Li-ion batteries involve electrode materials, such as iron phosphate and graphite, which tend to separate into Li-rich and Li-poor phases upon intercalation of lithium. In nanoparticles, this bulk thermodynamic relaxation competes with surface electrochemistry, leading to the fundamental question: What is the reaction rate during a phase transformation? A consistent answer is provided by a theory of chemical thermodynamics that unifies and extends the Cahn-Hilliard and Allen-Cahn equations for chemical kinetics and charge transfer. The reaction rate depends on concentration gradients, elastic stress, and other non-idealities. Simulations based on the theory shed light on the complex nonlinear dynamics of ion intercalation and nucleation in battery nanoparticles and phase transformation dynamics in porous electrodes.
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