Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowding

Abstract

We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of hard spheres in $d=3$ dimensions, and thus obtain an estimate of the random close packing (RCP) volume fraction, ${\varphi }_{\text{RCP}}$, as a function of size polydispersity. We first consider mixtures of particle sizes with discrete distributions. For binary systems, we show agreement between our predictions and simulations, using both our own and results reported in previous works, as well as agreement with recent experiments from the literature. We then apply our approach to systems with continuous polydispersity, using three different particle size distributions, namely the log-normal, Gamma, and truncated power-law distributions. In all cases, we observe agreement between our theoretical findings and numerical results up to rather large polydispersities for all particle size distributions, when using as reference our own simulations and results from the literature. In particular, we find ${\varphi }_{\text{RCP}}$ to increase monotonically with the relative standard deviation, $s_{\sigma }$, of the distribution, and to saturate at a value that always remains below 1. A perturbative expansion yields a closed-form expression for ${\varphi }_{\text{RCP}}$ that quantitatively captures a distribution-independent regime for $s_{\sigma }<0.5$. Beyond that regime, we show that the gradual loss in agreement is tied to the growth of the skewness of size distributions.

References in corpus (40)

• 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
• Jamming of Soft Particles: Geometry, Mechanics, Scaling and Isostaticity
• Hyperuniform States of Matter
• Models and algorithms for the next generation of glass transition studies
• Pair Correlation Function Characteristics of Nearly Jammed Disordered and Ordered Hard-Sphere Packings
• How to Simulate Billiards and Similar Systems
• Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
• Approximate analytical description of the nonaffine response of amorphous solids
• Close packing density of polydisperse hard spheres
• Hard Spheres: Crystallization and Glass Formation
• The glass transition of dense fluids of hard and compressible spheres
• Crystallization of hard-sphere glasses
• Why is Random Close Packing Reproducible?
• Equilibrium sampling of hard spheres up to the jamming density and beyond
• Exact theory of dense amorphous hard spheres in high dimension. III. The full RSB solution
• Jamming versus Glass Transitions
• A Landscape Analysis of Constraint Satisfaction Problems
• Basic Understanding of Condensed Phases of Matter via Packing Models
• A theory of amorphous packings of binary mixtures of hard spheres
• The ideal glass transition of Hard Spheres
• Random close packing of polydisperse hard spheres
• Equation of state of a multicomponent d-dimensional hard-sphere fluid
• Explicit Analytical Solution for Random Close Packing in d=2 and d=3
• Effect of controlled corrugation on capillary condensation of colloid-polymer mixtures
• Crystallization Mechanism of Hard Sphere Glasses
• Exactly Solvable Disordered Sphere-Packing Model in Arbitrary-Dimension Euclidean Spaces
• Exploring the jamming transition over a wide range of critical densities
• Toward the Jamming Threshold of Sphere Packings: Tunneled Crystals
• Two diverging length scales in the structure of jammed packings
• Non-Universality of Density and Disorder in Jammed Sphere Packings
• Additional transition line in jammed asymmetric bidisperse granular packings
• Connecting packing efficiency of binary hard sphere systems to their intermediate range structure
• Random Close Packing and the Hard Sphere Percus-Yevick Theory
• Phase transition in the binary mixture of jammed particles with large size dispersity
• Contact values for disparate-size hard-sphere mixtures
• Determining Pair Interactions from Structural Correlations
• A heuristic approach for the densest packing fraction of hard-sphere mixtures
• An unexplored valley of binary packing: The loose jamming state

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