Mathematical Modeling of Commercial LiFePO₄Electrodes Based on Variable Solid-State Diffusivity

A mathematical model of the 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.