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.     

Dynamics of nematic liquid crystal disclinations: the role of the backflow

We measure the electric-field-driven annihilation of nematic disclination pairs with strength +/- 1/2 in the 4-cyano-4'-n-pentylbiphenyl (5CB) liquid crystal. The use of a very weak azimuthal anchoring ensures a two-dimensional director field. The relaxation is governed by the formation of a pi wall connecting the two opposite charge defects. The +1/2 disclinations move almost twice as fast as the -1/2 disclinations. The simple used geometry allows a quantitative comparison with numerical studies based on the hydrodynamics of the tensorial order parameter. The simulations show that in the pi wall regime the symmetry breaking is due to the backflow and not to the elastic anisotropy.     

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.     

Topology and geometry of nematic braids

Topological analysis of disclinations in nematic liquid crystals is an interesting and diverse topic that goes from strict mathematical theorems to applications in elaborate systems found in experiments and numerical simulations. The theory of nematic disclinations is shown from both the geometric and topological perspectives. Entangled disclination line networks are analyzed based on their shape and the behavior of their cross section. Methods of differential geometry are applied to derive topological results from reduced geometric information. For nematic braids, systems of −1/2 disclination loops, created by inclusion of homeotropic colloidal particles, a formalism of rewiring is constructed, allowing comparison and construction of an entire set of different conformations. The disclination lines are described as ribbons and a new topological invariant, the self-linking number, is introduced. The analysis is generalized from a constant −1/2 profile to general profile variations, while retaining the geometric treatment. The workings of presented topological statements are demonstrated on simple models of entangled nematic colloids, estimating the margins of theoretical assumptions made in the formal derivations, and reviewing the behavior of the disclinations not only under topological, but also under free-energy driven constraints.     

Entangled nematic colloidal dimers and wires

It has been predicted, but never confirmed, that colloidal particles in a nematic liquid crystal could be self-assembled by delocalized topological defects and entangled disclinations. We show experimentally and theoretically that colloidal dimers and 1D structures bound by entangled topological defect loops can indeed be created by locally thermally quenching a thin layer of the nematic liquid crystal around selected colloidal particles. The topological entanglement provides a strong stringlike binding, which is ten thousand times stronger compared to water-based colloids. This unique binding mechanism could be used to assemble resonator optical waveguides and robust chiral and achiral structures of topologically entangled colloids that we call colloidal wires.     

Elastic properties of nematoid arrangements formed by amoeboid cells

In culture migrating and interacting amoeboid cells can form nematoid arrangements in analogy to a nematic liquid crystal phase. A nematoid arrangement is formed if the interaction has an apolar symmetry. Different cell types like human melanocytes (= pigment cells of the skin), human fibroblasts (= connective tissue cells), human osteoblasts (= bone cells), human adipocytes (= fat cells) etc., form a nematoid structure. Our hypothesis is that elastic properties of these nematoid structures can be described in analogy to that of classical nematic liquid crystals. The orientational elastic energy is derived and the orientational defects (disclination) of nematoid arrangements are investigated. The existence of half-numbered disclinations shows that the nematoid structure has an apolar symmetry. The density- and order parameter dependence of the orientational elastic constants and their absolute values are estimated. From the defect structure, one finds that the splay elastic constant is smaller than the bend elastic constant (melanocytes). The core of a disclination is either a cell free space or occupied by non oriented cells (isotropic state), by a cell with a different symmetry, or by another cell type. Received 3 May 1999 and Received in final form 29 September 1999     

Micro-wires self-assembled and 3D-connected with the help of a nematic liquid crystal

