Packing concave molecules in crystals and amorphous solids: on the connection between shape and local structure

Abstract

The structure of the densest crystal packings is determined for a variety of concave shapes in 2D constructed by the overlap of two or three discs. The maximum contact number per particle pair is defined and proposed as a useful means of categorizing particle shape. We demonstrate that the densest packed crystal exhibits a maximum in the number of contacts per particle but does not necessarily include particle pairs with the maximum contact number. In contrast, amorphous structures, generated by energy minimisation of high temperature liquids, typically do include maximum contact pairs. The amorphous structures exhibit a large number of contacts per particle corresponding to over-constrained structures. Possible consequences of this over-constraint are discussed.

Densest versus jammed packings of two-dimensional bent-core trimers

“…These results indicate a key difference between the densest packings of the r = R = 1 trimers considered here and those of the R = 1/2 trimers studied in Ref. [23] (wherein larger bases produce denser lattice packings for some r and θ 0 .) The simpler behavior for r = R = 1 appears to result from a reduction in the number of ways that small numbers of trimers can fit together when the trimers are composed of monodisperse tangent disks as opposed to bidisperse overlapping disks.…”

“…al. [23] found that for R = 1/2 trimers, double-lattice packings are not optimally dense for some θ 0 and r. In these special cases, the densest packings are lattices with bases containing more than two trimers. To see whether this is true for our r = R = 1 systems, we identify maximally dense lattice packings for bases of various sizes using a variant of Torquato et.…”

“…Optimal packing of molecules with the geometry shown in Figure 1 has been investigated only minimally; Ref. [23] reported the densest packings of 2D R = 1/2 trimers as a function of r and θ 0 . The tangent-disk (r = R = 1) case shown in Fig.…”

Packing, entropic patchiness, and self-assembly of non-convex colloidal particles: A simulation perspective

“…Such an intermediate state exhibits shear banding at a local level, and a hexatic-like behavior at the macroscopic level. For dumbbells with different lobe diameters and bond lengths, computer simulation studies using Monte Carlo simulation and free energy calculations have shown that the particles can exhibit a very rich phase behavior ranging from plastic crystals to aperiodic crystals, and aligned crystals 61,62,70 Changing the chemistry and the morphology (roughness) of one of the lobes of a dimer can also be used to target preferential interactions through the addition of depletants. This approach of controlling the interparticle interaction was demonstrated by Kraft and co-workers in a combined experimental and simulation study of asymmetric dimers comprised by one smooth lobe and one highly rough lobe 71 .…”