Defects In Nematic Liquid Crystals Research Articles

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.

Topological point defects in nematic liquid crystals

Point defects in nematics, also called hedgehogs, are topological entities that have no equivalent in ordered atomic solids, despite the homonymy. They have been the subject of intense experimental and, above all, theoretical (analytical and computational) investigations in the last thirty years. They are present in bulk specimens and at the specimen boundaries. This review article stresses the importance of the core structure of the defect, the possibility of it splitting into a disclination loop, and boundary conditions, as well as taking stock of the recent advances on point defects in nematic colloidal suspensions. An important topic is the formation of strings between opposite hedgehogs (radial and hyperbolic), and their role in the dynamic properties of nematics.

Annihilation dynamics of umbilical defects in nematic liquid crystals under applied electric fields

Umbilical defects were induced in a nematic liquid crystal with negative dielectric anisotropy, confined to Hele-Shaw cells with homeotropic boundary conditions, and their annihilation dynamics were investigated experimentally. Dynamic scaling laws, previously proposed for Schlieren defects, were verified also for electric field induced umbilical defects while varying external parameters, such as electric field amplitude, frequency, Hele-Shaw cell gap, and temperature. In all cases, scaling relations of rho(t) proportional to t(-1) for the defect density and D proportional to (t(0) - t)(1/2) for the defect pair separation were obtained, independent of external field parameters. The experimental results give evidence of the universality of scaling relations for the annihilation of topological defects in liquid crystals, extended to umbilical defects and their annihilation dynamics under applied external fields.

Laser Action Based on Electrically Controllable Defect Mode in One-Dimensional Photonic Crystal Containing Conducting Polymer and Liquid Crystal Defect Layers

ABSTRACT Electrical tuning of the wavelength of a defect mode lasing in a one-dimensional photonic crystal has been demonstrated using a conducting polymer as an active emission layer and a nematic liquid crystal as an electrically tunable defect layer in the periodic structure. Lasing wavelength is widely tuned upon applying the electric field, which follows a defect mode shift due to the refractive index change in the nematic liquid crystal defect layer caused by field-induced realignment of the liquid crystal molecules.

Light propagation analysis and high‐speed electro‐optic switching in one‐dimensional photonic crystal with nematic liquid crystal defect layer

AbstractIt is possible by the application of voltage to control the local level in a one‐dimensional photonic crystal with a liquid crystal defect layer. In the present paper, a nematic liquid crystal is used and high‐speed switching is attempted on the basis of the shift of the localized state wavelength by the photonic bandgap and liquid crystal orientation control. First, by the finite‐difference time‐domain method, the optical propagation characteristics inside a one‐dimensional photonic crystal with a liquid crystal defect layer are analyzed. It is shown that optical switching by control of the localized state wavelength is possible. TiO2 and SiO2 are periodically laminated as a one‐dimensional photonic crystal. A nematic liquid crystal layer is introduced as a defect layer to disturb the periodicity, resulting in a one‐dimensional photonic crystal with a liquid crystal defect layer. By application of a voltage, the orientation of the liquid crystal defect layer is varied in an attempt to perform optical switching by electric field control of the localized state. High‐speed optical switching of microsecond order is successful with nematic liquid crystals. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 88(4): 46–53, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20087

Electrically tunable lasing based on defect mode in one-dimensional photonic crystal with conducting polymer and liquid crystal defect layer

Electrical tuning of the wavelength of the defect mode lasing in a one-dimensional photonic crystal has been demonstrated using a conducting polymer as an active emission layer and a nematic liquid crystal as an electrically tunable defect layer in the periodic structure. Lasing wavelength is widely tuned upon applying the electric field, which follows a defect mode shift due to the refractive index change in the nematic liquid crystal defect layer caused by field-induced realignment of the liquid crystal molecules.

Physics of defects in nematic liquid crystals

Liquid-crystal phases are typical examples of soft and complex materials thatexhibit an abundance of different phenomena. In this paper we present some ofour results contributing to the understanding of the physics of defects in nematicliquid crystals. The examples presented exhibit many features that are also ofinterest for other branches of physics. We describe nematic point defects, theannihilation dynamics of a defect and anti-defect pair, and the coarseningdynamics of a dense pattern of defects after a sudden symmetry-breaking phasetransition.

Hydrodynamics of topological defects in nematic liquid crystals.

We show that backflow, the coupling between the order parameter and the velocity fields, has a significant effect on the motion of defects in nematic liquid crystals. In particular, the defect speed can depend strongly on the topological strength in two dimensions and on the sense of rotation of the director about the core in three dimensions.

Fine structure of defects in radial nematic droplets

We investigate the structure of defects in nematic liquid crystals confined in spherical droplets and subject to radial strong anchoring. Equilibrium configurations of the order-parameter tensor field in a Landau-de Gennes free energy are numerically modeled using a finite-element package. Within the class of axially symmetric fields, we find three distinct solutions: the familiar radial hedgehog, the small ring (or loop) disclination predicted by Penzenstadler and Trebin, and a solution that consists of a short disclination line segment along the rotational symmetry axis terminating in isotropic end points. Phase and bifurcation diagrams are constructed to illustrate how the three competing configurations are related. They confirm that the transition from the hedgehog to the ring structure is first order. The third configuration is metastable (in our symmetry class) and forms an alternate solution branch bifurcating off the radial hedgehog branch at the temperature below which the hedgehog ceases to be metastable. Dependence on temperature, droplet size, and elastic constants is investigated, and comparisons with other studies are made.

