Intercalation dynamics in lithium-ion batteries

Abstract

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.

(cont.) Multi-Particle Interactions: This work presents the results of parallel simulations of several nearby crystals linked together via common parameters in the boundary conditions. The results demonstrate the so-called "mosaic effect": the particles tend to fill one at a time, so much so that the particle being filled actually draws lithium out of the other ones. Moreover, it is shown that the smaller particles tend to phase separate first, a phenomenon seen in experiments but difficult to explain with any other theoretical model.