Sub-Jamming Transition in Binary Sphere Mixtures

Abstract

We study the influence of particle size asymmetry on structural evolution of randomly jammed binary sphere mixtures with varying large-sphere/small-sphere composition. Simulations of jammed packings are used to assess the transition from large-sphere dominant to small-sphere dominant mixtures. For weakly asymmetric particle sizes, packing properties evolve smoothly, but not monotonically, with increasing small sphere composition, $f$. Our simulations reveal that at high values of ratio $\alpha$ of large to small sphere radii, ($\alpha \ge {\alpha }_c\approx 5.75$) evolution of structural properties such as packing density, fraction of jammed spheres and contact statistics with $f$ exhibit features that suggest a sharp transition, either through discontinuities in structural measures or their derivatives. We argue that this behavior is related to the singular, composition dependence of close-packing fraction predicted in infinite aspect ratio mixtures $\alpha \to \infty$ by the Furnas model, but occurring for finite values range of $\alpha$ above a critical value, ${\alpha }_c\approx 5.75$. The existence of a sharp transition from small- to large-$f$ values for $\alpha \ge {\alpha }_c$ can be attributed to the existence of a {\it sub-jamming transition} of small spheres in the interstices of jammed large spheres along the line of compositions $f_{sub}(\alpha )$. We argue that the critical value of finite size asymmetry ${\alpha }_c\simeq 5.75$ is consistent with the geometric criterion for the transmission of small sphere contacts between neighboring tetrahedrally close packed interstices of large spheres, facilitating a cooperative sub-jamming transition of small spheres confined within the disjoint volumes.

12 pages, 7 figures

References in corpus (17)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Is Random Close Packing of Spheres Well Defined?
• Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
• Mean field theory of hard sphere glasses and jamming
• Pair Correlation Function Characteristics of Nearly Jammed Disordered and Ordered Hard-Sphere Packings
• Close packing density of polydisperse hard spheres
• Jamming transitions in amorphous packings of frictionless spheres occur over a continuous range of volume fractions
• Why is Random Close Packing Reproducible?
• Finite-Size Scaling at the Jamming Transition
• A theory of amorphous packings of binary mixtures of hard spheres
• The ideal glass transition of Hard Spheres
• Robust Algorithm to Generate a Diverse Class of Dense Disordered and Ordered Sphere Packings via Linear Programming
• Phase diagram and structural diversity of the densest binary sphere packings
• Entropy of jammed matter
• Percolation of disordered jammed sphere packings
• A simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres
• Geometrical Frustration and Static Correlations in Hard-Sphere Glass Formers

Cited by in corpus (10)

• Jamming of Bidisperse Frictional Spheres
• Large-scale frictionless jamming with power-law particle size distributions
• Additional transition line in jammed asymmetric bidisperse granular packings
• Segregation forces in dense granular flows: Closing the gap from single intruders to mixtures
• Bulk Modulus along Jamming Transition Lines of Bidisperse Granular Packings
• Phase transition in the binary mixture of jammed particles with large size dispersity
• Structural transitions in jammed asymmetric bidisperse granular packings
• Additional jamming transition in 2D bidisperse granular packings
• Molecular Dynamics Simulations of Binary Sphere Mixtures
• Predicting random close packing of binary hard-disk mixtures via third-virial-based parameters