Geometry and charging rate sensitively modulate surface stress-induced stress relaxation within cylindrical silicon anode particles in lithium-ion batteries

Surface effects, in general, and surface stresses, in particular, become increasingly important while venturing into the realm of nanoscale particles. A fundamental framework is developed, as a generalization of a small-deformation surface mechanics theory, to derive the surface stresses accompanying the huge volumetric changes of a cylindrical silicon nanoparticle in a lithium-ion battery under charging conditions. When embedded within a finite deformation, chemo-mechanical model for silicon anode particles, this framework illustrates how surface stresses render a relaxing effect on the diffusion-induced stresses. Importantly, the extent of this relaxation is sensitively modulated by the initial size of the anode particles and lithium influx rate. Surface stress-induced stress relaxation increases with increase in the level of influx rate and with decrease in the radius of curvature of the Si particle. In addition to this, the surface stresses also regulate the extent of plastic deformation of the particles. It is demonstrated that these effects further depend upon additional geometric considerations of whether the cylindrical particle is free to grow in the axial direction or is axially constrained. It is expected that this framework, targetted at nanoscale cylindrical particles, will provide a platform to carry out future investigations into various issues that are critically important for battery design.