The phase behavior of suspensions of colloidal hard tetragonal parallelepipeds ("TPs") (also known as rectangular nanorods or nanobars) was studied by using Monte Carlo simulations to gain a detailed understanding of the effect of flat-faceted particles on inducing regular local packing and long range structural order. A TP particle has orthogonal sides with lengths a, b, and c, such that a=b and its aspect ratio is r=c/a. The phase diagram for such perfect TPs was mapped out for particle aspect ratios ranging from 0.125 to 5.0. Equation of state curves, order parameters, particle distribution functions, and snapshots were used to analyze the resulting phases. Given the athermal nature of the systems studied, it is the interplay of purely entropic forces that drives phase transitions amongst the structures observed that include crystal, columnar, smectic, parquet, and isotropic phases. In the parquet phase that occurs for 0.54

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.

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.

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Nonspherical particles of pear-like and spherocylinder shape were organized into diverse two-dimensional (2D) structures, including the orientationally disordered rotator. Dry films with hexagonal, oblique, and centered rectangular symmetry were obtained by using convective assembly to condense and confine the system in a thin meniscus region. Monte Carlo simulations confirmed the transition from fluid to rotator simply as a function of system density and short-bond-length particle morphology.