Physio-Chemical Model-Based Gitt Evaluation for Determining the Solid-State Diffusion Coefficient and the Kinetic Rate of Electrode Materials

Accurately determining the solid-state diffusion coefficient and the kinetic rate is crucial to parametrize a valid and reliable physio-chemical battery model. The most common experimental method for evaluating parameters is the gravimetric intermittent titration technique (GITT), which was first proposed by Weppner and Huggins [1], and later refined and adapted for porous electrodes by Kang et al [2, 3]. An effective hybrid approach involves coupling a physio-chemical model with an optimization algorithm to achieve the best fit based on the root mean square error (RMSE) between the model results and the experimental GITT measurements [4]. This approach has the advantage of enabling the evaluation of the solid-state diffusion coefficient and the kinetic rate for each GITT pulse sequence. However, due to the non-linear search grid, finding the global minimum of the RMSE can be computationally intensive. This work deals with, how an efficient and accurate model-based optimization algorithm can be implemented to achieve a valid parametrization. In this paper, the hybrid approach is enhanced through a two-step optimization method which gives a rapid and accurate evaluation of the electrode parameters. For the experimental data, a commercial sodium-ion battery (Shenzhen Mushang Na18650-1250) was disassembled, and the electrode materials were extracted. Subsequently, half-cells of the extracted anode materials (hard carbon) were assembled in a three-electrode configuration and characterized using a GITT protocol, which involved short pulses (36 seconds) (see Figure a) followed by an extended relaxation phase (8 hours). The experimental results were evaluated following the methodology established by Kang et al. [2,3]. A half-cell model for the anode (hard carbon) was parameterized in PyBaMM [5]. The hybrid evaluation was carried out in two steps. In the first step, the relaxation phase of the GITT measurement was used to determine the minimum RMSE between the model and the measurements (see Figure b and c), utilizing the reinvented GITT technique proposed by Kang et al. In the second step, the kinetic rate was fitted over the pulse and the onset of the relaxation phase. The separate fitting is possible due to the different sensitivities of the electrode potentials in the pulse domain (sensitive to solid-state diffusion coefficient and kinetic rate) and the relaxation domain (only sensitive to the solid-state diffusion coefficient). Through the presented optimization process with the algorithm-based optimization of the solid-state diffusion coefficient in the relaxation range and the sequential optimization of the kinetic rates, a more accurate and faster determination of the electrode-specific parameters can be achieved and thus used for the parameterization. Additionally, comparisons between the experimental method and the hybrid methods reveal similar evaluated values across the different approaches. References: [1] W. Weppner and R. A. Huggins 1977 J. Electrochem. Soc. 124 1569 [2] Stephen Dongmin Kang and William C. Chueh 2021 J. Electrochem. Soc. 168 120504 [3] Stephen Dongmin Kang et al 2021 J. Electrochem. Soc. 168 120503 [4] K. Chayambuka et al. Journal of Power Sources Advances 9 (2021) 100056 [5] Sulzer et al. Journal of Open Research Software, 9: 14. DOI: https://doi.org/10.5334/ jors.309 Figure: Figure 1