Non-universal Voronoi cell shapes in amorphous ellipsoid packings

TL;DR

This study investigates local structural metrics in jammed packings of oblate ellipsoids, revealing universal behavior in local packing fractions but significant differences in cell shape compared to spheres, impacting understanding of jamming.

Contribution

It demonstrates that Voronoi cell shape in ellipsoid packings varies with density and aspect ratio, challenging the universality observed in spherical packings.

Findings

Voronoi cell shape differs significantly between sphere and ellipsoid packings.

The probability distribution of local packing fractions scales similarly across aspect ratios.

Cell shape anisotropy reveals non-universality in ellipsoid packings.

Abstract

In particulate systems with short-range interactions, such as granular matter or simple fluids, local structure plays a pivotal role in determining the macroscopic physical properties. Here, we analyse local structure metrics derived from the Voronoi diagram of configurations of oblate ellipsoids, for various aspect ratios $\alpha$ and global volume fractions $\phi_g$. We focus on jammed static configurations of frictional ellipsoids, obtained by tomographic imaging and by discrete element method simulations. In particular, we consider the local packing fraction $\phi_l$, defined as the particle's volume divided by its Voronoi cell volume. We find that the probability $P(\phi_l)$ for a Voronoi cell to have a given local packing fraction shows the same scaling behaviour as function of $\phi_g$ as observed for random sphere packs. Surprisingly, this scaling behaviour is further found to be independent of the particle aspect ratio. By contrast, the typical Voronoi cell shape, quantified by the Minkowski tensor anisotropy index $\beta=\beta_0^{2,0}$, points towards a significant difference between random packings of spheres and those of oblate ellipsoids. While the average cell shape $\beta$ of all cells with a given value of $\phi_l$ is very similar in dense and loose jammed sphere packings, the structure of dense and loose ellipsoid packings differs substantially such that this does not hold true. This non-universality has implications for our understanding of jamming of aspherical particles.