A mathematical model of the LiFePO 4 electrode is developed that is based on a thermodynamically-consistent treatment of solid-state lithium transport, in which the active material is described as a nonideal binary solution of Li-intercalated and empty sites. The nonideality is derived from the experimental open-circuit potential and manifested in a concentration-dependent diffusion coefficient throughout the entire composition range. Under certain operating conditions, a diffuse phase-boundary between Li-poor and Li-rich area is predicted. Furthermore, the actual active-particle-size distribution within the electrodes is captured by three different particle groups in the model. Without embedding porous-electrode effects into the model, simulation/experiment comparisons for three electrodes recovered from different commercial cells at rates up to 1C show the robustness of the variable solid-state diffusivity and particle-size distribution for simulating galvanostatic charges/discharges. In addition, it allows for analysis of the experimental data of various electrodes and to understand their rate limitations. Based on model-parameter comparison between the three designs, the resistive-reactant effect is identified as an additional limiting effect in the electrode comprising nano-particles. The proposed model is a promising candidate for various macroscopic applications, e.g., implementation into 3D battery-pack models for battery management system or comprehensive aging studies.

The variable solid-state diffusivity (VSSD) and the resistive-reactant (RR) models that focus on different physical phenomena are used to investigate the solid-state transport (bulk effects) and electronic conductivity (surface effects) of LiFePO 4 (LFP). For the first time, the models are effectively validated against experimental galvanostatic discharge data over a full range of applied currents. To achieve a reasonable degree of accuracy, particle-level parameters are estimated by fitting to experimental data obtained under low-rate discharge conditions, whereas electrode-level properties are derived based on high-rate conditions. Particle size distribution turns out to play a pivotal role in determining the rate capability of the electrode determined by the VSSD and a revised version of the RR model. Based on the full-range comparative study, both the resistive-reactant effect and bulk-related rate limitations prove to contribute significantly to the electrode polarization, especially at high C-rate. The resistive-reactant effect is expected to increase in an electrode made of smaller LFP particles.

A simple mesoscopic model is presented which accounts for the inhomogeneity of physical properties and bi-stable nature of phase-change insertion materials used in battery electrodes. The model does not include any geometric detail of the active material and discretizes the total active material domain into meso-scale units featuring basic thermodynamic (non-monotonic equilibrium potential as a function of Li content) and kinetic (insertion-de-insertion resistance) properties. With only these two factors incorporated, the model is able to simultaneously capture unique phenomena including the memory effect observed in lithium iron phosphate electrodes. The analysis offers a new physical insight into modeling of phase-change active materials which are of special interest for use in high power Li-ion batteries.