Systematic Model Development for Impedance Response of LiCoO2|C Batteries
Authors: Orazem Mark E. 
Published: May 2020

The objective of this presentation is to describe a systematic approach to model development that includes use of graphical methods to guide model development, use of electrical circuits to account for the geometry of a given system, and use of a phasor notation to facilitate calculation of a faradaic impedance based on proposed reaction mechanisms and mass transfer. The approach is represented for a set of data collected by Erol et al.1 from a commercial LiCoO2|C coin cell battery.
The normal operating potential range of the cells reported by the suppliers is between 3.0 V (0% state-of-charge) and 4.2 V (100% state-of-charge). In one experiment, a coin cell was initially discharged under constant 2 mA current to 3.00 V. The battery was then subjected to sequential 80 mV steps in cell voltage down to 2.20 V. After reaching a steady state, the battery was allowed to relax for two days at the open-circuit condition. When held at open circuit, the over-discharged battery slowly reached a cell potential within the normal operating range. Three impedance spectra, taken during the self-charge process, are used to demonstrate a systematic model development.
1. The three spectra were treated as pseudo-replicates, and the measurement model analysis was applied to identify the stochastic error structure. 2-4

2. The measurement model was used to evaluate consistency with the Kramers-Kronig relations to determine the frequency range suitable for analysis.2-4

3. An interpretation model was developed based on the treatment presented by Erol and Orazem5 for the coin cells within the usual operating potential range. An anomalous diffusion model was used to account for the diffusion impedance within the cathode.6

4. The process model was regressed to the Kramers-Kronig-consistent portion of the spectrum using a Levenberq-Marquardt regression algorithm.
Impedance spectroscopy is not a stand-alone technique, and models for impedance are not unique. The model identified by the procedure described in this presentation represents a process model intended to account for the hypothesized physical and chemical character of the system under study. The objective of the model is not to provide a good fit with the smallest number of parameters. The objective is rather to use the model to gain a physical understanding of the system. The model should be able to account for, or at least be consistent with, all experimental observations. The proposed model can suggest experiments needed to validate model hypotheses.

References

1. Erol, M. E. Orazem, and R. P. Muller, "Influence of Overcharge and Over-Discharge on the Impedance Response of LiCoO2/C Batteries," J. Power Sources, 270 (2014), 92-100.
2. Agarwal, M. E. Orazem, and L. H. García-Rubio, “Measurement Models for Electrochemical Impedance Spectroscopy: 1. Demonstration of Applicability,” J. Electrochem. Soc., 139 (1992), 1917-1927.
3. Agarwal, Oscar D. Crisalle, M. E. Orazem, and L. H. García-Rubio, “Application of Measurement Models to Electrochemical Impedance Spectroscopy: 2. Determination of the Stochastic Contribution to the Error Structure,” J. Electrochem. Soc., 142 (1995), 4149-4158.
4. Agarwal, M. E. Orazem, and L. H. García-Rubio, “Application of Measurement Models to Electrochemical Impedance Spectroscopy: 3. Evaluation of Consistency with the Kramers-Kronig Relations,” J. Electrochem. Soc., 142 (1995), 4159-4168.
5. Erol and M. E. Orazem, “The Influence of Anomalous Diffusion on the Impedance Response of LiCoO2|C Batteries,” J. Power Sources, 293 (2015), 57-64.
6. Bisquert and A. Compte, “Theory of the Electrochemical Impedance of Anomalous Diffusion,” J. Electroanal. Chem.,
499 (2001), 112-120.