Level-Set Optimization of Si-Nanowires Constituting New LIB Anodes Considering Electrochemical Diffusion and Large Volume Expansion

Silicon nanowires (NWs) have been attracting attention as an anode material for the high-performance lithium-ion batteries (LIBs) despite its large volume expansion over 400% when charging that causes early material failure or degradation due to high contact stresses between particles. In order to solve such problems, a numerical method is proposed to find the optimum arrangements and dimensions of NWs at an anode. As a result of multi-physical analyses on the cylindrical and spherical silicon particles, it is found that the cylinder type is more suitable. The two dimensional (2D) topology optimization method based on the level-set algorithm, Li-ion transportation, changing Si NW properties with the state of charge, and finite element method is formulated and coded numerically for the first time. After the level-set topology optimization, the optimum radius and arrangement of cylindrical Si NWs at the anode that do not cause excessive contact stresses among NWs without compromising the performance and durability of LIBs. Finally, the detailed finite element analyses are done on the optimum dimensions of NWs to confirm that the stress and strain are within the specified limits.