Determination of state-of-charge dependent diffusion coefficients and kinetic rate constants of phase changing electrode materials using physics-based models

The simplified gravimetric intermittent titration technique (GITT) model, which was first proposed by Weppner and Huggins in 1977, remains a popular method to determine the solid-state diffusion coefficient ($D_1$) and the electrochemical kinetic rate constant ($k$). This is despite the model having been developed on the premise of a single-slab electrode and other gross simplification which are not applicable to modern-day porous battery electrodes. Recently however, more realistic and conceptually descriptive models have emerged, which make use of the increased availability of computational power. Chief among them is the P2D model developed by Newman et al., which has been validated for various porous battery electrodes. Herein, a P2D GITT model is presented and coupled with grid search optimization to determine state-of-charge (SOC) dependent $D_1$ and $k$ parameters for a sodium-ion battery (SIB) cathode. Using this approach, experimental GITT steps could be well fitted and thus validated at different SOC points. This work demonstrates the first usage of the P2D GITT model coupled with optimization as an analytical method to derive and validate physically meaningful parameters. The accurate knowledge of $D_1$ and $k$ as a function of the SOC gives further insight into the SIB intercalation dynamics and rate capability.