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

journal contribution

posted on 08.12.2005, 00:00 by Bettina S. John, Fernando A. EscobedoThe 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.