Mesoscopic modeling of Li insertion in phase-separating electrode materials: application to lithium iron phosphate

Abstract

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.

Mesoscopic Modeling of a LiFePO4Electrode: Experimental Validation under Continuous and Intermittent Operating Conditions

“…Model parameters including the equilibrium potential and resistance distribution are somewhat different from those used in Ref. 49 as detailed later in this section. The mesoscopic model is embedded into porous-electrode theory (one-dimensional across the electrode thickness) to give a more realistic account of the electrode performance under various operating conditions.…”

“…In the simplest approximation, the regular solution model (one-parameter Margules model) may be used to describe the thermodynamic state of each unit. 49 However, this model turns out to be too simple to capture the actual single-unit thermodynamic behavior of elementary units which is key for a realistic simulation of the charge/discharge dynamics of an LFP electrode. Consequently, we employ the following modified Margules expression for U k , which enables an asymmetric dependence of the excess free energy of the binary solution (i.e., solution of the inserted species and empty sites) on composition:…”

“…With this view, the geometrical description of LFP units becomes irrelevant as far as the diffusion length is concerned. The unit-level model presented previously 49 is then embedded into porous-electrode theory which accounts for ionic and electronic transport losses across the electrode.…”

“…In order to simulate the performance of an actual LFP electrode, the previously proposed mesoscopic model 49 is used to describe the many-unit interactions in the electrode. Model parameters including the equilibrium potential and resistance distribution are somewhat different from those used in Ref.…”

“…Moreover, despite being able to acceptably estimate the electrode polarization in the intermediate SOC range, the model over-predicts the end-ofdischarge capacities to a large extent. 48 In a previous publication, 49 we presented a simple mesoscopic model that makes no assumption regarding whether lithiation/delithiation occurs by inter-particle or intra-particle phase transformation mechanisms. The model defines elementary mesoscopic units which are large enough to contain a substantial number of reaction sites (i.e., vacancies and inserted species), but small enough that no intra-unit phase separation occurs.…”