June 9, 2006
We present a reduced-dimension, ballistic deposition, Monte Carlo particle packing algorithm and discuss its application to the analysis of the microstructure of hard-sphere systems with broad particle size distributions. We extend our earlier approach (the ``central string'' algorithm) to a reduced-dimension, quasi-3D approach. Our results for monomodal hard-sphere packs exhibit a calculated packing fraction that is slightly less than the generally accepted value for a maximally random jammed state. The pair distribution functions obtained from simulations of composite structures with large particle size differences demonstrate that the algorithm provides information heretofore not attainable with existing simulation methods, and yields detailed understanding of the microstructure of these composite systems.
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March 25, 2000
Despite its long history, there are many fundamental issues concerning random packings of spheres that remain elusive, including a precise definition of random close packing (RCP). We argue that the current picture of RCP cannot be made mathematically precise and support this conclusion via a molecular dynamics study of hard spheres using the Lubachevsky-Stillinger compression algorithm. We suggest that this impasse can be broken by introducing the new concept of a maximally ...
December 3, 2016
In this paper, we perform molecular dynamics (MD) simulations to study the two-dimensional packing process of both monosized and random size particles with radii ranging from $1.0 \, \mu m$ to $7.0 \, \mu m$. The system was allowed to settle under gravity towards the bottom of a $300 \, \mu m \times 500 \, \mu m$ rectangular box. The initial positions as well as the radii of five thousand fine particles were defined along the box by using a random number generator. Both the t...
We apply a recent one-dimensional algorithm for predicting random close packing fractions of polydisperse hard spheres [Farr and Groot, J. Chem. Phys. 133, 244104 (2009)] to the case of lognormal distributions of sphere sizes and mixtures of such populations. We show that the results compare well to two much slower algorithms for directly simulating spheres in three dimensions, and show that the algorithm is fast enough to tackle inverse problems in particle packing: designin...
February 13, 2024
Understanding the way disordered particle packings transition between jammed (rigid) and unjammed (fluid) states is of both great practical importance and strong fundamental interest. The values of critical packing fraction (and other state variables) at the jamming transition are protocol dependent. Here, we demonstrate that this variability can be systematically traced to structural measures of packing, as well as to energy measures inside the jamming regime. A novel genera...
February 24, 2014
Random packings of objects of a particular shape are ubiquitous in science and engineering. However, such jammed matter states have eluded any systematic theoretical treatment due to the strong positional and orientational correlations involved. In recent years progress on a fundamental description of jammed matter could be made by starting from a constant volume ensemble in the spirit of conventional statistical mechanics. Recent work has shown that this approach, first intr...
May 4, 2022
We present a theoretical prediction on random close packing factor \phi_RCP^b of binary granular packings based on the hard-sphere fluid theory. An unexplored regime is unravelled, where the packing fraction \phi_RCP^b is smaller than that of the mono-sized one \phi_RCP^m, i.e., the so-called loose jamming state. This is against our common perception that binary packings should always reach a denser packing than mono-sized packings at the jamming state. Numerical evidence fur...
March 24, 2009
We study jammed configurations of hard spheres as a function of compression speed using an event-driven molecular dynamics algorithm. We find that during the compression, the pressure follows closely the metastable liquid branch until the system gets arrested into a glass state as the relaxation time exceeds the compression speed. Further compression yields a jammed configuration that can be regarded as the infinite pressure configuration of that glass state. Consequently, we...
July 31, 2012
We consider a composite medium, which consists of a homogeneous matrix containing a statistically homogeneous set of multimodal spherical inclusions. This model is used to represent the morphology of heterogeneous solid propellants (HSP) that are widely used in the rocket industry. The Lubachevsky-Stillinger algorithm is used to generate morphological models of HSP with large polydisperse packs of spherical inclusions. We modify the algorithm by proposing a random shaking pro...
August 10, 2010
It is presented a numerical study on the unjamming packing fraction of bi- and polydisperse disk packings, which are generated through compression of a monodisperse crystal. In bidisperse systems, a fraction f_+ = 40% up to 80% of the total number of particles have their radii increased by \Delta R, while the rest has their radii decreased by the same amount. Polydisperse packings are prepared by changing all particle radii according to a uniform distribution in the range [-\...
January 6, 2011
We show for the first time that collectively jammed disordered packings of three-dimensional monodisperse frictionless hard spheres can be produced and tuned using a novel numerical protocol with packing density $\phi$ as low as 0.6. This is well below the value of 0.64 associated with the maximally random jammed state and entirely unrelated to the ill-defined ``random loose packing'' state density. Specifically, collectively jammed packings are generated with a very narrow d...