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

Abstract

A mathematical model is developed to simulate the discharge of a LiFePO4 cathode. This model contains three size scales, which match with experimental observations present in the literature on the multiscale nature of LiFePO4 material. A shrinking core is used on the smallest scale to represent the phase transition of LiFePO4 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 LiFePO4 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.

Current-induced transition from particle-by-particle to concurrent intercalation in phase-separating battery electrodes

“…We obtain good fits, with an of 0.2 and a of 0.6 A m -2 , yielding an average exchange current density of ~ 0.3 A m -2 . The exchange current density is higher than most reported values in literature; however, past work did not consider the active particle fraction and likely overestimated the active reaction area [20][21][22][23] . The fittings may also be affected by departures from Butler-Volmer kinetics at high rates that that lead to curved Tafel plots and small effective values of 27 .…”

“…Dreyer et al proposed that the thermodynamic origin of this behaviour arises from the non-monotonic chemical potential of Li as a function of the particle's composition 17 . On the other hand, a concurrent intercalation pathway, whereby most particles intercalate at once, has also been observed in LFP 18,19 .Despite its crucial importance, the active population has been largely neglected in models describing electrode cycling [20][21][22][23] . Differing approximations in the active population may have contributed to the vast range of experimentally-measured specific exchange current densities, which range from 10 -6 A m -2 to 10 -1 A m -2 in LFP [20][21][22][23] .…”

“…Despite its crucial importance, the active population has been largely neglected in models describing electrode cycling [20][21][22][23] . Differing approximations in the active population may have contributed to the vast range of experimentally-measured specific exchange current densities, which range from 10 -6 A m -2 to 10 -1 A m -2 in LFP [20][21][22][23] .…”

“…Differing approximations in the active population may have contributed to the vast range of experimentally-measured specific exchange current densities, which range from 10 -6 A m -2 to 10 -1 A m -2 in LFP [20][21][22][23] . The active population has sometimes been considered in terms of an electrode-level lithiation front from the separator to the current collector 24 .…”

“…The experimentally measured voltage, however, shows a strong Ohmic-like dependence (Figs S3 and S10). Low percolation of the carbon network (with a technologically-relevant carbon loading of 6 wt%) likely leads to weaklyconnected patches in the electrode that rely on interparticle contact resistance for electronic transport 22 , resulting in the observed Ohmic resistance. The sequence in which particles (de)lithiate is determined by their distance from the closest carbon network (Fig.…”