Fundamental Physical Parameter Fitting via Electrochemical Impedance Spectroscopy
Authors: Civan Fazlı Eren , Katırcı Gökberk , Ülgüt Burak 
Published: August 2024

Electrochemical impedance spectroscopy (EIS) is a non-destructive technique that plays a crucial role in the investigations of batteries. EIS enables to analyze essential information regarding what is happening in a battery. The most important information that can be obtained from an EIS data is the effects of kinetic and diffusion related events. Having an idea about these physical events enables doing battery diagnostics and development. Therefore, several methods of EIS data analysis had been developed in order to clearly understand what is underlying an EIS spectra.
One of the developed methods for EIS data analysis is using equivalent circuits. The very first example was done by Randles in 1947[1]. In his paper, he was able to separately obtain kinetic and diffusion-related parameters with the equivalent circuit method. However, he focused on just one reaction in a single interface using a three-electrode setup. Therefore, by lowering the complexity of the system, he was able to separately identify kinetic and diffusion related events. However, the systems that are currently investigated are much more complicated. Therefore, using the equivalent circuit method is plagued by ambiguity and multivalued fits.
On the other hand, in 2018, Murbach and Schwartz published on a new way of analysis[2]. They have simulated 38800 impedance spectra with variety of physical constants and tried to match the experimentally provided impedance spectra. However, this method suffers from the above-mentioned ambiguity. That is, several impedance spectra calculated with very different physical constants fitted the experimental data equally well. Therefore, reducing or eliminating this ambiguity of EIS data is essential.
Temperature-dependent EIS is one of the ways to reduce this ambiguity. In our group, we have previously shown that even with equivalent circuits, it is possible to distinguish diffusion and kinetic-related events with temperature-dependent EIS[3]. Kinetic events such as lithium-ion transfer has a strong dependence of temperature. Therefore, we were able to separate the kinetic and diffusion events by varying the temperature and looking the Arrhenius plots.
In addition to the temperature dependence, non-linear impedance can further reduce the complexity of the EIS data. Again, in our group, we have shown that higher harmonics contain valuable information about redox reactions happening in the system[4]. Also, non-linear impedance response, especially the second harmonic, provides crucial information regarding the diffusion parameters at the low frequency region which is also showed by Murbach and Schwartz [5]. Therefore, we will show that using temperature-dependent linear and non-linear EIS can unlock the secrets of an EIS spectrum.
In the current study, we will report temperature-dependent linear and non-linear simulations on an Li-ion battery with the NMC/Graphite chemistry. Here, we will show that temperature-dependent impedance measurements will enhance the discernibility of various kinetic parameters. Also, non-linear impedance response will improve the discernibility of diffusion related events. Combination of temperature dependence and non-linear response is collected in an objective function. The derived objective function is employed for the analysis of variations between experimental and simulated data, considering weights assigned to each parameter during the calculation process.By monitoring the value of this difference as a function of various fundamental parameters, we will show that meticulously adjusted weights can further improve the objective function to converge proper values. Ultimately, we will show that it is possible to correctly separate and identify the physical constants related to kinetic and diffusion events with temperature-dependent linear and non-linear EIS in an unequivocal manner.
References:
[1] Randles et al. "Kinetics of rapid electrode reactions." Discussions of the Faraday Society 1 (1947): 11-19.
[2] Murbach, Matthew D., and Daniel T. Schwartz. "Analysis of li-ion battery electrochemical impedance spectroscopy data: An easy-to-implement approach for physics-based parameter estimation using an open-source tool." Journal of The Electrochemical Society 165.2 (2018): A297.
[3] Zabara, Mohammed Ahmed, Gökberk Katırcı, and Burak Ülgüt. "Operando investigations of the interfacial electrochemical kinetics of metallic lithium anodes via temperature-dependent electrochemical impedance spectroscopy." The Journal of Physical Chemistry C 126.27 (2022): 10968-10976
[4] Zabara et al. "Non-linear harmonics in EIS of batteries with lithium anodes: Proper controls and analysis." Electrochimica Acta 429 (2022): 140969
[5] Murbach, Matthew D., and Daniel T. Schwartz. "Extending Newman's pseudo-two-dimensional lithium-ion battery impedance simulation approach to include the nonlinear harmonic response." Journal of The Electrochemical Society164.11 (2017): E3311

Figure 1