The random close packing (RCP) fraction of hard spheres in 3D is approximately 64% for monodisperse spheres. However, real systems — from granular materials to colloidal suspensions to pharmaceutical powders — are always polydisperse. This project studied how the shape of the particle size distribution affects the achievable packing fraction.
Using the RCP algorithm developed at Emory and extended at UCSB, we performed large-scale packing simulations across a wide range of particle size distributions (uniform, log-normal, Gaussian, and bidisperse). The results revealed systematic trends: broader distributions consistently achieve higher packing fractions, and the packing fraction depends primarily on the distribution width, with only a weak dependence on its precise shape.
Quantitative relationships between the size-distribution parameters (mean, variance, skewness) and the resulting packing fraction were established. These scaling laws are useful for engineering dense packings in materials processing, battery electrode design, and concrete formulation.