Effective triplet interactions in nematic colloids

Three-body effective interactions emerging between parallel cylindrical rods immersed in a nematic liquid crystals are calculated within the Landau-de Gennes free-energy description. Collinear, equilateral and midplane configurations of the three colloidal particles are considered. In the last two cases the effective triplet interaction is of the same magnitude and range as the pair one.

Colloidal particles at a nematic-isotropic interface: effects of confinement

When captured by a flat nematic-isotropic interface, colloidal particles can be dragged by it. As a result spatially periodic structures may appear, with the period depending on particle mass, size, and interface velocity (J.L. West, A. Glushchenko, G.X. Liao, Y. Reznikov, D. Andrienko, M.P. Allen, Phys. Rev. E 66, 012702 (2002)). If liquid crystal is sandwiched between two substrates, the interface takes a wedge-like shape, accommodating the interface-substrate contact angle and minimizing the director distortions on its nematic side. Correspondingly, particles move along complex trajectories: they are first captured by the interface and then "glide" towards its vertex point. Our experiments quantify this scenario, and numerical minimization of the Landau-de Gennes free energy allows for a qualitative description of the interfacial structure and the drag force.

Capillary bridging and long-range attractive forces in a mean-field approach

When a mixture is confined, one of the phases can condense out. This condensate, which is otherwise metastable in the bulk, is stabilized by the presence of surfaces. In a sphere-plane geometry, routinely used in atomic force microscope and surface force apparatus, it can form a bridge connecting the surfaces. The pressure drop in the bridge gives rise to additional long-range attractive forces between them. By minimizing the free energy of a binary mixture we obtain the force-distance curves as well as the structural phase diagram of the configuration with the bridge. Numerical results predict a discontinuous transition between the states with and without the bridge and linear force-distance curves with hysteresis. We also show that similar phenomenon can be observed in a number of different systems, e.g., liquid crystals and polymer mixtures.

Interaction of colloids with a nematic-isotropic interface

The Landau-de Gennes free energy is used to calculate the interaction between long cylindrical colloids and the nematic-isotropic (NI) interface. This interaction has two contributions: one is specific of liquid crystals and results from the deformation of the director field close to the particles or to the interface, while the other is generic and results from wetting and surface tension effects. Deep in the nematic phase the director field of long cylindrical colloids, with strong homeotropic anchoring, exhibits two half-integer defect lines. As the colloid moves towards the interface, the director configuration changes through a series of discontinuous transitions, where one or two of the defects are annihilated. In addition, the NI interface bends towards the colloid in order to minimize the elastic free energy in the nematic. In the isotropic phase, the colloid is surrounded by a thin nematic layer that reduces the surface free energy under favorable wetting conditions. The interaction has a well-defined minimum near the interface. In this region the director and interfacial structures are complex and cannot be described analytically. Using the numerical results for the Landau-de Gennes free energy in the harmonic region, we obtained simple scaling laws for the (linear) force on the colloid.

Forces between elongated particles in a nematic colloid

Using molecular dynamics simulations we study the interactions between elongated colloidal particles (length to breath ratio >>1) in a nematic host. The simulation results are compared to the results of a Landau-de Gennes elastic free energy. We find that depletion forces dominate for the sizes of the colloidal particles studied. The tangential component of the force, however, allows us to resolve the elastic contribution to the total interaction. We find that this contribution differs from the quadrupolar interaction predicted at large separations. The difference is due to the presence of nonlinear effects, namely, the change in the positions and structure of the defects and their annihilation at small separations.

Entropic torque

Quantitative predictions are presented of a depletion-induced torque and force acting on a single colloidal hard rod immersed in a solvent of hard spheres close to a planar hard wall. This torque and force, which are entirely of entropic origin, may play an important role for the key-lock principle, according to which a biological macromolecule (the key) is functional only in a particular orientation with respect to a cavity (the lock).

Computer simulation of topological defects around a colloidal particle or droplet dispersed in a nematic host

We use molecular dynamics to study the ordering of a nematic liquid crystal around a spherical particle or droplet. Homeotropic boundary conditions and strong anchoring create a hedgehog (radial point defect) director configuration on the particle surface and in its vicinity; this topological defect is canceled by nearby defect structures in the surrounding liquid crystal, so as to give a uniform director field at large distances. We observe three defect structures for different particle sizes: a quadrupolar one with a ring defect surrounding the particle in the equatorial plane; a dipolar one with a satellite defect at the north or south pole; and a transitional, nonequatorial, ring defect. These observations are broadly consistent with the predictions of the simplest elastic theory. By studying density and order-parameter maps, we are able to examine behavior near the particle surface, and in the disclination core region, where the elastic theory is inapplicable. Despite the relatively small scale of the inhomogeneities in our systems, the simple theory gives reasonably accurate predictions of the variation of defect position with particle size.

Nematic director slippage: role of the angular momentum of light

We propose a theoretical model of the light-induced director slippage effect. In this effect the bulk director reorientation contributes to the surface director reorientation. It is found that the director and ellipticity profiles, obtained in the geometric optics approximation, are dependent on the ellipticity of the incident light wave. The director distribution is spatially modulated in linearly polarized light but grows monotonically in circularly polarized light. The surface director deviation has been examined, and comparison made with existing experimental data, which then permits the magnitude of the orientational nonlinearity coefficient to be calculated.

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.

Molecular simulation and theory of a liquid crystalline disclination core

Molecular simulations of a nematic liquid crystal confined in cylinder geometry with homeotropic anchoring have been carried out. The core structure of a disclination line defect of strength +1 has been examined, and comparison made with various theoretical treatments, which are presented in a unified way. It is found that excellent fits to the cylindrically symmetrized order tensor profiles may be obtained with appropriate parameter choices; notwithstanding this, on the time scales of the simulation, the cylindrical symmetry of the core is broken and two defects of strength +1 / 2 may be resolved.