Cahn-Hilliard Reaction Model for Isotropic Li-ion Battery Particles

• Main Authors: Zeng, Yi (Contributor), Bazant, Martin Z. (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Chemical Engineering (Contributor), Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: Cambridge University Press/Materials Research Society, 2014-10-29T19:00:50Z.
• Subjects: Article
• Online Access: Get fulltext

 Using the recently developed Cahn-Hilliard reaction (CHR) theory, we present a simple mathematical model of the transition from solid-solution radial diffusion to two-phase shrinking-core dynamics during ion intercalation in a spherical solid particle. This general approach extends previous Li-ion battery models, which either neglect phase separation or postulate a spherical shrinking-core phase boundary under all conditions, by predicting phase separation only under appropriate circumstances. The effect of the applied current is captured by generalized Butler-Volmer kinetics, formulated in terms of the diffusional chemical potential in the CHR theory. We also consider the effect of surface wetting or de-wetting by intercalated ions, which can lead to shrinking core phenomena with three distinct phase regions. The basic physics are illustrated by different cases, including a simple model of lithium iron phosphate (neglecting crystal anisotropy and coherency strain).