Physics-based models are important tools for simulating and optimizing the performance of Li-ion batteries, with the Doyle-Fuller-Newman (DFN) model being the most widely adopted [1]. However, the accuracy of this model depends heavily on its parameters. Two of the most critical parameters for the model are the solid-phase diffusion coefficient (Ds) and the reaction-rate constant (k0) [2]. These parameters are critical because Ds controls the diffusion overpotential, while k0 governs the charge-transfer overpotential. Together, these two overpotentials account for more than half of the total overpotential in a battery. Therefore, precise determination of Ds and k0 will enhance battery state-estimation, improve fast-charging protocols, and provide deeper insights into battery degradation mechanisms, leading to more efficient and reliable Li-ion battery applications.
Since Ds and k0 cannot be directly measured, they must be estimated, a process that can be quite complex. A review of the literature reveals that many studies have inaccurately determined these parameters. In this work, we have re-evaluated the estimation methods to address these inaccuracies and improve the reliability of the estimation process. This work uses galvanostatic and potentiostatic intermittent titration techniques (GITT and PITT, respectively) to estimate these key parameters using half-cells with Li(Ni0.4Co0.6)O2 electrodes. The two compared estimation methods are the widely used analytical approach based on Weppner and Huggins’s work [3] and a physics-based approach with the DFN model.
Figures 1a and 1b show the estimated values of Ds and k0 obtained using various methods. Figure 1c and 1d presents DFN model simulation results under dynamic current-loading conditions with Ds and k0 determined from various measurement and estimation techniques. The combination of GITT measurements with a newly proposed physics-based protocol for determining Ds and k0 gives the highest simulation accuracy, achieving an average root mean square error (RMSE) of 5.5 mV, as shown in Figure 1c. In contrast, the analytical method in combination with GITT measurements for determining Ds and k0, which is the most used in literature, shows the least accuracy, with an RMSE of 24.2 mV, as shown in Figure 1d. This higher error is attributed to the limitations inherent in the analytical approach’s core assumptions.
This study introduces a novel protocol for optimizing Ds and k0 as a function of lithiation degree from a single measurement, eliminating the need for expensive and complex techniques such as electrochemical impedance spectroscopy (EIS).

Figure 1. Determined values of Ds (a) and k0 (b) obtained from each measurement method (GITT and PITT) and estimation method (DFN model and analytical) as a function of lithiation degree. The DFN model simulations (solid lines) compared to measured data (dashed lines) for a dynamic battery load cycle, using different estimation methods and measurement techniques for obtaining Ds and k0 for GITT-DFN model (c) and GITT-Analytical (d). The error between simulated and measured data is shown below each plot.

References:
[1] M. Doyle, T.F. Fuller, J. Newman, Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell, J. Electrochem. Soc. 140 (1993) 1526. https://doi.org/10.1149/1.2221597.
[2] H.A.A. Ali, L.H.J. Raijmakers, K. Chayambuka, D.L. Danilov, P.H.L. Notten, R.-A. Eichel, A comparison between physics-based Li-ion battery models, Electrochimica Acta (2024) 144360. https://doi.org/10.1016/j.electacta.2024.144360.
[3] W. Weppner, R.A. Huggins, Determination of the Kinetic Parameters of Mixed‐Conducting Electrodes and Application to the System Li3Sb, J. Electrochem. Soc. 124 (1977) 1569. https://doi.org/10.1149/1.2133112.