We discuss a method for producing automatic 3D connections at right places between substrates in front of one another. The idea is based on the materialization of disclination lines working as templates. The lines are first created in the nematic liquid crystal (5CB) at the very place where microwires have to be synthesized. Due to their anchoring properties, colloids dispersed into the nematic phase produce orientational distortions around them. These distortions, which may be considered as due to topological charges, result in a nematic force, able to attract the colloids towards the disclinations. Ultimately, the particles get trapped onto them, forming micro- or nano-necklaces. Before being introduced in the nematic phase, the colloids are covered with an adhering and conducting polypyrrole film directly synthesized at the surface of the particles (heterogeneous polymerization). In this manner, the particles become conductive so that we may finally perform an electropolymerization of pyrrole monomers solved in 5CB, and definitely stick the whole necklace. The electric connection thus synthesized is analyzed by AFM, and its strength is checked by means of hydrodynamic tests. This wiring method could allow Moore's law to overcome the limitations that arise when down-sizing the electronic circuits to nanometer scale.     

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.     

Quantum spin nematics, dimerization, and deconfined criticality in quasi-1D spin-one magnets

We study theoretically the destruction of spin nematic order due to quantum fluctuations in quasi-one-dimensional spin-1 magnets. If the nematic ordering is disordered by condensing disclinations, then quantum Berry phase effects induce dimerization in the resulting paramagnet. We develop a theory for a Landau-forbidden second order transition between the spin nematic and dimerized states found in recent numerical calculations. Numerical tests of the theory are suggested.     

Transformation of director configuration upon changing boundary conditions in droplets of nematic liquid crystal

The transformation of the director configuration upon changing boundary conditions from planar to homeotropic for bipolar nematic droplets dispersed in a polymeric matrix was studied. The characteristic textural patterns are presented for droplets with different concentrations of homeotropic surfactants, and their orientational structure is identified. The scenario predicted earlier by G.E. Volovik and O.D. Lavrentovich (ZhETF 85, 1997 (1983)) for the transformation of orientational structure of nematic droplets from bipolar to radial, without the formation of additional disclinations, is revealed. It is shown that, by using the computational method of minimization of the director elastic-strain energy in the droplet bulk and by introducing the inhomogeneous boundary conditions, one can obtain orientational structures that are analogous to the observed ones.     

Imperfections in focal conic domains: the role of dislocations

It is usual to think of focal conic domains (FCDs) as perfect geometric constructions in which the layers are folded into Dupin cyclides about an ellipse and a hyperbola that are conjugate. This ideal picture is often far from reality. We have investigated in detail the FCDs in several materials that have a transition from a smectic A (SmA) to a nematic phase (N). The ellipse and the hyperbola are seldom perfect, and the FCD textures also suffer large transformations (in shape and/or in nature) when approaching the transition to the nematic phase, or appear imperfect on cooling from the nematic phase. We interpret these imperfections as due to the interaction of FCDs with dislocations. We analyze theoretically the general principles subtending the interaction mechanisms between FCDs and finite Burgers vector dislocations, namely the formation of kinks on disclinations, to which dislocations are attached, and we present models relating to some experimental results. Whereas the principles of the interactions are very general, their realizations can differ widely in function of the boundary conditions.     

Misfit disclinations at crystal/crystal and crystal/glass interfaces

Theoretical concepts have been developed for a new type of misfit defects, misfit disclinations, at crystal/crystal and crystal/glass interfaces. It is shown, in particular, that the formation of misfit disclinations is an efficient physical micromechanism of misfit stress relaxation at crystal/crystal interfaces. A model describing misfit disclinations at crystal/glass interfaces has been constructed. The energy characteristics of phase boundaries with misfit disclination ensembles are estimated. Fiz. Tverd. Tela (St. Petersburg) 41, 1637–1643 (September 1999)     

Topological aspect of disclinations in two-dimensional crystals

By using topological current theory, this paper studies the inner topological structure of disclinations during the melting of two-dimensional systems. From two-dimensional elasticity theory, it finds that there are topological currents for topological defects in homogeneous equation. The evolution of disclinations is studied, and the branch conditions for generating, annihilating, crossing, splitting and merging of disclinations are given.     

