Analytical solutions and numerical simulations of diffusion-induced stresses and concentration distributions in porous electrodes with particles of different size and shape

Analytical solutions of exact lithium-ion (Li-ion) concentration distributions and diffusion-induced stresses (DISs) within elliptical and spherical particles are obtained. A two-dimensional scanning electron microscopy image-dependent model of porous electrodes that accounts for the diffusion, DIS, and the size and shape polydispersity of electrode particles is developed. The effects of the size and shape polydispersity on concentration profiles, DIS evolution, and mechanical failure mechanisms are numerically discussed. Simulations show that small particles experienced less DIS than larger particles, primarily because of their reduced strain mismatch. In elliptical electrode particles, simple cracks appear at the endpoints of the major axis, while more complicated and severe cracks appear at the endpoints of the minor axis. Small particles with a spherical geometry are most favorable for alleviating DIS. Thus, the microscopic state of charge (SOC) values and mass fractions of differently sized and shaped particles should be considered simultaneously when determining the optimal macroscopic SOC of a porous electrode.