Smectic Ordering of Parallel Hard Spherocylinders: An Entropy-Based Monte Carlo Study

Nematic-smectic transition of parallel hard spheroellipsoids

Spheroellipsoids are truncated ellipsoids with spherical end caps. If gradients are assumed to change smoothly at the junction of body and cap, the truncation height z0 determines the geometry uniquely. The resulting model particle has only two shape parameters, namely, the aspect ratio c/a of the basic ellipsoid and the cutoff z0/a. These two parameters can be tuned to yield a continuous transformation between a pure ellipsoid and a spherocylinder. Since parallel hard spherocylinders display a nematic-smectic A phase transition, while ellipsoids do not, the influence of the particle shape on the possibility of a smectic phase may be investigated. A density functional analysis is used to detect the dividing line, in the (c/a, z0/a) plane, between the presence and absence of the N-S transition. Since spheroellipsoids may be useful as generic model particles for anisotropic molecules, we provide a computationally efficient overlap criterion for a pair in a general, non-parallel configuration.

Excess entropy and structural transitions in a two-dimensional square-shoulder fluid

Metropolis Monte Carlo simulations on the square-shoulder fluid of Malescio and Pellicane are used to trace the temperature dependent excess entropy, the heat capacity, and configurational energy along several isochores, including those for which mechanically stable zero-temperature structures have been predicted. Thermodynamic signatures of structural phase transitions are identified along several isochores, in addition to the low-density triangular solid and stripe phase transitions identified earlier. The finite temperature phases illustrate the competition between cluster formation and stripe formation as competing mechanisms for generating minimum free energy configurations as a function of density, consistent with earlier results at zero temperature. We also critically examine the usefulness of a phase-ordering rule based on the residual multiparticle entropy (RMPE) in predicting the formation of this diverse set of ordered structures from a disordered fluid phase. For the majority of the isochores studied, the RMPE prediction and the thermodynamic evidence for a phase transition were consistent. However, this criterion fails along isochores that are in regions of coexistence. Thus, the zero-RMPE rule is only likely to be approximately predictive in systems with small phase coexistence regimes, e.g., in the case of liquid crystal forming systems.

Monte Carlo simulation of two-dimensional hard rectangles: confinement effects

We use orientational-bias Monte Carlo simulations to examine the phase behavior of two-dimensional hard rectangles in the bulk and under confinement by hard walls. For all of the rod aspect ratios and area fractions studied, we find that confinement increases the degree of nematic ordering over the bulk, as confined rods tend to align their long axes parallel to the confining walls. The extent of nematic ordering increases as the separation between the confining walls decreases. If the aspect ratio of the rectangles is sufficiently large, they exhibit nematic ordering in both the bulk and under confinement, where the nematic director is set by the walls. Rods with a small aspect ratio are isotropic in the bulk and exhibit weak tetratic tendencies for sufficiently high densities. From studies of density profiles, angular distributions, and orientational correlation functions for confined, low-aspect-ratio rods, it is apparent that they align their long axes parallel to the wall in the near-wall region, where layering occurs for sufficiently high rod densities. However, confined rods with low aspect ratios still exhibit weak tetratic (isotropic) tendencies near the center of the confined region for all but the smallest wall separations. We note that although our studies probe the ordering of hard rectangles, the entropic tendencies that we observe here will be present for rods with energetic interactions. Thus, these studies serve as a general starting point for understanding and controlling the assembly of rods in two-dimensional confining geometries.