Phase Separation Dynamics in Isotropic Ion-Intercalation Particles
Lithium-ion batteries exhibit complex nonlinear dynamics, resulting from diffusion and phase transformations coupled to ion-intercalation reactions. Using the recently developed Cahn--Hilliard reaction (CHR) theory, we investigate a simple mathematical model of ion intercalation in a spherical solid...
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| Other Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Society for Industrial and Applied Mathematics,
2014-12-29T22:01:09Z.
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| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | Lithium-ion batteries exhibit complex nonlinear dynamics, resulting from diffusion and phase transformations coupled to ion-intercalation reactions. Using the recently developed Cahn--Hilliard reaction (CHR) theory, we investigate a simple mathematical model of ion intercalation in a spherical solid nanoparticle, which predicts transitions from solid-solution radial diffusion to two-phase shrinking-core dynamics. This general approach extends previous lithium-ion battery models, which either neglect phase separation or postulate a spherical shrinking-core phase boundary, 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 diffusional chemical potentials, and the model consistently links the evolving concentration profile to the battery voltage. We examine sources of charge/discharge asymmetry, such as asymmetric charge transfer and surface "wetting" by ions within the solid, which can lead to three distinct phase regions. In order to solve the fourth-order nonlinear CHR initial-boundary-value problem, a control-volume discretization is developed in spherical coordinates. The basic physics are illustrated by simulating many representative cases, including a simple model of the popular cathode material, lithium iron phosphate (neglecting crystal anisotropy and coherency strain). Analytical approximations are also derived for the voltage plateau as a function of the applied current. National Science Foundation (U.S.). Graduate Research Fellowship Program (Grant 1122374) Samsung-MIT Alliance Samsung (Firm) |
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