Phase Behavior of Colloidal Hard Tetragonal Parallelepipeds (Cuboids):  A Monte Carlo Simulation Study

Abstract

The impact of particle geometry on the phase behavior of hard colloidal tetragonal parallelepipeds (TPs) was studied by using Monte Carlo simulations in continuum space. TPs or "cuboids" of aspect ratios varying from 0.25 to 8 were simulated by approximating their shapes with multisite objects, i.e., via rigid clusters of hard spheres. Using equation of state curves, order parameters, radial distribution functions, particle distribution functions along three directions, and visual analysis of configurations, an approximate phase diagram for the TPs was mapped out as a function of aspect ratio (r) and volume fraction. For r > 3 and intermediate concentrations, the behavior of the TPs was similar to that of spherocylinders, exhibiting similar liquid crystalline mesophases (e.g., nematic and smectic phases). For r = 1, a cubatic phase occurs with orientational order along the three axes but with little translational order. For 1 < r < 4, the TPs exhibit a cubatic-like mesophase with a high degree of order along three axes where the major axes of the particles are not all aligned in the same direction. For r < 1, the TPs exhibit a smectic-like phase where the particles have rotational freedom in each layer but form stacks with tetratic order. The equation of state for perfect hard cubes (r = 1) was also simulated and found to be consistent with that of the rounded-edge r = 1 TPs, except for its lack of discontinuity at the cubatic-solid transition.

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.…”

Poisson’s ratio of orientationally disordered hard dumbbell crystal in three dimensions

“…The hard sphere system [8,9], which provided a good insight into physics underlying the freezing of rare gases [10,11], is probably the most widely known example. Monte Carlo (MC) simulations of anisotropic hard-body systems have shown that they are able to mimic various liquid-crystalline and solid phases [12][13][14][15][16][17][18][19][20][21][22]. In particular, it was shown [23][24][25][26] that a crude model of a diatomic molecule, the hard homonuclear dumbbell -formed by two fused spheres, each of diameter r, with centers separated by distance d -can form the above-mentioned rotator phase besides the fluid and the fully-ordered crystalline phases.…”

Design strategies for self-assembly of discrete targets

“…53 The more general algorithms for detecting the overlap of two orthorhombic boxes are then simplified to the case of cubes with edge d, following the same approach used for simple hard cubes. 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.…”