Mesophase formation in a system of top-shaped hard molecules: Density functional theory and Monte Carlo simulation

Abstract

We present the phase diagram of a system of mesogenic top-shaped molecules based on the Parsons-Lee density functional theory and Monte Carlo simulation. The molecules are modeled as a hard spherocylinder with a hard sphere embedded in its center. The stability of five different phases is studied, namely, isotropic, nematic, smectic A, smectic C, and columnar phases. The positionally ordered phases are investigated only for the case of parallel alignment. It is found that the central spherical unit destabilizes the nematic with respect to the isotropic phase, while increasing the length of the cylinder has the opposite effect. Also, the central hard sphere has a strong destabilizing effect on the smectic A phase, due the inefficient packing of the molecules into layers. For large hard sphere units the smectic A phase is completely replaced by a smectic C structure. The columnar phase is first stabilized with increasing diameter of the central unit, but for very large hard sphere units it becomes less stable again. The density functional results are in good agreement with the simulations.

On the stability and finite-size effects of a columnar phase in single-component systems of hard-rod-like particles

“…We modify the particle shape by considering top-shaped rods [42], a minimal model for mimicking rods with a larger diameter in the middle. The particles consist of a hard spherocylinder with an aspect ratio L/D and a hard sphere with a sphere-to-rod-diameter ratio σ/D embedded in its centre.…”

“…In Ref. [42], a density functional theory was employed to determine the liquid crystal behaviour of parallel top-shaped rods using various approximations. Irrespective of the aspect ratio, a region of stability of the Col + was predicted for intermediate values of σ/D at sufficiently high packing fractions η.…”

“…Additionally, simulation results obtained by compressing small systems, N = 256, of parallel top-shaped rods with L/D = 9 were presented in Ref. [42] for very small σ/D ≤ 1.06 and for σ/D = 1.80, 1.85, 1.90. In the first case, a drop in the smectic order parameter τ u , signifying the formation of a Col + phase, was observed upon increasing η, reminiscent of the spherocylinder behaviour.…”

“…Inspired by the experimental observation of the Col + phase in suspensions of fd-viruses, intrigued by the simulation results of Refs. [41][42][43], and with the knowledge of the finite-size effects reported by Veerman and Frenkel in Ref. [38], we investigate whether or not the Col + phase can be stabilised by entropy alone.…”

“…[41], a Col + phase was observed in the phase diagram of bent spherocylinders in a very narrow range of bending angles close to 180 • , whereas Ref. [42] reported a Col + phase in systems of top-shaped rods, which consist of a hard spherocylinder with a larger hard sphere embedded in its centre. Finally, a stable Col + phase was reported in a large region of the phase diagram of hard cuboidal particles in Ref.…”