Modeling and simulation of the non-equilibrium process for a continuous solid solution system in lithium-ion batteries

Abstract

The capacity loss and cycling aging of lithium-ion batteries at high (dis)charging rate (C-rate) hinders the development of emerging technologies. To improve the performance of Li-ion batteries, it is important to understand the coupling effect of the mechanical behaviors and the electrochemical response of electrodes, as the capacity loss and cycling aging are related to the mechanics of electrodes during (dis)charging. Many studies have formulated the distribution of stress, strain and lithium-ion fraction of electrodes during lithiation/delithiation. However, few of them reported a self-consistent formulation that contains mechanical-diffusional-electrochemical coupling effects, solid viscosity, and diffusion-induced creep for an electrode with large deformation under non-equilibrium process. This paper considers the electrode of a Li-ion battery as a solid solution system. Based on continuum mechanics, non-equilibrium thermodynamics and variational theory, we develop a generalized theory to describe the variations of stress distribution, electrode material deformation and lithium-ion fractions of the solid solution system over a non-equilibrium process. The finite deformation, mass transfer, phase transformation, chemical reaction and electrical potential of the system are coupled with each other in a fully self-consistent formulation. We apply the developed theory to numerically simulate a Sn anode particle using the finite difference method. Our results compare the influences of different C-rates on the non-equilibrium process of the anode particle. Higher C-rate corresponds to stronger dissipation effects including faster plastic deformation, larger viscous stress, more polarization in the electrical potential, longer relaxation time and less electrical energy. With the formulation and simulation of the non-equilibrium process, this study refines our understanding of the mechanical-diffusional-electrochemical coupling effect in Li-ion batteries with high C-rate.