Spin glasses on the basis of rare earth metal compounds

A new class of materials is constructed of rare earth metals and their compounds by introduction of a large number of defects into the crystal lattice-dislocations and unelastic disclinations. It is shown that superconductive phase state is possible in these materials having spin glass magnetic structure. A technique of such a state observation is suggested.     

Deformation and fracture processes in graphene nanoribbons with linear quadrupoles of disclinations

The deformation and fracture processes in graphene nanoribbons containing linear quadrupoles of disclinations are investigated by the method of molecular dynamics. Special attention is given to estimating the effect of the curvature formed by disclinations and free boundaries in graphene nanoribbons with linear quadrupoles of disclinations on their mechanical characteristics (the stress–strain curve, the strength at the single-axis tension, and the degree of plastic deformation).     

Electro-optics of bipolar nematic liquid crystal droplets

We directly visualize the response and relaxation dynamics of bipolar nematic liquid crystal droplets to an applied electric field E. Despite strong planar anchoring, there is no critical field for switching. Instead, upon application of E, the surface region first reorients, followed by movement of the disclinations and the bipolar axis. After removing E, elastic forces restore the drop to its original state. The collective electro-optic properties of ordered hexagonal-close-packed monolayers of drops are probed by diffraction experiments confirming the proposed switching mechanism.     

Transition entropy of defect melting

We use the newly developed gauge theory of line-like defects to calculate, in the mean field approximation, the entropy for the combined proliferation of dislocations and disclinations. The result is ΔS ≈ 2.4 per site, in good agreement with the melting entropy in most materials.     

Structure,elasticity and phase transitions in liquid crystals with deformations

ABSTRACT

A molecular-statistical theory describing the nematic liquid crystals (LCs) with spherical inclusions (or point defects) is proposed. At given size of inclusions and nematic order parameters at the surfaces of inclusions (zero in the case of point defects) and far from inclusions (where the nematic LC is almost uniform), the distribution of nematic order parameters in the bulk of LC with inclusions was found to be fully determined by the elastic constants of LC. We have found and explained the two-step heat-driven transformation from the nematic phase into the isotropic phase, with the intermediate phase in between. The nematic order parameters and the elastic constants are evaluated in the framework of a unified approach based on the features of pair interaction potentials of the individual LC molecules. It is shown that, in the case of K₃₃ < K₁₁, the point defects should destroy the conventional nematic phase.     

Selective imaging of 3D director fields and study of defects in biaxial smectic A liquid crystals

We report on the selective imaging of different director fields in a biaxial smectic A (SmAb) liquid crystal using Fluorescence Confocal Polarizing Microscopy (FCPM) and Polarizing Microscopy (PM). The patterns of two directors, namely the director perpendicular to the lamellae and the director in their planes are visualized by doping the liquid crystal with two fluorescent dyes with different orientation of the transition dipoles with respect to the lamellar matrix. The properties of defects such as disclinations and focal conic domains (FCDs) are consistent with the non-polar D2h-symmetry of the SmAb mesophase in the studied mixture of bent-core and rod-like molecules: ([see full textsee full text]) majority of defects in the director are half-integer ±1/2 disclinations; ([see full textsee full text]) the integer-strength ±1 defects tend to split into the ± 1/2 disclinations. We compare the vertical cross-sections of the ±1 disclinations in the field in SmAb and uniaxial nematic samples. In SmAb, the ±1 disclinations do not escape into the third dimension, while in the nematic samples with Schlieren textures they do despite the surface anchoring at the plates; the experimentally determined director field around the escaped disclination capped by a pair of surface point defects – boojums matches the one predicted recently [C. Chiccoli et al., Phys. Rev. E 66, 030701 (2002)]. The FCD structure in SmAb is similar to that in SmA and SmC in terms of the normal to the layers but differs significantly in terms of the director field parallel to the smectic layers. The FCDs in SmAb can be associated with topologically non-trivial configurations of in the surrounding matrix that are equivalent to the disclination lines.