Streamline Image Analysis: a new tool for investigating defects in nematic liquid crystals

A bidimensional investigation of the director field near defects normal to the symmetry plane in a nematic liquid crystal is here presented, based upon a new 'streamline' image processing of the data obtained by polarized light microscopy. With a visualization of vector field streamlines related to the actual director configuration, the disclination topological strength is revealed. The streamline visualization is also suitable for detecting smooth local variations of the director of field as functions of both space and time. Moreover, the orientation of the director field projection in the cell plane is determined with high sensitivity (2%) and the possible presence of the out-of-plane escape of the director field is evaluated.

Critical radius of loop defects in homeotropic nematic liquid crystals

We describe an experimental situation with a looped line defect in nematic liquid crystals observed by polarizing optical microscopy. We measured the critical size of the loop below which it spontaneously shrinks and transforms into a point defect. The experiment was done with 5CB which gives rise to twist disclinations as do most of the usual nematics. For this kind of disclination an in-plane force due to the boundary conditions acts on the line and influences the critical radius. W e have constructed a model which is in good agreement with experimental measurements and deduced the line tension of the disclination.

Dynamics of point defects in nematic liquid crystals

The topological theory of defects assigns a charge to every point defect exhibited by nematic liquid crystals. Complex phenomena have been observed in capillary tubes involving the appearance and the disappearance of periodic arrays of defects with alternating sign of the charge. Here we move a step towards understanding these phenomena by considering a simple system, which would serve as an instructive example. We develop a mathematical model fit to describe the evolution in time of three defects. We write the differential equations that rule this peculiar dynamical system: they show, in particular, how a defect is dragged in the wake of another with a velocity which depends on the distance between them.

Modelling the capillary locking of point defects in nematic liquid crystals

It has long been known that the equilibrium configuration with minimum energy of a nematic liquid crystal within a cylinder subject to homeotropic conditions on the lateral boundary is escaped along the axis of the cylinder, and there is no singularity of the orientation field. So problems of explaining the presence of point defects in capillary tubes and of exploring their stability arise. There is enough evidence to believe that the menisci play a central role in preventing the orientation field around a point defect from unwinding towards the escaped configuration. We propose a variational model which describes how a point defect interacts with a meniscus. This interaction fades away at a finite distance. When active, it is two-sided, being repulsive at first and then attractive when the defect comes closer to the centre of curvature of the meniscus. Thus, when a defect is enclosed between two menisci they can become antagonists, so that there is a metastable equilibrium position where the defect could be locked in.

Disclination Loop in Mori-Nakanishi Ansatz: Role of the Divergence Elasticity

Energetic stability of loop defects in nematic liquid crystal is analyzed using Mori-Nakanishi ansatz and Frank-Oseen theory with non-zero K 24 divergence term. The ratio of the bulk and divergence elastic constants defines a characteristic material length, which is the equilibrium radius a* of the disclination ring. Positive K 24 forces the ring to shrink.

The Topological Microstructure of Defects In Nematic Liquid Crystals

We study the core of line and point defects in nematic liquid crystals. The topological theory of defects allows us to prove that a uniaxial nematic has two ways to avoid a topologically stable defect: either it melts, by becoming isotropic on the putative defect, or a complex biaxial structure arises, that we describe in the paper.

Annihilation of point defects in nematic liquid crystals.

Point defects are likely to be generated in the process of filling a capillary tube subject to homeotropic conditions on the boundary. There is plenty of experimental evidence to hold that, when two defects with opposite topological charge happen to be closer than a critical distance, they attract each other. At first, they move very slowly; then, as the distance between them becomes less than a diameter, their relative speed increases dramatically, until they annihilate one other. In this paper we describe, by means of a simple dynamical model, the attraction and annihilation of two defects in an infinite tube. We write the balance between the rate of change in the elastic free energy and the energy dissipated in the director motion. Hence, we derive and solve the differential equation that describes the evolution in time of the distance between the defects. The outcomes of our analysis confirm many qualitative aspects of the experimental evidence. \textcopyright{} 1996 The American Physical Society.

Alignment tensor versus director: Description of defects in nematic liquid crystals.

The core structure of nematic defects cannot be represented by the usual director field, but requires the description by the full orial calculus.

On the Formation and Motion of Defects in Nematic Liquid Crystals

On the Formation and Motion of Defects in Nematic Liquid Crystals

Numerical Minimization of the Landau-de Gennes Free Energy: Defects in Cylindrical Capillaries

Abstract In order to study the structure of defects in nematic liquid crystals, we have constructed a numerical procedure that minimizes the Landau-de Gennes free energy model. Using a new representation, a finite-element discretization, and a direct minimization scheme based on Newton's method and successive overrelaxation, this procedure determines the order parameter tensor field in three dimensions for a general physical problem with Dirichlet boundary conditions. As a sample problem, we have considered a nematic liquid crystal in a cylindrical capillary with boundary conditions that necessarily give rise to at least one defect. We find that for our parameters, two biaxial defects appear near the ends of a capillary with homeotropic alignment, and that near the center, the director is perpendicular to the axis of the cylinder.

Nonlinear theory of defects in nematic liquid crystals; Phase transition and flow phenomena

AbstractThis is a summary of some recent mathematical advances in the theory of defects in nematic liquid crystals. It also includes some new results concerning disclinations (line defects) which have not been published elsewhere.