Characterization of maximally random jammed sphere packings: Voronoi correlation functions

Abstract

We characterize the structure of maximally random jammed (MRJ) sphere packings by computing the Minkowski functionals (volume, surface area, and integrated mean curvature) of their associated Voronoi cells. The probability distribution functions of these functionals of Voronoi cells in MRJ sphere packings are qualitatively similar to those of an equilibrium hard-sphere liquid and partly even to the uncorrelated Poisson point process, implying that such local statistics are relatively structurally insensitive. This is not surprising because the Minkowski functionals of a single Voronoi cell incorporate only local information and are insensitive to global structural information. To improve upon this, we introduce descriptors that incorporate nonlocal information via the correlation functions of the Minkowski functionals of two cells at a given distance as well as certain cell-cell probability density functions. We evaluate these higher-order functions for our MRJ packings as well as equilibrium hard spheres and the Poisson point process. We find strong anticorrelations in the Voronoi volumes for the hyperuniform MRJ packings, consistent with previous findings for other pair correlations [A. Donev et al., Phys. Rev. Lett. 95, 090604 (2005)], indicating that large-scale volume fluctuations are suppressed by accompanying large Voronoi cells with small cells, and vice versa. In contrast to the aforementioned local Voronoi statistics, the correlation functions of the Voronoi cells qualitatively distinguish the structure of MRJ sphere packings (prototypical glasses) from that of the correlated equilibrium hard-sphere liquids. Moreover, while we did not find any perfect icosahedra (the locally densest possible structure in which a central sphere contacts 12 neighbors) in the MRJ packings, a preliminary Voronoi topology analysis indicates the presence of strongly distorted icosahedra.

13 pages, 10 figures

References in corpus (10)

• Analysis of Granular Flow in a Pebble-Bed Nuclear Reactor
• Hypoconstrained Jammed Packings of Nonspherical Hard Particles: Ellipses and Ellipsoids
• A deductive statistical mechanics approach for granular matter
• Robust Algorithm to Generate a Diverse Class of Dense Disordered and Ordered Sphere Packings via Linear Programming
• Suppressed compressibility at large scale in jammed packings of size disperse spheres
• Toward the Jamming Threshold of Sphere Packings: Tunneled Crystals
• Effect of Dimensionality on the Percolation Threshold of Overlapping Nonspherical Hyperparticles
• Non-Universality of Density and Disorder in Jammed Sphere Packings
• Combining tomographic imaging and DEM simulations to investigate the structure of experimental sphere packings
• Local Anisotropy of Fluids using Minkowski Tensors

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• Cuddling Ellipsoids: Densest local structures of uniaxial ellipsoids