Abstract
We computer-generated monodisperse and polydisperse frictionless hard-sphere packings of 10(4) particles with log-normal particle diameter distributions in a wide range of packing densities φ (for monodisperse packings φ = 0.46-0.72). We equilibrated these packings and searched for their inherent structures, which for hard spheres we refer to as closest jammed configurations. We found that the closest jamming densities φ(J) for equilibrated packings with initial densities φ ≤ 0.52 are located near the random close packing limit φ(RCP); the available phase space is dominated by basins of attraction that we associate with liquid. φ(RCP) depends on the polydispersity and is ∼ 0.64 for monodisperse packings. For φ > 0.52, φ(J) increases with φ; the available phase space is dominated by basins of attraction that we associate with glass. When φ reaches the ideal glass transition density φ(g), φ(J) reaches the ideal glass density (the glass close packing limit) φ(GCP), so that the available phase space is dominated at φ(g) by the basin of attraction of the ideal glass. For packings with sphere diameter standard deviation σ = 0.1, φ(GCP) ≈ 0.655 and φ(g) ≈ 0.59. For monodisperse and slightly polydisperse packings, crystallization is superimposed on these processes: it starts at the melting transition density φ(m) and ends at the crystallization offset density φ(off). For monodisperse packings, φ(m) ≈ 0.54 and φ(off) ≈ 0.61. We verified that the results for polydisperse packings are independent of the generation protocol for φ ≤ φ(g).
Highlights
We found that the closest jamming densities 4J for equilibrated packings with initial densities 4 # 0.52 are located near the random close packing limit 4RCP] converges to a J-point (4RCP); the available phase space is dominated by basins of attraction that we associate with liquid. 4RCP depends on the polydispersity and is $0.64 for monodisperse packings
When 4 reaches the ideal glass transition density 4g, 4J reaches the ideal glass density 4GCP, so that the available phase space is dominated at 4g by the basin of attraction of the ideal glass
This simple yet powerful model exhibits a range of diverse phenomena, including melting and freezing transitions,[1,4,5,6,7,8,9] the ideal glass transition,[1,7,10,11,12,13] the ideal glass or the glass close packing (GCP) limit,[1,14] as well as the random close packing (RCP) limit.[1,14,15,16]
Summary
Frictionless hard-sphere packings represent a useful model for atomic systems, liquids, glasses, and crystals,[1] aside from being a system directly utilized in materials science and chemical engineering.[2,3] This simple yet powerful model exhibits a range of diverse phenomena, including melting and freezing transitions,[1,4,5,6,7,8,9] the ideal glass transition,[1,7,10,11,12,13] the ideal glass or the glass close packing (GCP) limit,[1,14] as well as the random close packing (RCP) limit.[1,14,15,16]There are several attempts to merge the multitude of these effects into a single picture.[1,10] It is a difficult task, as signi cant debate on some of the concepts above is underway. There exist at least three estimates for the RCP limit, with distinct densities 4: (i) 4 1⁄4 0.634– 0.636;2,16–18 (ii) 4 z 0.64;15,19–21 and (iii) 4 z 0.65.22–29 In our previous studies,[14,30] we suggested that 4 z 0.64 and 4 z 0.65 refer to different phenomena and represent the RCP limit 4RCP (in the sense of the J-point15) and a lower bound of the GCP limit 4GCP,[1] respectively It implies that random jammed packings can systematically be produced at any density in the range [4RCP, 4GCP].1,10,31. It implies that random jammed packings can systematically be produced at any density in the range [4RCP, 4GCP].1,10,31 The de nition and determination of the GCP
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