Modeling diffusion-induced stress in nanowire electrode structures

Abstract

There is an intense, worldwide effort to develop durable lithium ion batteries with high energy and power densities for a wide range of applications, including electric and hybrid electric vehicles. One of the critical challenges in advancing lithium ion battery technologies is fracture and decrepitation of the electrodes as a result of lithium diffusion during charging and discharging operations. When lithium is inserted in either the positive or negative electrode, a large volume change on the order of a few to several hundred percent, can occur. Diffusion-induced stresses (DISs) can therefore cause the nucleation and growth of cracks, leading to mechanical degradation of the active electrode materials. Our work is aimed at developing a mathematical model relating surface energy with diffusion-induced stresses in nanowire electrodes. With decreasing size of the electrode, the ratio of surface area to volume increases. Thus, surface energy and surface stress can play an important role in mitigating DISs in nanostructured electrodes. In this work, we establish relationships between the surface energy, surface stress, and the magnitude of DISs in nanowires. We find that DISs, especially the tensile stresses, can decrease significantly due to the surface effects. Our model also establishes a relationship between stress and the nanowire radius. We show that, with decreasing size, the electrode material will be less prone to mechanical degradation, leading to an increase in the life of lithium ion batteries, provided other phenomena are unaffected by increased surface area (e.g., chemical degradation reactions). Also we show that, in the case of nanostructures, surface strain energy is significant in magnitude comparing with bulk strain energy. A mathematical tool to calculate total strain energy is developed that can be used to compare strain energy with the fracture energy of that material in electrode system.