(276f) Orientational (Dis)Order in Crystals of Hard Polyhedra

Systems of nano- and colloidal polyhedra self-assemble a shape-dependent plethora of phases with different types of order. Fully ordered crystal, as well as (orientationally—but not translationally—ordered) liquid crystal phases, are not uncommon. Data suggest that more common, however, are so-called "plastic" or "rotator crystals", which exhibit translational order and—at least partial—rotational disorder. Comparatively, these plastic crystals are less well understood.

To construct a systematic understanding of colloidal plastic crystals, we use symmetry arguments to propose a representative set of shapes that, all within a cubic close-packed structure, manifest a broad range of forms of rotational disorder and phase behavior. We classify and distinguish these behaviors by developing appropriate order parameters that elucidate the thermodynamic and kinetic effects of rotational disorder.

We then leverage these approaches to investigate another family of polyhedra that form complex ordered structures with multiple, distinct crystallographic positions. We show that particles located at these different crystallographic positions exhibit qualitatively different physical behavior, even if the particle types are all identical. We describe and discuss the implications of this phase behavior for the formation of complex structures in other seemingly simple systems.