A continuum approach to modelling hysteresis in phase-change lithium-ion battery electrodes

Voltage hysteresis in some lithium-ion battery electrode materials, such as lithium iron phosphate (LFP), persists even at negligible currents, posing challenges for accurate performance prediction and control. Traditional physics-based models, such as the Doyle–Fuller–Newman (DFN) framework, are fundamentally unable to capture this hysteresis due to their reliance on purely diffusive, single-particle dynamics that neglect history-dependent behaviour and ensemble variability. The recently proposed Composite Phase-change Model (CPM) addressed this by incorporating a finite set of interacting representative particles undergoing phase separation, but remains limited by computational constraints that restrict particle numbers to many orders of magnitude smaller than found in real electrodes. In this work, we present the Continuum Composite Phase-change Model (CCPM), a natural extension of the CPM that takes the mathematical limit of infinitely many particles. This formulation eliminates the numerical artefacts associated with finite ensembles and provides a robust framework for simulating phase-change electrodes. We demonstrate the CCPM’s predictive capability under various operating conditions and integrate it within a Newman-style full cell model implemented in the open-source PyBaMM platform. This work offers a scalable and physically consistent tool for modelling voltage hysteresis in battery electrodes arising from collective phase-transition statistics without resorting to empirical fitting parameters. This has particular relevance for LFP-based systems and opens new research avenues that might seek to use physically grounded principles to reduce the complexity of the CCPM for higher computational efficiency.