E. Velasco

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.

Stable smectic phase in suspensions of polydisperse colloidal platelets with identical thickness.

We report the nematic and smectic ordering in an aqueous suspension of monolayer alpha -Zirconium phosphate platelets possessing a high polydispersity in diameter but uniform thickness. We observe an isotropic-nematic transition as the platelet volume fraction increases, followed by the formation of a smectic, an elusive phase that has been rarely seen in discotic liquid crystals. The smectic phase is characterized by x-ray diffraction high-resolution transmission electron microscopy, and optical microscopy. The phase equilibria in this highly polydisperse suspension are rationalized in terms of a theoretical approach based on density-functional theory.

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...

Wetting and drying at a solid-fluid interface

We have studied the wetting and drying transitions in a solid–fluid interace with truncated Lennard‐Jones interactions, for which there have been reported molecular dynamics results by Sikkenk et al. [Phys. Rev. Lett. 59, 98 (1987)]. We consider in detail the differences resulting from the use of a ‘‘real’’ solid substrate instead of the ‘‘inert wall’’ model which has been used in all previous calculations.

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...

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.

FtsZ Bacterial Cytoskeletal Polymers on Curved Surfaces: The Importance of Lateral Interactions

A recent theoretical article provided a mechanical explanation for the formation of cytoskeletal rings and helices in bacteria assuming that these shapes arise, at least in part, from the interaction of the inherent mechanical properties of the protein polymers and the constraints imposed by the curved cell membrane (Andrews, S., and A. P. Arkin. 2007. Biophys. J. 93:1872-1884). Due to the lack of experimental data regarding the bending rigidity and preferential bond angles of bacterial polymers, the authors explored their model over wide ranges of preferred curvature values. In this letter, we present the shape diagram of the FtsZ bacterial polymer on a curved surface but now including recent experimental data on the in vitro formed FtsZ polymers. The lateral interactions between filaments observed experimentally change qualitatively the shape diagram and indicate that the formation of rings over spirals is more energetically favored than estimated in the above-mentioned article.

Low melting temperature and liquid surface layering for pair potential models

We have recently proposed [Phys. Rev. Lett. 87, 166101 (2001)] that any isotropic fluid should exhibit surface layering at its liquid–vapor interface above the triple temperature provided that the system has a low triple temperature. In this article we present an extensive study of systems with different isotropic pair interactions, some of which present a very low triple temperature. We have confirmed that surface layering is a general characteristic of very cold liquids, independent of the specific shape of the potential, and that only pair potentials presenting a low triple-point temperature do exhibit surface oscillations; in other cases layering is preempted by solidification. Finally, we study the damping of surface oscillations due to capillary waves and conclude that for any model pair potential the temperature threshold below which layering would be observed for the typical experimental transverse sampling sizes is 15% of the critical temperature.

Solid-solid transitions induced by repulsive interactions

We show that a rich variety of crystalline structures, and a corresponding diversity of the associated phase diagrams, result from the presence in the pair potential of a soft repulsion in addition to a hard core. We use different forms for the soft repulsion, and show that the results are sensitive to the details of the potentials (in particular, their convexity) even if the range of the soft repulsion is limited to a small fraction of the hard-core diameter. Our demonstration combines exact ground-state analysis with first-order perturbation theory at finite temperatures. The relevance of our work to certain features found in real systems is also discussed.

Hard-body models of bulk liquid crystals.

Hard models for particle interactions have played a crucial role in the understanding of the structure of condensed matter. In particular, they help to explain the formation of oriented phases in liquids made of anisotropic molecules or colloidal particles and continue to be of great interest in the formulation of theories for liquids in bulk, near interfaces and in biophysical environments. Hard models of anisotropic particles give rise to complex phase diagrams, including uniaxial and biaxial nematic phases, discotic phases and spatially ordered phases such as smectic, columnar or crystal. Also, their mixtures exhibit additional interesting behaviours where demixing competes with orientational order. Here we review the different models of hard particles used in the theory of bulk anisotropic liquids, leaving aside interfacial properties and discuss the associated theoretical approaches and computer simulations, focusing on applications in equilibrium situations. The latter include one-component bulk fluids, mixtures and polydisperse fluids, both in two and three dimensions, and emphasis is put on liquid-crystal phase transitions and complex phase behaviour in general.