Fluctuations, structure factor and polytetrahedra in random packings of sticky hard spheres

TL;DR

This study numerically investigates the local fluctuations, structure factors, and polytetrahedral arrangements in large, randomly built sphere packings across a range of packing fractions, revealing growth of polytetrahedra and structural heterogeneity.

Contribution

The paper introduces fast geometrical algorithms for large-scale sphere packing simulations and provides detailed analysis of fluctuations, structure factors, and polytetrahedral structures in random packings.

Findings

Fluctuations follow a power law with packing fraction.

Voronoi cell volume FWHM varies regularly with packing fraction.

Polytetrahedra grow larger as packing fraction decreases, affecting structure factors.

Abstract

Sequentially-built random sphere-packings have been numerically studied in the packing fraction interval $0.329 < \gamma < 0.586$. For that purpose fast running geometrical algorithms have been designed in order to build about 300 aggregates, containing $10^6$ spheres each one, which allowed a careful study of the local fluctuations and an improved accuracy in the calculations of the pair distribution $P(r)$ and structure factors $S(Q)$ of the aggregates. Among various parameters (Voronoi tessellation, contact coordination number distribution,...), fluctuations were quantitatively evaluated by the direct evaluation of the fluctuations of the local sphere number density, which appears to follow a power law. The FWHM of the Voronoi cells volume shows a regular variation over the whole packing fraction range. Dirac peaks appear on the pair correlation function as the packing fraction of the aggregates decreases, indicating the growth of larger and larger polytetrahedra, which manifest in two ways on the structure factor, at low and large $Q$values. These low PF aggregates have a composite structure made of regular polytetrahedra embedded in a more disordered matrix. Incidentally, the irregularity index of the building tetrahedron appears as a better parameter than the packing fraction to describe various features of the aggregates structure.