L. Mederos

Liquid–crystal phase diagrams of binary mixtures of hard spherocylinders

We have built the liquid crystal phase diagram of several binary mixtures of freely rotating hard spherocylinders employing a second-order virial density functional theory with Parsons scaling, suitably generalized to deal with mixtures and smectic phases. The components have the same diameter and aspect ratio of moderate value, typical of many mesogens. Attention has been paid to smectic-smectic demixing and the types of arrangement that rods can adopt in layered phases. Results are shown to depend on the aspect ratio of the individual components and on the ratio of their lengths. Smectic phases are seen not to easily mix together at sufficiently high pressures. Layered phases where the longer rods are the majority component have a smectic-A structure. In the opposite case, a smectic-A(2) phase is obtained where the shorter particles populate the layers and the longer ones prefer to stay parallel to the latter in the interlayer region.

A model for membranes, vesicles and micelles in amphiphilic systems

We present a microscopic model for the aggregates of amphiphilic molecules, based on a simple density functional approximation for the free energy. The different molecular aggregates are described as self-structured density distributions at the relative minima of the grand potential energy. We search for these structures with planar and spherical geometries, and obtain the phase diagram for bilayer membranes, and the curvature energies for vesicles and different types of micelles. The study of a global phase diagram, to get the density of micelles and isolated amphiphilic molecules, at equilibrium with free membranes, requires me link between two description levels of micelles: as self-structured density distributions, or as molecular clusters in the solution of amphiphilic molecules in water. This is done with the help of a simple harmonic model which provides an appropriate choice of the configurational unit cell for micelles.

LIQUID-CRYSTAL PHASE DIAGRAM OF THE GAY-BERNE FLUID BY PERTURBATION THEORY

A thermodynamic linear perturbation theory for the Gay–Berne intermolecular potential has been developed which is able to predict the occurrence of isotropic liquid‐vapour coexistence as well as the stability of a nematic phase. The theory can be regarded as a generalisation to molecular fluids of the Weeks, Chandler, Andersen (WCA) pertubative scheme for simple fluids. The reference system, a hard Gaussian overlap model, is analysed within density‐functional theory using a standard Onsager‐like approach, the ‘‘decoupling approximation,’’ where density correlations are treated to all orders (albeit approximately) whereas orientational correlations are approximated by the low density limit. We implement this idea by using an equivalent system of hard spheres to approximate the density‐dependent part of the excess free energy. The structure of the reference system is approximated by the radial distribution function of an equivalent system of hard spheres, scaled with the contact distance of the hard core. T...

Phase diagrams of systems of particles interacting via repulsive potentials

We use a recently developed density-functional perturbation theory, which has been applied successfully to predict phase diagrams of systems of attractive particles, to describe the phase diagram of particles interacting via repulsive potentials. We consider potentials composed of a hard-sphere core plus a repulsive term. Specifically, we have investigated square shoulder and repulsive Yukawa terms. We show that, when the range of the interaction is very short, the shoulder potential leads to solid–solid coexistence involving two face-centered cubic structures, in analogy to an attractive square-well potential. Comparison with simulation results shows that the theory is quantitatively correct. If the range of the potentials is sufficiently long, we also find that a body-centered cubic structure can be stabilized. By considering the phase behavior at zero temperature, we argue that several triple points, involving coexistence of fluid and/or solid phases, may occur. A repulsive Yukawa term also shows a reg...

Theoretical approach to the correlations of a classical crystal

We present the first theoretical approach to the angular-average of the two-body correlation function

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

\tilde g(r)

The nematic-isotropic phase transition in semiflexible fused hard-sphere chain fluids

for simple solids. It is based on three sum rules for

Solid-solid transitions induced by repulsive interactions

\tilde g(r)

Hard-body models of bulk liquid crystals.

: the compressibility and virial equations and the normalization. We apply the theory to determine this correlation function for the case of the FCC solid phase of hard spheres. The agreement with simulation data is excellent over all the density range. The application to other simple systems is discussed. The approach opens a new route to perturbation theories for simple solids.

Effects of wetting and anchoring on capillary phenomena in a confined liquid crystal

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.