Abstract
A Doyle–Fuller–Newman (DFN) model for the charge and discharge of nano-structured lithium iron phosphate (LFP) cathodes is formulated on the basis that lithium transport within the nanoscale LFP electrode particles is much faster than cell discharge, and is therefore not rate limiting. We present some numerical solutions to the model and show that for relevant parameter values, and a variety of C-rates, it is possible for sharp discharge fronts to form and intrude into the electrode from its outer edge(s). These discharge fronts separate regions of fully utilised LFP electrode particles from those that are not. Motivated by this observation an asymptotic solution to the model is sought. The results of the asymptotic analysis of the DFN model lead to a reduced order model, which we term the reaction front model (or RFM). Favourable agreement is shown between solutions to the RFM and the full DFN model in appropriate parameter regimes. The RFM is significantly cheaper to solve than the DFN model, and therefore has the potential to be used in scenarios where computational costs are prohibitive, e.g. in optimisation and parameter estimation problems or in engineering control systems.
Highlights
Lithium iron phosphate (LFP) has been developed as a cathode material for lithium-ion batteries [37]
The main results of the asymptotic analysis can be summarised in the form of a simplified reduced order model, termed the reaction front model (RFM), that provides a good approximation of the DFN model in the distinguished limit Υ → ∞
We have derived a simplification to the Doyle-Fuller-Newman (DFN) model for thecharge of nano-structured lithium iron phosphate (LFP) cathodes in which it is assumed that the particles are so small that transport inside the electrode particles can be taken to be infinitely fast on the timescales of interest (i.e. that of cellcharge)
Summary
Lithium iron phosphate (LFP) has been developed as a cathode material for lithium-ion batteries [37]. Previous modelling studies of LFP half-cells using the DFN framework include work by Srinivasan and Newman [49] and Dargaville and Farrell [10, 11] Both [49] and [10] adopt a “shrinking core” model to describe lithium transport and phase change within the electrode particles. In both these works comparison was made to experimental discharge curves measured from a half cell cathode with micron sized LFP electrode particles in [49]. In particular they show that by increasing the diffusivity of the electrolyte they were able to discharge at much faster rates They compare their results to a sharp discharge front (SDF) model in which an interface propagates into the half-cell from the separator; behind this front the electrode material is fully discharged (i.e. fully lithiated) and in front of it is fully charged (i.e. fully de-lithiated).
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