Intercalation dynamics in lithium-ion batteries

A new continuum model has been proposed by Singh, Ceder, and Bazant for the ion intercalation dynamics in a single crystal of rechargeable-battery electrode materials. It is based on the Cahn-Hilliard equation coupled to reaction rate laws as boundary conditions to handle the transfer of ions between the crystal and the electrolyte. In this thesis, I carefully derive a second set of boundary conditions--necessary to close the original PDE system--via a variational analysis of the free energy functional; I include a thermodynamically-consistent treatment of the reaction rates; I develop a semi-discrete finite volume method for numerical simulations; and I include a careful asymptotic treatment of the dynamical regimes found in different limits of the governing equations. Further, I will present several new findings relevant to batteries: Defect Interactions: When applied to strongly phase-separating, highly anisotropic materials such as LiFePO4, this model predicts phase-transformation waves between the lithiated and unlithiated portions of a crystal. This work extends the analysis of the wave dynamics, and describes a new mechanism for current capacity fade through the interactions of these waves with defects in the particle. Size-Dependent Spinodal and Miscibility Gaps: This work demonstrates that the model is powerful enough to predict that the spinodal and miscibility gaps shrink as the particle size decreases. It is also shown that boundary reactions are another general mechanism for the suppression of phase separation.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2009

Author dc:creator

• Burch, Damian

Advisor dc:contributor.advisor

• Martin Z. Bazant.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/54233

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/54233