Cubatic liquid-crystalline behavior in a system of hard cuboids

Abstract

The lyotropic phase behavior of cuboidal particles was investigated via Monte Carlo simulations. Hard cubes were approximated by suitably shaped clusters of hard spheres. Changes in concentration and structure of the system were monitored as a function of osmotic pressure P* (imposed in an isobaric ensemble). As expected, an isotropic phase prevailed at low concentrations (low P*) and a crystalline phase formed at high concentrations (high P*). A third distinct phase was also observed for an intermediate range of concentrations (approximately marked by breaks in the P* versus concentration curve). The structure of this mesophase was characterized both visually and analytically by calculating radial distribution functions and order parameters. It was found that such a mesophase exhibits orientational ordering along three axes (cubatic order) but significant translational disorder, thus having a structure clearly distinct from both isotropic and crystalline phases.

Mesophase behaviour of polyhedral particles

“…In contrast to earlier conjectures [11][12][13] , we now find clear evidence of layering in the cubatic phase (also observed in [32]) which becomes visible in our redefined particle distribution functions (see details in SI). While the finite size of our system prevents us from ascertaining the range of such a positional order, the appreciable D values observed at these densities indicates that the system has liquid-like behaviour and there is sufficient translational disorder for layers to rearrange dynamically.…”

“…These ordered assemblies have distinctive electronic, optical, and dynamical properties 4,5 and are highly desirable for fabrication of advanced electronic, photonic, and rheological devices 6,7 . Although numerous theoretical [8][9][10][11][12][13] and experimental 14,15 studies on mesophase behaviour of particles with anisotropic shapes have been reported, a roadmap marking out the most probable mesophases that could be formed by constituent particles with particular geometrical features is still incomplete. Exploring such relations will translate into a deeper understanding of the phase behaviour of colloidal systems with different particle shapes; e.g., Jiao et al 16 reported that unlike ellipsoids, convex superballs can be optimally packed in dense Bravais lattices because they are less symmetric but more isotropic than the former.…”

Local chiral symmetry breaking in triatic liquid crystals

“…In three dimensions (3D), differences in particle shapes give rise to a variety of liquid crystal phases, such as smectic 16 and discoidal phases 17 . Beyond classic liquid crystals 16 , new forms, such as the cubatic phase 9,24 , have been predicted but thus far not observed.…”

Design strategies for self-assembly of discrete targets

“…47,54 An alternative approach to modelling a polyhedron as a single object is by fusing repulsive spheres into a rigid body. Such models were used in early simulations of colloidal cubes, 55 although the slight corrugations of the cube surfaces introduced some noticeable artefacts. 54 Fused-sphere models with attractive spots have also provided the basis for seminal work on the self-assembly of virus capsids.…”