Understanding rapid charge and discharge in nano-structured lithium iron phosphate cathodes

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.

A continuum of physics-based lithium-ion battery models reviewed

“…The Doyle-Fuller-Newman (DFN) model, also known as the pseudo-two-dimensional (P2D) or Newman model, is probably the most popular, physics-based model for lithium-ion batteries. Since the DFN model was first posed in [42] this model, and its variants, have been widely used in many different applications [3,19,28,41,42,65] and has been the basis of multiple extensions [121,142].…”

“…It follows that, in such scenarios, their behaviour is well approximated by a single representative particle in each electrode. This holds for most materials, however lithium iron phosphate is a notable exception due to its flat open-circuit potential, and requires a different approach (see [19]). In scenarios where the current applied to the battery is given as part of the problem formulation, the current density on the surfaces of the electrode particles can be computed in advance.…”

Parameterising continuum level Li-ion battery models & the LiionDB database

“…These two branches are connected by a number of nonlinear elements in parallel with one another, representing the (de)intercalation reactions that transfer charge between the electrolyte and solid. A sketch of this transmission line interpretation is given in Castle et al [26].…”

Overpotential from Cosolvent Imbalance in Battery Electrolytes: LiPF6 in EMC:EC

“…Despite the advanced state of P2D battery modeling, almost every implementation for lithium-ion batteries has neglected the multicomponent nature of the electrolyte’s solvent. − Parametrization efforts focused on transport within the electrolyte also typically treat solvent blends as a single entity. ,− This ‘single-solvent approximation’ is ubiquitous, despite the fact that solvent mobility has increasingly been recognized as a factor controlling battery performance. , Several groups have observed that applied currents can drive bulk motion of both polymer and liquid electrolytes, showing that electrically uncharged solvent molecules can be driven to migrate. − …”