Common Packing Patterns for Jammed Particles of Different Power Size Distributions

We introduce a model for particles that are extremely polydisperse in size compared to monodisperse and bidisperse systems. In two dimensions (2D), size polydispersity inhibits crystallization and increases packing fraction at jamming points. However, no packing pattern common to diverse polydisperse particles has been reported. We focused on polydisperse particles with a power size distribution $r^{-a}$ as a ubiquitous system that can be expected to be scale-invariant. We experimentally and numerically constructed 2D random packing for various polydisperse particles with different size exponents, $a$. Analysis of the packing pattern revealed a common contact number distribution for $a<3$ and a higher jamming point in $2<a<3$ than monodisperse systems. These findings demonstrate that the ambiguity of the characteristic length provides the common properties that leads to a novel classification scheme for polydisperse particles.