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Ferguson Thesis

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Ferguson thesis about modeling of Li-ion battery in diverse computing programs.
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  Lithium-ion Battery Modeling UsingNon-equilibrium Thermodynamics by Todd R. Ferguson B.S., Rensselaer Polytechnic Institute (2008)Submitted to the Department of Chemical Engineeringin partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemical Engineeringat theMASSACHUSETTS INSTITUTE OF TECHNOLOGYFebruary 2014c   Massachusetts Institute of Technology 2014. All rights reserved.Author ..............................................................Department of Chemical EngineeringNovember 15, 2013Certified by..........................................................Martin Z. BazantProfessorThesis SupervisorAccepted by.........................................................Patrick S. DoyleGraduate Officer  2  Lithium-ion Battery Modeling Using Non-equilibriumThermodynamics byTodd R. Ferguson Submitted to the Department of Chemical Engineeringon November 15, 2013, in partial fulfillment of therequirements for the degree of Doctor of Philosophy in Chemical Engineering Abstract The focus of this thesis work is the application of non-equilibrium thermodynamicsin lithium-ion battery modeling. As the demand for higher power and longer lastingbatteries increases, the search for materials suitable for this task continues. Tradi-tional battery modeling uses dilute solution kinetics and a fit form of the open circuitpotential to model the discharge. This work expands on this srcinal set of equationsto include concentrated solution kinetics as well as thermodynamics-based modelingof the open circuit potential. This modification is advantageous because it does notrequire the cell to be built in order to be modeled. Additionally, this modification alsoallows phase separating materials to be modeled directly using phase field models.This is especially useful for materials such as lithium iron phosphate and graphite,which are currently modeled using a fit open circuit potential and an artificial phaseboundary (in the case of lithium iron phosphate).This thesis work begins with a derivation of concentrated solution theory, begin-ning with a general reaction rate framework and transition state theory. This deriva-tion includes an overview of the thermodynamic definitions used in this thesis. Afterthe derivation, transport and conduction in porous media are considered. Effectivetransport properties for porous media are presented using various applicable models.Combining concentrated solution theory, mass conservation, charge conservation, andeffective porous media properties, the modified porous electrode theory equations arederived. This framework includes equations to model mass and charge conservationin the electrolyte, mass conservation in the solid intercalation particles, and electronconservation in the conducting matrix. These mass and charge conservation equa-tions are coupled to self-consistent models of the charge transfer reaction and theNernst potential. The Nernst potential is formulated using the same thermodynamicexpressions used in the mass conservation equation for the intercalation particles.The charge transfer reaction is also formulated using the same thermodynamic ex-pressions, and is presented in a form similar to the Butler-Volmer equation, whichdetermines the reaction rate based on the local overpotential. This self-consistent setof equations allows both homogeneous and phase separating intercalation materials  to be modeled.After the derivation of the set of equations, the numerical methods used to solvethe equations in this work are briefly presented, including the finite volume methodand solution methods for differential algebraic equations. Then, example simulationsat constant current are provided for homogeneous and phase separating materials todemonstrate the effect of changing the solid diffusivity and discharge rate on the cellvoltage. Other effects, such as coherency strain, are also presented to demonstratetheir effect on the behavior of particles inside the cell (e.g. suppression of phase sepa-ration). After the example simulations, specific simulations for two phase separatingmaterials are presented and compared to experiment. These simulations include slowdischarge of a lithium iron phosphate cell at constant current, and electrolyte-limiteddischarge of a graphite cell at constant potential. These two simulations are shownto agree very well with experimental data. In the last part of this thesis, the mostrecent work is presented, which is based on modeling lithium iron phosphate particlesincluding coherency strain and surface wetting. These results are qualitatively com-pared with experimental data. Finally, future work in this area is considered, alongwith a summary of the thesis.Thesis Supervisor: Martin Z. BazantTitle: Professor
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