Predicting random close packing of binary hard-disk mixtures via third-virial-based parameters

Area of Science:

• Statistical Mechanics
• Materials Science
• Computational Physics

Background:

• Random close packing (RCP) is a fundamental concept in condensed matter physics, describing the densest possible disordered packing of particles.
• Estimating the RCP fraction for mixtures, especially binary hard-disk systems, is complex due to multi-particle interactions and size variations.

Purpose of the Study:

• To propose a simple and accurate method for estimating the random close packing (RCP) fraction of binary hard-disk mixtures.
• To demonstrate the near-universality of RCP in these systems and provide a more consistent prediction model.

Main Methods:

• Introduction of a novel parameter derived from the reduced third virial coefficient to account for three-body correlations and excluded-area constraints.
• Analysis of simulation data for binary hard-disk mixtures across a wide range of size ratios and compositions.
• Comparison of the proposed method's predictions with existing models (Brouwers and Zaccone).

Main Results:

• The RCP fraction exhibits a nearly linear dependence on the introduced parameter.
• A near-universal collapse of simulation data is observed when plotting RCP fraction against this parameter.
• The proposed approach yields more accurate and consistent predictions compared to previous models.

Conclusions:

• The developed method offers a simple yet accurate way to estimate RCP fractions for binary hard-disk mixtures.
• The findings highlight a near-universal behavior in RCP for these systems, linked to excluded-volume effects and correlations.
• The method's extensibility to polydisperse systems and consistency with equation-of-state formulations provide a robust framework for understanding particle packing.