A heuristic approach for the densest packing fraction of hard-sphere mixtures

TL;DR

This paper presents an extended heuristic method to estimate the densest packing fractions of hard-sphere mixtures using a simple formula based on monocomponent close-packing and a single parameter, showing good agreement with recent data.

Contribution

An extension of a previous approach providing an approximate formula for the densest packing of hard-sphere mixtures based on monocomponent close-packing and a single parameter.

Findings

Reasonable agreement with recent binary and ternary system data.

The formula effectively captures the dependence on size ratios and number of spheres.

Provides a practical tool for estimating densest packings in mixtures.

Abstract

In a previous work, a simple approach to derive the jamming packing fraction of a hard-sphere mixture from the knowledge of the random close-packing fraction of the monocomponent system was proposed. Now, an extension of that approach is applied to provide an approximate formula for the densest packing fraction of a given hard-sphere mixture in terms of the fcc close-packing fraction of a monocomponent hard-sphere system and of a single parameter encapsulating the dependence on the size ratios and the number of spheres in the unit cell. Comparison with recent results for such densest packing fraction of binary and ternary systems is performed and reasonable agreement is obtained.