A geometric probabilistic approach to random packing of hard disks in a plane

Article Chemistry, Physical

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

Carmine Anzivino et al.

Summary: We investigate the density dependence of the kissing number for numerically generated jammed states by analogizing the crowding in fluid and jammed phases of hard spheres. We extend this analogy to mixtures of hard spheres in three dimensions and estimate the random close packing volume fraction, phi(RCP), for different size polydispersities. Our predictions and simulations on binary systems agree with previous studies and experimental results. We find that phi(RCP) increases with the relative standard deviation of size distributions and saturates below 1. A closed-form expression for phi(RCP) captures a distribution-independent regime for small skewness of size distributions.

JOURNAL OF CHEMICAL PHYSICS (2023)

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Article Physics, Multidisciplinary

Explicit Analytical Solution for Random Close Packing in d=2 and d=3

Alessio Zaccone

Summary: We present an analytical derivation of the volume fractions for random close packing in both 3D and 2D, and compare the derived values with those reported in the literature using different methods. The derivation suggests that random close packing corresponds to the onset of mechanical rigidity and is determined by the coordination number. The article also points out the possibility of achieving volume fractions above the maximum random jammed state by creating some order, with the coordination number at the fcc limit acting as a boundary condition.

PHYSICAL REVIEW LETTERS (2022)

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Correction Physics, Multidisciplinary