Molecular simulation and theory of a liquid crystalline disclination core

Nematic-isotropic phase transitions in thin slabs of liquid crystals with topological defect arrays

We study the nematic-to-isotropic phase transitions in thin slabs of nematic liquid crystals with photopatterned director fields of topological defect arrays at constant heating rates and show that the transition kinetics is significantly impacted by both the heating rate and the topological strengths of these defects. Specifically, with ±1/2 defect arrays, the isotropic domains emerge from the defect cores when the heating rate is high, while from random places when the heating rate is low. With ±1 defect arrays, the isotropic domains always emerge from the defect cores regardless of the heating rate. Furthermore, the isotropic domains show significant movements at slow heating rates, and the total area of the isotropic domains grows with the temperature T following a simple power law (T - T')γ, where the exponent γ is approximately 1 in most cases and is 2/3 for the ±1 defect arrays at low heating rates when the isotropic domains are pinned on the defect cores. We attribute this phenomenon to an interplay between the surface tension and bulk free energy.

Segregation of liquid crystal mixtures in topological defects

The structure and physical properties of liquid crystal (LC) mixtures are a function of composition, and small changes can have pronounced effects on observables, such as phase-transition temperatures. Traditionally, LC mixtures have been assumed to be compositionally homogenous. The results of chemically detailed simulations presented here show that this is not the case; pronounced deviations of the local order from that observed in the bulk at defects and interfaces lead to significant compositional segregation effects. More specifically, two disclination lines are stabilized in this work by introducing into a nematic liquid crystal mixture a cylindrical body that exhibits perpendicular anchoring. It is found that the local composition deviates considerably from that of the bulk at the interface with the cylinder and in the defects, thereby suggesting new assembly and synthetic strategies that may capitalize on the unusual molecular environment provided by liquid crystal mixtures.

Liquid crystal mixtures are used in commercial applications and their composition affects their properties. Here Rahimi et al. use atomistic simulations to show that defects influence the molecular arrangement of the mixture components leading to a deviation of the local order from that of the bulk.

How to define variation of physical properties normal to an undulating one-dimensional object

One-dimensional flexible objects are abundant in physics, from polymers to vortex lines to defect lines and many more. These objects structure their environment and it is natural to assume that the influence these objects exert on their environment depends on the distance from the line object. But how should this be defined? We argue here that there is an intrinsic length scale along the undulating line that is a measure of its stiffness (i.e., orientational persistence), which yields a natural way of defining the variation of physical properties normal to the undulating line. We exemplify how this normal variation can be determined from a computer simulation for the case of a so-called bottle-brush polymer, where side chains are grafted onto a flexible backbone.

Topological defects in a two-dimensional liquid crystal confined in a circular nanocavity

Using a microscopic theory based on excluded-volume interactions, we analyze the structure and thermodynamic stability of configurations in a two-dimensional liquid crystal confined into a (small) circular nanocavity. Weak homeotropic anchoring conditions are considered, and topological defects of total charge k=+1 are discussed. It is found that, for small cavity radii, the cavity is free of defects at the expense of surface free energy not being optimized. For larger cavities, a configuration with two repulsive k=+1/2-charge point defects is always stable. The two configurations are equally stable thermodynamically (structural or Frederiks transition) on a curve in the chemical potential-cavity radius plane. This curve ends for chemical potential and cavity radius below some critical values. Elastic-theory arguments are used to explain the stability of the defected structure compared with the one free of defects. Our results indicate that the two-defect structure is always more stable than the one with a single point defect of charge k=+1 at the cavity center, which, in agreement with computer simulation, is never found to be stable. Finally, the relation with the bulk behavior of the fluid is discussed.

Nematic cells with defect-patterned alignment layers

Using Monte Carlo simulations of the Lebwohl-Lasher model we study the director ordering in a nematic cell where the top and bottom surfaces are patterned with a lattice of +/-1 point topological defects of lattice spacing a . As expected on general physical grounds we find that the nematic order depends on the ratio of the height of the cell H to a . For thick cells (Ha > or = 0.9) we find that the system is very well ordered and the frustration induced by the lattice of defects is relieved in a novel way by a network of half-integer defect lines which emerge from the point defects and hug the top and bottom surfaces of the cell. When Ha < or = 0.9 the system has zero nematic order parameter and the half-integer defect lines thread through the cell joining point defects on the top and bottom surfaces. We present a simple physical argument in terms of the length of the defect lines to explain these results. To facilitate eventual comparison with experimental systems we also simulate optical textures in the presence of crossed polarizers.

Simulation and visualization of topological defects in nematic liquid crystals

We present a method of visualizing topological defects arising in numerical simulations of liquid crystals. The method is based on scientific visualization techniques developed to visualize second-rank tensor fields, yielding information not only on the local structure of the field but also on the continuity of these structures. We show how these techniques can be used to first locate topological defects in fluid simulations of nematic liquid crystals where the locations are not known a priori and then study the properties of these defects including the core structure. We apply these techniques to simulation data obtained by previous authors who studied a rapid quench and subsequent equilibration of a Gay-Berne nematic. The quench produces a large number of disclination loops which we locate and track with the visualization methods. We show that the cores of the disclination lines have a biaxial region and the loops themselves are of a hybrid wedge-twist variety.

Prediction of disclinations in nematic elastomers

We present a theory for uniaxial nematic elastomers with variable asphericity. As an application of the theory, we consider the time-independent, isochoric extension of a right circular cylinder. Numerical solutions to the resulting differential equation are obtained for a range of extensions. For sufficiently large extensions, there exists an isotropic core of material surrounding the cylinder axis where the asphericity vanishes and in which the polymeric molecules are shaped as spherical coils. This region, corresponding to a disclination of strength +1 manifesting itself along the axis, is bounded by a narrow transition layer across which the asphericity drops rapidly and attains a nontrivial negative value. Away from the disclination, the material is anisotropic, and the polymeric molecules are shaped as ellipsoidal coils of revolution oblate about the radial direction. Along with the area of steeply changing asphericity between isotropic and anisotropic regimes, a marked drop in the free-energy density is observed. The boundary of the disclination core is associated with the location of this energy drop. For realistic choices of material parameters, this criterion yields a core on the order of 10(-2) microm, which coincides with observations in conventional liquid crystal melts. Finally, we find that the total energy definitively shows a preference for disclinated states.

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.

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.

Topological defects in nematic droplets of hard spherocylinders

Using computer simulations we investigate the microscopic structure of the singular director field within a nematic droplet. As a theoretical model for nematic liquid crystals we take hard spherocylinders. To induce an overall topological charge, the particles are either confined to a two-dimensional circular cavity with homeotropic boundary or to the surface of a three-dimensional sphere. Both systems exhibit half-integer topological point defects. The isotropic defect core has a radius of the order of one particle length and is surrounded by free-standing density oscillations. The effective interaction between two defects is investigated. All results should be experimentally observable in thin sheets of colloidal liquid crystals.