Stochastic many-particle model for LFP electrodes

Abstract

In the framework of non-equilibrium thermodynamics we derive a new model for many-particle electrodes. The model is applied to LiFePO 4 (LFP) electrodes consisting of many LFP particles of nanometer size. The phase transition from a lithium-poor to a lithium-rich phase within LFP electrodes is controlled by both different particle sizes and surface fluctuations leading to a system of stochastic differential equations.An explicit relation between battery voltage and current controlled by the thermodynamic state variables is derived. This voltage-current relation reveals that in thin LFP electrodes lithium intercalation from the particle surfaces into the LFP particles is the principal rate limiting process. There are only two constant kinetic parameters in the model describing the intercalation rate and the fluctuation strength, respectively. The model correctly predicts several features of LFP electrodes, viz. the phase transition, the observed voltage plateaus, hysteresis and the rate limiting capacity. Moreover we study the impact of both the particle size distribution and the active surface area on the voltage-charge characteristics of the electrode. Finally we carefully discuss the phase transition for varying charging/discharging rates.Keywords lithium-ion battery • lithium iron phosphate • phase transitions • many particle electrode

Pathwise McKean-Vlasov Theory with Additive Noise

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“…Last not least, our motivation comes from a recent battery model, cf. (1.6) below, taken from [23], which is of the form (1.1) but with reflecting boundary as given in (1.5).…”

“…exposed in Sznitmann [38]. Our study was prompted by some concrete problems in battery modelling [23], and also by recent progrss on rough-pathwise McKean-Vlasov theory, notably Cass-Lyons [10], and then Bailleul, Catellier and Delarue [4]. Such a "pathwise McKean-Vlasov theory" can be traced back to Tanaka [40].…”

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