Predicting Active Material Utilization in LiFePO[sub 4] Electrodes Using a Multiscale Mathematical Model

A mathematical model is developed to simulate the discharge of a cathode. This model contains three size scales, which match with experimental observations present in the literature on the multiscale nature of material. A shrinking core is used on the smallest scale to represent the phase transition of during discharge. The model is then validated against existing experimental data and this validated model is then used to investigate parameters that influence active material utilization. Specifically, the size and composition of agglomerates of crystals is discussed, and we investigate and quantify the relative effects that the ionic and electronic conductivities within the oxide have on oxide utilization. We find that agglomerates of crystals can be tolerated under low discharge rates. The role of the electrolyte in limiting (cathodic) discharge is also discussed, and we show that electrolyte transport does limit performance at high discharge rates, confirming the conclusions of recent literature.