A van der Waals theory of nematic liquid crystals: a ‘convex peg in a round hole’ potential

Density functional theory and simulation of the columnar phase of a system of parallel hard ellipsoids with attractive interactions

A simple molecular model consisting of parallel hard oblate ellipsoids with superimposed square-well attractive interactions of variable range is considered for the study of the phase behavior of thermotropic discotic molecules. A density functional theory appropriate for nonuniform fluids is formulated in which the hard-core contributions to the free energy are treated within a nonlocal weighted-density approximation (WDA) while the attractive contributions are treated at a mean-field level. It is shown that the columnar phase becomes stable relative to the nematic phase at fluid densities for a range of values of the range of the attractive well. In these cases, the region of stability of the columnar phase is bounded at high temperatures by a nematic-columnar-solid triple point. The calculations show that if the attractions are made too long ranged (lambda/D> or approximately =0.84 for particles of aspect ratio of L/D=0.1, where lambda/D is the range of the attractive interaction in units of the molecular diameter D), columnar ordering becomes unstable and the nematic phase dominates at all fluid densities. It is shown that columnar ordering is also predicted when the density functional theory is supplemented with the smoothed-density approximation (SDA). Computer simulations have also been carried out for a particular choice of model parameters; our simulation data confirm the stabilization of the hexagonal columnar phase between the solid and nematic phases. A comparison with simulation data allows us to conclude that the WDA provides a fairly good description of the columnar phase and very good agreement for the nematic-columnar transition properties. On the other hand, our calculations show that the SDA largely underestimates the transition pressure and predicts a too-strongly first-order nematic-columnar transition

Smectic phase in a system of hard ellipsoids with isotropic attractive interactions

The smectic phase is studied for a thermotropic fluid model consisting of aligned hard ellipsoids with superimposed square-well attractive interactions of variable range. The system is analyzed using a density functional theory in which the hard-core contributions to the free-energy functional are treated within a nonlocal weighted density approximation and the attractive contributions are considered at a mean-field level. In the absence of attractions the model reduces, under appropriate scaling, to a fluid of hard spheres and therefore does not exhibit smectic ordering. It is shown that above a certain value of the square-well range, smectic ordering is stable relative to the nematic state at densities well inside the fluid region. The nematic-smectic-A transition is found to be continuous at high temperatures and first order at low temperatures, these two regimes being separated by a tricritical point at an intermediate temperature. These predictions have been confirmed by computer simulation of the model fluid. The results highlight that smectic ordering can be stabilized by coupling anisotropic short-range repulsions with the isotropic contribution of the soft attractive interactions. By increasing the pressure, the range of stability of the smectic phase is seen to decrease. At sufficiently high pressure, the smectic phase is suppressed, and the solid phase dominates. Our calculations show that smectic ordering is no longer stable if the range of the attractions is made too long ranged.

Effect of particle geometry on phase transitions in two-dimensional liquid crystals

Using a version of density-functional theory which combines Onsager approximation and fundamental-measure theory for spatially nonuniform phases, we have studied the phase diagram of freely rotating hard rectangles and hard discorectangles. We find profound differences in the phase behavior of these models, which can be attributed to their different packing properties. Interestingly, bimodal orientational distribution functions are found in the nematic phase of hard rectangles, which cause a certain degree of biaxial order, albeit metastable with respect to spatially ordered phases. This feature is absent in discorectangles, which always show unimodal behavior. This result may be relevant in the light of recent experimental results which have confirmed the existence of biaxial phases. We expect that some perturbation of the particle shapes (either a certain degree of polydispersity or even bimodal dispersity in the aspect ratios) may actually destabilize spatially ordered phases thereby stabilizing the biaxial phase.

Density-functional theory of inhomogeneous systems of hard spherocylinders

The smectic-A phase boundaries of a hard-spherocylinder fluid are calculated using a density-functional theory based on one proposed earlier by Somoza and Tarazona [Phys. Rev. A 41, 965 (1990)]. Our calculations do not employ the translation-rotation decoupling approximation used in previous density-functional theories. The calculated phase boundaries agree well with computer simulation results up to aspect ratios L/D approximately 5 and are in better agreement with the simulations than are previous theories. We generalize the model fluid by including long-range interactions with quadrupolar orientational symmetry, which are taken into account by mean-field approximation. For sufficiently large strength, these interactions produce a smectic-C phase, which undergoes either a continuous or weakly first-order transition to the smectic-A phase. The theory and numerical methods discussed here can be applied to the analysis of interfacial phenomena.