Mechanical and Vibrational Properties of Three-Dimensional Dimer Packings Near the Jamming Transition

Abstract

We comprehensively study mechanical and vibrational properties of dimer packings in three-dimensional space with particular attention on critical scaling behaviors near the jamming transition. First, we confirm the dependence of the packing fraction at the transition on the aspect ratio, the isostatic contact number at the transition, and the scaling dependence of the excess contact number on the excess density. Second, we study the elastic moduli, bulk and shear moduli, and establish power-law scaling of them. Finally, we study the vibrational density of states and its characteristic frequency. The vibrational density of states shows two plateaus in the lower-and higher-frequency regions, which are characterized by rotational and translational vibrational modes, respectively. The onset frequency of the lower-frequency plateau scales linearly to the square root of excess density. The scaling laws in the mechanical and vibrational properties are consistent between two-and three-dimensional dimers, and they are identical to those in spheres.

Structural analysis of disordered dimer packings

“…3, the packing fraction f j has a non-monotonic relationship with a, i.e., it increases as a increases until reaching a peak at f j = 0.707 for a = a max = 1.4, beyond that it decreases. These results are in agreement with previous studies 21,22 and also show reasonably good agreement with results from a mean-field calculation, 40 shown in Fig. 3.…”

“…By comparison, the studies in ref. 22, 41 and 42 find that dimers are almost exactly isostatic, which is thus in line with our findings. The observation of a constant z for all aspect ratios of dimers is an important difference with the behaviour of convex elongated shapes such as ellipsoids and spherocylinders, which are hypostatic (z o 2d f ) at small aspect ratios and show a smooth increase upon shape deformation from the sphere like the coordination number z c here.…”

“…Such problematic contact configurations for dimers were also identified in the recent work by Shiraishi et al 22,41 and separated into ''double'' and ''cusp'' contacts, see Fig. 5.…”

“…The qualitative behaviour is in line with the results of ref. 22, where dimer packings were generated using an energy Fig. 2 The bulk region shown in the x-ẑ-plane.…”

“…4). For example, many polyhedra, [5][6][7][8][9] ellipsoids, [10][11][12][13] spherocylinders, [14][15][16][17][18][19][20] and dimers, 21,22 as well as irregular shapes such as those composed of a number of overlapping spheres 23,24 achieve packing densities f j Z 0.7, with the densest disordered packings so far found for tetrahedra at f j E 0.78. 5 Plotting the packing density as a function of a continuous shape descriptor, such as the aspect ratio a (for rotationally symmetric elongated shapes), exhibits a nonmonotonic behaviour with a peak at a E 1.4-1.5 for ellipsoids, spherocylinders, and dimers, with some variations due to the packing protocol.…”