Phase-field Simulation of Lithium Ion Diffusion in Solid Electrolyte Interphase

Silicon materials have been recognized as one of the new electrode materials in the next generation of lithium ion batteries (LIBs) with high energy density and large specific capacity. However, there is still a significant limitation to use the silicon based composite electrodes since the fracture occurs as a result of the huge volume change and fast lithium diffusion during the electrochemical lithiation process. A stable solid electrolyte interface (SEI) can help prevent fraction. However, the lithium diffusion inside SEI layer is still not fully understood. In this study, we focus on two dimensions (2-D) lithium diffusion simulation inside SEI layer with considering its morphology evolution. Our previous research (1) has proven that SEI morphology evolution can be regarded as a solification process, and phase field method shows great advantage to deal with the solification problem. The phase field variable  is applied to simulate the SEI morphology evolution without tracking the multiple interfaces directly. The detailed chemistry of SEI species formation reaction has not been considered in the phase field modelling. The simulation assumes that SEI is composed of hydrocarbons, PEO-type oligomers, LiF, Li_xPF_y, and Li_xPF_yO_z products based on the XPS experiments in the literature. We apply different formation contact angles to represent the different surface energy of different SEI specis. We are able to track different material species in SEI layer with defining the properties of each species for lithium diffusion simulation. In this work, a new model will be developed to simulate lithium diffusion during SEI growth and its morphology evolution based on our previous research and the computational method reported Han’s work (2). The concentration field can be regarded as a conserved property during the long-range diffusion. Therefore, the Cahn-Hilliard equations can be applied to formulate the phase transformations and description of diffusion inside the silicon based electrode. The chemical potential can be achieved by driving the total free energy equation. And the flux, which is assumed to be proportional to the gradient of the diffusion potential, can be presented by Fick’s Law. With the combination of the Cahn-Hilliard formulation and Fick’s Law, we are able to predict the lithium diffusion coefficient and lithium concentration distribution inside SEI layer. With the improvement of the current model, it is expected that the understanding on lithium diffusion inside SEI layer could be advanced to more accurately predict the fracture of silicon based composite electrodes during the electrochemical lithiation process. In addition, the developed model could be applied to other interface region problems and it has great potential to be extended to three-dimensions.

1.         P. Guan, X. Lin and L. Liu, ECS Transactions, 61, 29 (2014).

2.         B. C. Han, A. Van der Ven, D. Morgan and G. Ceder, Electrochimica Acta, 49, 4691 (2004).