Phase Separation Dynamics in Isotropic Ion-Intercalation Particles
Name
Zeng-2014-Phase separation dyn.pdf
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2.56 MB
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Adobe PDF
Checksum (MD5)
09f30d57a24f132eb3693c6e9971b749
Author(s)
Zeng, Yi
Bazant, Martin Z.
Date Issued
July 2014
Journal
SIAM Journal on Applied Mathematics
Publisher
Society for Industrial and Applied Mathematics
Citation
Zeng, Yi, and Martin Z. Bazant. “Phase Separation Dynamics in Isotropic Ion-Intercalation Particles.” SIAM Journal on Applied Mathematics 74, no. 4 (January 2014): 980–1004. © 2014, Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1137/130937548
