We report computer simulations of two-dimensional convex hard superellipse particle phases vs. particle shape parameters including aspect ratio, corner curvature, and sidewall curvature. Shapes investigated include disks, ellipses, squares, rectangles, and rhombuses, as well as shapes with non-uniform curvature including rounded squares, rounded rectangles, and rounded rhombuses. Using measures of orientational order, order parameters, and a novel stretched bond orientational order parameter, we systematically identify particle shape properties that determine liquid crystal and crystalline phases including their coarse boundaries and symmetry. We observe phases including isotropic, nematic, tetratic, plastic crystals, square crystals, and hexagonal crystals (including stretched variants). Our results catalog known benchmark shapes, but include new shapes that also interpolate between known shapes. Our results indicate design rules for particle shapes that determine two-dimensional liquid, liquid crystalline, and crystalline microstructures that can be realized via particle assembly.
Symmetries in hard polygon systems determine plastic colloidal crystal mesophases in two dimensions
Orientational ordering is a necessary step in the crystallization of molecules and anisotropic colloids. Plastic crystals, which are possible mesophases between the fluid and fully ordered crystal, are translationally ordered but exhibit no long range orientational order. Here, we study the two-dimensional phase behavior of hard regular polygons with edge number n = 3–12. This family of particles provides a model system to isolate the effect of shape and symmetry on the existence of plastic crystal phases. We show that the symmetry group of the particle, G , and the symmetry group of the local environment in the crystal, H , together determine plastic colloidal crystal phase behavior in two dimensions. If G contains completely the symmetry elements of H , then a plastic crystal phase is absent. If G and H share some but not all nontrivial symmetry elements, then a plastic crystal phase exists with preferred particle orientations that recover the absent symmetry elements of the crystal; we call this phase the discrete plastic crystal phase. If G and H share no nontrivial symmetry elements, then a plastic crystal phase exists without preferred orientations, which we call an indiscrete plastic crystal.
- Award ID(s):
- 1409620
- Publication Date:
- NSF-PAR ID:
- 10090824
- Journal Name:
- Soft Matter
- Volume:
- 15
- Issue:
- 12
- Page Range or eLocation-ID:
- 2571 to 2579
- ISSN:
- 1744-683X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Publisher's Version of Record
- https://doi.org/10.1039/C9SM00016J
