Computer-simulation studies of diskotic liquid crystals

Abstract

We have developed a single site anisotropic pair potential suitable for computer-simulation studies of systems composed of disklike molecules. The general dependence of the potential on the intermolecular separation is taken to be the shifted 12-6 Lennard-Jones form. The range and strength parameters in the potential depend on the orientations of the molecules and that of the intermolecular vector, as introduced by Corner; we propose that the form of this dependence may be represented by an $S$-function expansion. A hard oblate spherocylinder with a shape anisotropy $(D+L)/L$ of 3, where $D$ is the diameter of the cylinder with length $L,$ is considered to be a more realistic model for disklike molecules. The expansion coefficients for the range parameter were determined by mapping the expansion onto a set of center of mass separations at the closest approach of a pair of such disks. Each term in the expansion of the strength parameter can be associated with a specific type of interaction: isotropic, anisotropic (nematic favoring, columnar favoring, smectic favoring), and quadrupolar (tilt favoring). This allows fine tuning of each coefficient in the expansion of the strength parameter to reflect the relative strength of a specific type of interaction. To facilitate comparison with studies of the more successful Gay-Berne (GB) potential model, we have determined the expansion coefficients for the strength parameter by mapping the expansion onto that of the GB model. To explore the value of the model potential for studies of diskotic liquid crystals, we have carried out a detailed Monte Carlo simulation at a packing fraction ${(Nv}_{0}/V)$ of 0.55. The system was found to exhibit isotropic, diskotic-nematic ${(N}_{D}),$ diskotic-columnar ${(D}_{\mathrm{ho}}^{\ensuremath{'}}{,D}_{\mathrm{ho}}{,D}_{\mathrm{hd}}),$ and crystal phases. The effect of temperature, density, and the form of the attractive contribution to the potential on the phase stability and the nature of the transitions between the diskotic mesophases is investigated. Such phase behavior contrasts with those for a system of hard oblate spherocylinders and for cut hard spheres with the same shape anisotropy which only form isotropic and crystalline phases and the GB model, which has difficulty in forming columnar phases. Spherical harmonics can be evaluated efficiently by computers. This makes our model potential computationally cheaper.