On the jamming phase diagram for frictionless hard-sphere packings

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).

Worms under Pressure: Bulk Mechanical Properties of C. elegans Are Independent of the Cuticle

“…Similar behavior is widely observed in the jamming of emulsions or other soft colloidal suspensions, and the rearrangement of the gonad relative to other organs in Fig. 6 suggests that the internal volume may eventually become small enough that the organs, cells, and subcellular structures crowd together and cease to rearrange, leading to divergence in the apparent modulus (55)(56)(57). The linear and nonlinear mechanical properties of the worm would thus arise from two key parameters: 1) the effective volume fraction occupied by relatively incompressible internal structures, f; and 2) the intrinsic modulus of these internal structures, k 0 .…”

A local view on the role of friction and shape

“…In figure 5 this boundary is indicated by a solid magenta line. The pressure of a hard sphere gas diverges at the so called Glass Close Packing (GCP) point with φ GCP ≈ 0.65 [20,21,23]. From which follows that the system runs out of nonoverlapping configurations and S HS goes to zero.…”

“…This excludes both packings crystallizing in FCC and HCP configurations at volume fractions above φ g ≈ 0.65 [15][16][17][18][19][20][21] 1 and the "tunneled crystal" packings at φ g = 0.49 [22]. Neither of these two configurations are extensive, i.e.…”

“…There is still some debate [7,21,26,27] if the onset of mechanical stability happens for frictionless spheres at the so called Jamming point of φ J ≈ 0.64 or slightly below at φ g ≈ 0.635. However, it is known that the actual volume fraction of a packing of uncompressed frictionless spheres will depend on the preparation history.…”

“…The exact value of φ g of a frictionless packing at zero pressure does depend on the preparation history [20,21,28,51]. However, the scaling laws of these packings are normally studied by preparing pressure free packings with a given protocol and then increasing φ g by compressing this packing [7,26].…”