Random-close packing limits for monodisperse and polydisperse hard spheres

Area of Science:

• Physics
• Materials Science
• Computational Science

Background:

• Understanding the densest possible packing of spheres is fundamental in condensed matter physics and materials science.
• Jammed configurations represent the densest states achievable without macroscopic rearrangements, relevant to granular materials and glasses.
• Previous research has explored random close packing (RCP) limits, but a comprehensive understanding of characteristic densities remains elusive.

Purpose of the Study:

• To computationally investigate and characterize the distribution of densities for closest jammed configurations of frictionless hard spheres.
• To introduce and utilize a novel algorithm for generating closest jammed configurations and determining their densities.
• To identify and define characteristic densities, including lowest typical (LT), random-close packing (RCP), and glass close packing (GCP) limits, for both monodisperse and polydisperse sphere packings.

Main Methods:

• Development and application of a computational algorithm to generate closest jammed configurations.
• Simulation of 10^4 frictionless hard spheres using the Lubachevsky-Stillinger and force-biased algorithms.
• Analysis of density distributions for monodisperse packings under varying compression rates.
• Determination of characteristic densities for polydisperse packings with log-normal sphere radii distributions.

Main Results:

• Monodisperse packings generated at high compression rates exhibit closest jamming densities in a narrow range (φ = 0.634–0.636 to φ≈ 0.64).
• Low compression rates for monodisperse packings lead to densities converging around φ≈ 0.65, with rapid increases indicating crystallization.
• Identified three characteristic densities: φLT (0.634–0.636), φRCP (≈ 0.64), and φGCP (≈ 0.65), and determined these for polydisperse packings.

Conclusions:

• The study establishes distinct characteristic densities (φLT, φRCP, φGCP) that define the limits of jammed configurations for hard sphere systems.
• The findings provide a quantitative framework for understanding the transition from random close packing to glass close packing.
• The developed methods and identified densities offer valuable insights into the structural properties of disordered materials.