous fitting of opposite parity of EIS and 2nd-NLEIS signals contributes to an internal self-consistency check on the uniqueness and assignment of parameters to each of the electrodes. [5]
In this work, we will demonstrate a numerical framework that extends linear TLMs to second-harmonic nonlinear TLMs (2nd-nTLMs), enabling electrochemical analysts to benefit from the descriptive power of TLMs and the model discriminating power of combined EIS and 2nd-NLEIS analysis. Specifically, we will show that the overlapping time constant can be effectively separated by using EIS and 2nd-NLEIS with TLMs and 2nd-nTLMs in half-cells. We show how TLMs and 2nd-nTLMs can be combined to extract parameters from the complex electrochemical reactions in aging battery electrodes, allowing parameter estimation that includes the nonlinear charge transfer symmetry and curvature of thermodynamic open circuit voltage data at specific states of charge. Moreover, we will demonstrate the application of TLMs/2nd-nTLMs in obtaining current distribution within the porous electrode, which could guide the future design of high-performance battery electrodes.

References

[1] J. Moškon, M. Gaberšček, Transmission line models for evaluation of impedance response of insertion battery electrodes and cells, Journal of Power Sources Advances 7 (2021) 100047. https://doi.org/10.1016/j.powera.2021.100047.
[2] S. Drvarič Talian, J. Bobnar, A.R. Sinigoj, I. Humar, M. Gaberšček, Transmission Line Model for Description of the Impedance Response of Li Electrodes with Dendritic Growth, J. Phys. Chem. C 123 (2019) 27997–28007. https://doi.org/10.1021/acs.jpcc.9b05887.
[3] U. Westerhoff, K. Kurbach, F. Lienesch, M. Kurrat, Analysis of Lithium-Ion Battery Models Based on Electrochemical Impedance Spectroscopy, Energy Technology 4 (2016) 1620–1630. https://doi.org/10.1002/ente.201600154.
[4] Y. Ji, D.T. Schwartz, Second-Harmonic Nonlinear Electrochemical Impedance Spectroscopy: Part I. Analytical Theory and Equivalent Circuit Representations for Planar and Porous Electrodes, J. Electrochem. Soc. 170 (2023) 123511. https://doi.org/10.1149/1945-7111/ad15ca.
[5] Y. Ji, D. Schwartz, Second-Harmonic Nonlinear Electrochemical Impedance Spectroscopy: Part II. Model-Based Analysis of Lithium-Ion Battery Experiments, J. Electrochem. Soc. (2024). https://doi.org/10.1149/1945-7111/ad2596.