Intercalation dynamics in lithium-ion batteries

摘要: 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 Cahn-Hilliard equation coupled to reaction rate laws as boundary conditions handle transfer ions between electrolyte. In this thesis, I carefully derive second set conditions—necessary close original PDE system—via variational analysis free energy functional; include thermodynamically-consistent treatment rates; develop semi-discrete finite volume method numerical simulations; careful asymptotic dynamical regimes found different limits governing equations. Further, will present several findings relevant batteries: Defect Interactions: When applied strongly phase-separating, highly anisotropic materials such LiFePO4, predicts phase-transformation waves lithiated unlithiated portions crystal. This work extends wave dynamics, describes mechanism current capacity fade through interactions these with defects particle. Size-Dependent Spinodal Miscibility Gaps: demonstrates that powerful enough predict spinodal miscibility gaps shrink particle size decreases. also shown reactions are another general suppression phase separation. Multi-Particle presents results parallel simulations nearby crystals linked together via common parameters conditions. The demonstrate so-called “mosaic effect”: particles tend fill one at time, so much being filled actually draws lithium out other ones. Moreover, it smaller separate first, phenomenon seen experiments but difficult explain any theoretical model. Thesis Supervisor: Martin Z. Title: Associate Professor Chemical Engineering Mathematics