A Phase Field Model of Solid Electrolyte Interface Formation in Lithium-ion Batteries
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A Phase Field Model of Solid Electrolyte Interface Formation in Lithium-ion Batteries Jie Deng1, Gregory J. Wagner1 and Richard P. Muller2 1 Sandia National Laboratories, Livermore, CA 94550, USA 2 Sandia National Laboratories, Albuquerque, NM 87185, USA ABSTRACT A phase field model is developed to investigate the formation of a solid electrolyte interface layer on the anode surface in lithium-ion batteries. Numerical results show that the growth of solid electrolyte interface exhibits power-law scaling with respect to time, and the growth rate depends on various factors such as temperature, diffusivity of electrons, and rates of electrochemical reactions. INTRODUCTION The solid electrolyte interface (SEI) layer formed on the anode surface plays an important role in lithium ion battery life and performance [1]. Many mathematical models have been developed to describe the growth of SEI layer [2-6]. In these models, various rate-limiting processes for SEI growth such as electronic conductivity [3] and ionic transport [4] are proposed, and the detailed SEI chemistry is also incorporated [5, 6]. While previous models show the capacity for predicting SEI growth, they generally ignore the double-layer structure or charge separation at the SEI/electrolyte interface. In addition, since the position of the SEI/electrolyte interface needs to be tracked explicitly all the time, it becomes inconvenient to capture the microstructure evolution of SEI in two or three dimensional space. Here we propose a phase field model that treats SEI growth as a phase transformation process. During that process, electrolyte is transformed to SEI due to the electrochemical reactions at the SEI/electrolyte interface, and the motion of the SEI/electrolyte interface characterizes the SEI growth. The proposed model captures the charge separation at the SEI/electrolyte interface during SEI growth, and moreover, due to its diffuse interface nature, it is able to handle complex morphology of SEI in higher dimensional space. In this paper, the model is applied to reveal the growth law of SEI and its dependence on electronic diffusivity, electrochemical reaction rate and temperature. The microstructure evolution of the SEI will be studied in a future publication. PHASE FIELD MODEL The phase field method has been applied to model various electrochemical processes such as electrodeposition and electrochemical impedance spectroscopy [7-11]. The model in this study extends the work of Guyer et. al. [7, 8] by accounting for the electrochemical reactions at the SEI/electrolyte interface that drive SEI growth. In this model, we consider two bulk phases: SEI (α phase) and electrolyte (β phase). The interface between these two bulk phases is diffuse such that the material properties such as concentration of species or electric potential change smoothly across the interface. One phase field variable η is used to represent the state of the phase such that η = 1 in SEI and η = 0 in electrolyte. At the SEI/electrolyte interface, η changes smoothly from 1 to 0. It is
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