(565b) Mathematical Modeling of Lithium Ion Batteries: A Paradigm Shift

The standard approach to modeling Li-ion batteries, based on porous electrode theory, assumes Butler-Volmer reaction kinetics, isotropic diffusion of intercalated ions, and an open circuit voltage (OCV) vs. composition fitted to experiments. Although not fully predictive, this model can fit the discharge of some solid-solution electrodes, but it fails to describe phase-separating materials, which are currently the most promising for high power density. In this talk, we present a new modeling paradigm based on statistical thermodynamics, which coherently describes the OCV, intercalation, and phase separation. The homogeneous free energy in the Cahn-Hilliard equation is related to the OCV, and a new boundary condition is proposed for intercalation kinetics, which depends on the full chemical potential, including the gradient term. For phase-separating materials, such as lithium iron phosphate, the model predicts, for the first time, many features of recent experiments: (i) the phase boundary aligns with the crystal axis of greatest lattice-mismatch strain; (ii) intercalation proceeds as a nonlinear wave along the crystal surface, filling it layer by layer; (iii) a composite electrode in the miscibility gap undergoes a ``mosaic instability'', where reservoir crystals spontaneously phase separate and fill with ions, one by one; and (iv) ``ultrafast'' battery charging, in seconds rather than hours, can be attained with surface coatings that distribute ions across each active crystal facet. [This work is supported by the National Science Foundation via contract DMS-0842504.]