Interface in nematics

Summary The structures of the interface between an isotropic liquid and a nematic liquid crystal and also between different uniaxial nematic phases are studied. It is shown that, at a planar orientation in the case of the nematic-isotropic liquid interface and also at a mutually orthogonal orientation of the director in the case of two nematic phases, the interface has the structure of a biaxial nematic liquid crystal. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Giant flexoelectricity in polyvinylidene fluoride films

Recent studies have shown that giant flexoelectricity may exist in certain elastomers with bent-core molecular structures, which contradicts the previous theoretical estimation that the flexoelectric coupling is small in those materials. In this Letter, we report an analogous phenomenon, i.e., the giant direct flexoelectric effect, observed in a polyvinylidene fluoride (PVDF) film. Our experimental studies indicate that such an enhanced flexoelectric effect might be induced by the interaction between the energy couplings of the apolar and the polar molecular structures of the polymer film under elastic deformation.     

Stability of Disclinations in Nematic Liquid Crystals

In the light of φ-mapping method and topological current theory, the stability of disclinations around a spherical particle in nematic liquid crystals is studied. We consider two different defect structures around a spherical particle: disclination ring and point defect at the north or south pole of the particle. We calculate the free energy of these different defects in the elastic theory. It is pointed out that the total Frank free energy density can be divided into two parts. One is the distorted energy density of director field around the disclinations. The other is the free energy density of disclinations themselves, which is shown to be concentrated at the defect and to be topologically quantized in the unit of (k-k₂₄)π/2. It is shown that in the presence of saddle-splay elasticity a dipole (radial and hyperbolic hedgehog) configuration that accompanies a particle with strong homeotropic anchoring takes the structure of a small disclination ring, not a point defect.     

Mecanochromatic effect in nematics

We consider a nematic slab, with homeotropic boundary orientations (easy axis z) subjected to two simultaneous perturbations = a uniform shear flow along x and a magnetic field H oriented at 45° in the xz-plane. We find that, in a certain range of H-values, the orientation of the molecules in the mid plane of a thick slab does not correspond to a fixed angle = in this region the director rotates by many turns between the walls and the mid plane. In suitable cases, the periodicity may became comparable to an optical wavelength and the sample may become colored.     

Shear-flow-induced transition in nematics

The distortion, induced by a shear flow in a nematic (MBBA) layer having its director initially normal to the velocity and to the velocity gradient, has been observed by a conoscopic technique. At low velocity, the sample retains an ideal planar texture. Above a certain velocity threshold v_c, a distortion is observed. The threshold is inversely proportional to the sample thickness, and can also be modified by a magnetic field. These results are in agreement with a simple calculation based on the Leslie equations.     

Colloidal interactions in two-dimensional nematics

The interaction between two disks immersed in a 2D nematic is investigated i) analytically using the tensor order parameter formalism for the nematic configuration around isolated disks and ii) numerically using finite-element methods with adaptive meshing to minimize the corresponding Landau-de Gennes free energy. For strong homeotropic anchoring, each disk generates a pair of defects with one-half topological charge responsible for the 2D quadrupolar interaction between the disks at large distances. At short distance, the position of the defects may change, leading to unexpected complex interactions with the quadrupolar repulsive interactions becoming attractive. This short-range attraction in all directions is still anisotropic. As the distance between the disks decreases, their preferred relative orientation with respect to the far-field nematic director changes from oblique to perpendicular. Received 1 October 2002 and Received in final form 12 November 2002 RID="a" ID="a"e-mail: miko@cii.fc.ul.pt     

Active turbulence in active nematics

Dense, active systems show active turbulence, a state characterised by flow fields that are chaotic, with continually changing velocity jets and swirls. Here we review our current understanding of active turbulence. The development is primarily based on the theory and simulations of active liquid crystals, but with accompanying summaries of related literature.     

