A model nematic liquid crystal revisited: some new phase diagrams from density-functional theory

Phase behavior of a lattice-gas model for biaxial nematics

We employ a lattice-gas extension of the Maier-Saupe model with discrete orientation states to study the phase behavior of a statistical model for biaxial nematogenic units in mean-field theory. The phase behavior of the system is investigated in terms of the strength of isotropic interaction between anisotropic objects, as well as the degree of biaxiality and the concentration of those units. We obtain phase diagrams with isotropic phases and stable biaxial and uniaxial nematic structures, various phase coexistences, many types of critical and multicritical behaviors, such as ordinary vapor-liquid critical points, critical end points, and tricritical points, and distinct Landau-like multicritical points. Our results widen the possibilities of relating the phenomenological coefficients of the Landau-de Gennes expansion to microscopic parameters, allowing an improved interpretation of theoretical fittings to experimental data.

Perturbation Theory versus Thermodynamic Integration. Beyond a Mean-Field Treatment of Pair Correlations in a Nematic Model Liquid Crystal

The phase behavior and structure of a simple square-well bulk fluid with anisotropic interactions is described in detail. The orientation dependence of the intermolecular interactions allows for the formation of a nematic liquid-crystalline phase in addition to the more conventional isotropic gas and liquid phases. A version of classical density functional theory (DFT) is employed to determine the properties of the model, and comparisons are made with the corresponding data from Monte Carlo (MC) computer simulations in both the grand canonical and canonical ensembles, providing a benchmark to assess the adequacy of the DFT results. A novel element of the DFT approach is the assumption that the structure of the fluid is dominated by intermolecular interactions in the isotropic fluid. A so-called augmented modified mean-field (AMMF) approximation is employed accounting for the influence of anisotropic interactions. The AMMF approximation becomes exact in the limit of vanishing density. We discuss advantages and disadvantages of the AMMF approximation with respect to an accurate description of isotropic and nematic branches of the phase diagram, the degree of orientational order, and orientation-dependent pair correlations. The performance of the AMMF approximations is found to be good in comparison with the MC data; the AMMF approximation has clear advantages with respect to an accurate and more detailed description of the fluid structure. Possible strategies to improve the DFT are discussed.

Structure and phase behaviour of diblock copolymer monolayers investigated by means of Monte Carlo simulation

We use grand canonical Monte Carlo simulation paired with multiple histogram reweighting, hyperparallel tempering and finite size scaling to investigate the structure and phase behaviour of monolayers of diblock copolymers. The chain molecules are arranged on the square lattice and we consider both fully flexible and rod-coil polymer models. In contrast to the majority of previous studies we assume that the interactions between the segments belonging to one of the two subunits are weaker than the remaining segment-segment interactions. We find that when the diblock copolymer is fully flexible, this choice of the interactions leads to a suppression of the ordered phase, and the phase behaviour is analogous to that of the fully flexible homopolymer model. However, when one of the subunits is rigid, we observe the formation of a novel hairpin chessboard ordered structure with fully stretched chains bent in the middle. The topology of the phase diagram depends on the chain length. For shorter chains the global phase diagram features a critical point and a triple point. For longer chains the gas-disordered liquid phase transition is suppressed and only the order-disorder transition remains stable. The resulting phase diagram is of the swan neck type.

Phase behavior of a hard sphere Maier-Saupe nematogenic system in three dimensions

We present a detailed computer simulation and integral equation study of the phase behavior of a nematogenic system composed of hard spheres with embedded three-dimensional Maier-Saupe spins. For this well-known system, we map the gas-liquid equilibrium, which is coupled to a first-order isotropic-nematic transition. The anisotropic integral equation theory is found to yield excellent agreement with the simulation data within the fluid regime. Additionally, we determine the fluid-solid equilibrium transition by means of computer simulation.