Influence of Homeotropic Anchoring Walls upon Nematic and Smectic Phases

McMillan liquid crystal model sandwiched between strong homeotropic anchoring walls is studied. Phase transitions between isotropic, nematic, and smectic A phases are investigated for wide ranges of an interaction parameter and of the system thickness. It is confirmed that the anchoring walls induce an increase in transition temperatures, dissappearance of phase transitions, and an appearance of non-spontaneous nematic phase. The similarity between influence of anchoring walls and that of external fields is discussed.Comment: 5 pages, 6 figure

Numerical study of surface-induced reorientation and smectic layering in a nematic liquid crystal

Surface-induced profiles of both nematic and smectic order parameters in a nematic liquid crystal, ranging from an orienting substrate to "infinity", were evaluated numerically on base of an extended Landau theory. In order to obtain a smooth behavior of the solutions at "infinity" a boundary energy functional was derived by linearizing the Landau energy around its equilibrium solutions. We find that the intrinsic wave number of the smectic structure, which plays the role of a coupling between nematic and smectic order, strongly influences the director reorientation. Whereas the smectic order is rapidly decaying when moving away from the surface, the uniaxial nematic order parameter shows an oscillatory behavior close to the substrate, accompanied by a non-zero local biaxiality.Comment: LaTeX, 17 pages, with 4 postscript figure

Orientational transitions in a nematic confined by competing surfaces

The effect of confinement on the orientational structure of a nematic liquid crystal model has been investigated by using a version of density-functional theory (DFT). We have focused on the case of a nematic confined by opposing flat surfaces, in slab geometry (slit pore), which favor planar molecular alignment (parallel to the surface) and homeotropic alignment (perpendicular to the surface), respectively. The spatial dependence of the tilt angle of the director with respect to the surface normal has been studied, as well as the tensorial order parameter describing the molecular order around the director. For a pore of given width, we find that, for weak surface fields, the alignment of the nematic director is perpendicular to the surface in a region next to the surface favoring homeotropic alignment, and parallel along the rest of the pore, with a interface separating these regions (S phase). For strong surface fields, the director is distorted uniformly, the tilt angle exhibiting a linear dependence with the distance normal to the surface (L phase). Our calculations reveal the existence of a first-order transition between the two director configurations, which is driven by changes in the surface field strength, and also by changes in the pore width. In the latter case the transition occurs, for a given surface field, between the S phase for narrow pores and the L phase for wider pores. A link between the L-S transition and the anchoring transition observed for the semi-infinite case is proposed. We also provide calculations with a phenomenological approach that yields the same main result that DFT in the scale length where this is valid.Comment: submitted to PR

Membranes in rod solutions: a system with spontaneously broken symmetry

We consider a dilute solution of infinitely rigid rods near a curved, perfectly repulsive surface and study the contribution of the rod depletion layer to the bending elastic constants of membranes. We find that a spontaneous curvature state can be induced by exposure of BOTH sides of the membrane to a rod solution. A similar result applies for rigid disks with a diameter equal to the rod's length. We also study the confinement of rods in spherical and cylindrical repulsive shells. This helps elucidate a recent discussion on curvature effects in confined quantum mechanical and polymer systems.Comment: 10 pages, 2 figures, 1 table; submitted to PR

Theory and simulation of the nematic zenithal anchoring coefficient

Combining molecular simulation, Onsager theory and the elastic description of nematic liquid crystals, we study the dependence of the nematic liquid crystal elastic constants and the zenithal surface anchoring coefficient on the value of the bulk order parameter

Elastic constants of nematic liquid crystals of uniaxial symmetry

We study in detail the influence of molecular interactions on the Frank elastic constants of uniaxial nematic liquid crystals composed of molecules of cylindrical symmetry. A brief summary of the status of theoretical development for the elastic constants of nematics is presented. Considering a pair potential having both repulsive and attractive parts numerical calculations are reported for three systems MBBA, PAA and 8OCB. For these systems the length-to-width ratio ${x_0}$ is estimated from the experimentally proposed structure of the molecules. The repulsive interaction is represented by a repulsion between hard ellipsoids of revolution (HER) and the attractive potential is represented by the quadrupole and dispersion interactions. From the numerical results we observe that in the density range of nematics the contribution of the quadrupole and dispersion interactions are small as compared to the repulsive HER interaction. The inclusion of attractive interaction reduces the values of elastic constants ratios. The temperature variation of elastic constants ratios are reported and compared with the experimental values. A reasonably good agreement between theory and experiment is observed

Liquid crystal director fluctuations and surface anchoring by molecular simulation

We propose a simple and reliable method to measure the liquid crystal surface anchoring strength by molecular simulation. The method is based on the measurement of the long-range fluctuation modes of the director in confined geometry. As an example, molecular simulations of a liquid crystal in slab geometry between parallel walls with homeotropic anchoring have been carried out using the Monte Carlo technique. By studying different slab thicknesses, we are able to calculate separately the position of the elastic boundary condition, and the extrapolation length

Phase ordering in bulk uniaxial nematic liquid crystals

The phase-ordering kinetics of a bulk uniaxial nematic liquid crystal is addressed using techniques that have been successfully applied to describe ordering in the O(n) model. The method involves constructing an appropriate mapping between the order-parameter tensor and a Gaussian auxiliary field. The mapping accounts both for the geometry of the director about the dominant charge 1/2 string defects and biaxiality near the string cores. At late-times t following a quench, there exists a scaling regime where the bulk nematic liquid crystal and the three-dimensional O(2) model are found to be isomorphic, within the Gaussian approximation. As a consequence, the scaling function for order-parameter correlations in the nematic liquid crystal is exactly that of the O(2) model, and the length characteristic of the strings grows as $t^{1/2}$. These results are in accord with experiment and simulation. Related models dealing with thin films and monopole defects in the bulk are presented and discussed.Comment: 21 pages, 3 figures, REVTeX, submitted to Phys. Rev.

Hard-Sphere Fluids in Contact with Curved Substrates

The properties of a hard-sphere fluid in contact with hard spherical and cylindrical walls are studied. Rosenfeld's density functional theory (DFT) is applied to determine the density profile and surface tension $\gamma$ for wide ranges of radii of the curved walls and densities of the hard-sphere fluid. Particular attention is paid to investigate the curvature dependence and the possible existence of a contribution to $\gamma$ that is proportional to the logarithm of the radius of curvature. Moreover, by treating the curved wall as a second component at infinite dilution we provide an analytical expression for the surface tension of a hard-sphere fluid close to arbitrary hard convex walls. The agreement between the analytical expression and DFT is good. Our results show no signs for the existence of a logarithmic term in the curvature dependence of $\gamma$.Comment: 15 pages, 6 figure