Representation of pair correlations in nematics

A complete expansion of equilibrium pair correlation functions for a uniaxial nematic phase composed of axially symmetric, non-polar and chiral molecules is proposed. Full advantage is taken of the symmetry of the nematic state and of the molecules. The explicit analysis and classification of the terms involving spherical harmonics with indices not exceeding 4 is given and illustrated using computer simulations for the nematic phase of a Gay-Berne mesogen. The theory is contrasted with the commonly used approach employing invariants that describe orientational correlations in molecular fluids. The role of the new representation in obtaining a correct understanding of a variety of observables, like the elastic constants, is demonstrated. In particular, the long-standing puzzle concerning the splay-bend degeneracy is resolved. Received 11 April 2000 and Received in final form 19 July 2000     

Disclinations in the nematic phase of a magnet with spin 1

Two-dimensional topological defects, spin disclinations, exist for a magnet with spin 1 and strong biquadratic interaction, in which the spin nematic state is realized. The spin disclinations have a nonsingular macroscopic core with a saturated magnetic moment and destroyed nematic order. These singular lines have common features with disclinations in nematic liquid crystals, singular disclinations in antiferromagnets, and magnetic vortices. However, significant differences of their properties from the above-mentioned topological defects also exist. The dynamic properties of a disclination in the spin nematic are characterized by the “freezing in the condensate” and by the gyroscopic force.     

Polarization-universal bandgap in periodically twisted nematics

Cholesteric liquid crystals are known to possess bandgap and exhibit strong reflection for one of two circular polarizations of light. We suggest a periodically twisted nematic liquid crystal as a medium, which possesses bandgap and exhibits strong reflection for any polarization of normally incident light. Two possible structures are considered: a sinusoidal modulation profile and a rectangular modulation profile. In both cases, the maximum bandgap of a periodically twisted structure is approximately twice as narrow as that of cholesterics. However, the polarization properties of these structures may make them more advantageous than cholesterics in a variety of applications.     

Excitable patterns in active nematics

We analyze a model of mutually propelled filaments suspended in a two-dimensional solvent. The system undergoes a mean-field isotropic-nematic transition for large enough filament concentrations, and the nematic order parameter is allowed to vary in space and time. We show that the interplay between nonuniform nematic order, activity, and flow results in spatially modulated relaxation oscillations, similar to those seen in excitable media. In this regime the dynamics consists of nearly stationary periods separated by "bursts" of activity in which the system is elastically distorted and solvent is pumped throughout. At even higher activity, the dynamics becomes chaotic.     

Topological defects in spherical nematics

We study the organization of topological defects in a system of nematogens confined to the two-dimensional sphere (S2). We first perform Monte Carlo simulations of a fluid system of hard rods (spherocylinders) living in the tangent plane of S2. The sphere is adiabatically compressed until we reach a jammed nematic state with maximum packing density. The nematic state exhibits four +1/2 disclinations arrayed on a great circle. This arises from the high elastic anisotropy of the system in which splay (K1) is far softer than bending (K3). We also introduce and study a lattice nematic model on S2 with tunable elastic constants and map out the preferred defect locations as a function of elastic anisotropy. We find a one-parameter family of degenerate ground states in the extreme splay-dominated limit K_{3}/K_{1}-->infinity. Thus the global defect geometry is controllable by tuning the relative splay to bend modulus.     

Theory of quantum Hall nematics

Transport measurements on two-dimensional electron systems in moderate magnetic fields suggest the existence of a spontaneously orientationally ordered, compressible liquid state. We develop and analyze a microscopic theory of such a "quantum Hall nematic" (QHN) phase, predict the existence of a novel, highly anisotropic q(3) density-director mode, find that the T = 0 long-range orientational order is unstable to weak disorder, and compute the tunneling into such a strongly correlated state. This microscopic approach is supported and complemented by a hydrodynamic model of the QHN, which, in the dissipationless limit, reproduces the modes of the microscopic model.     

Giant flexoelectricity of bent-core nematic liquid crystals

Flexoelectricity is a coupling between orientational deformation and electric polarization. We present a direct method for measuring the flexoelectric coefficients of nematic liquid crystals (NLCs) via the electric current produced by periodic mechanical flexing of the NLC's bounding surfaces. This method is suitable for measuring the response of bent-core liquid crystals, which are expected to demonstrate a much larger flexoelectric effect than traditional, calamitic liquid crystals. Our results reveal that not only is the bend flexoelectric coefficient of bent-core NLCs gigantic (more than 3 orders of magnitude larger than in calamitics) but also it is much larger than would be expected from microscopic models based on molecular geometry. Thus, bent-core nematic materials can form the basis of a technological breakthrough for conversion between mechanical and electrical energy.     

The Theory of the eleastic constants of nematics

Expressions are derived for the elastic constants of nematic liquid crystals by conceiving the molecular models as tensor fields. It is shown that the anisotropic part of the intermolecular pair potential can be dealt with completely.