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.     

Inclusions in Smectic C Films as Modeled by Disclinations

A simplified model of an inclusion represented by (+1)-wedge disclination and two accompanying (– 1/2)-wedge disclinations on the surface of inclusion in smectic C free standing films is used to describe the elastic interaction of inclusions. The orientation of the axis connecting positions of all three disclinations relatively to the director orientation at far distances due to elastic anisotropy is investigated. The configuration with the lowest director perturbations and the lowest anisotropy elastic energy is such that the axis connecting disclinations is parallel to the distant director orientation. The interaction between inclusions at far distances is quadrupolar. The chaining of inclusions is approximately described considering their repulsion due to molecular anchoring at inclusion surfaces.     

Arrays of Charged (±2π)-Twist Disclinations in Ferroelectric Liquid Crystals

The notion of an electrostatic charge of (±2)-twist disclinations is used to approximate the evaluation of the electrostatic interaction energy among disclinations forming arrays in finite samples of ferroelectric chiral smectic C liquid crystals. Screening effects of free charges in a material surrounding the disclination are taken into account by introducing a phenomenological depolarisation factor.The electrostatic interaction energy is important in chiral smectic C materials with high values of the spontaneous polarisation when screening effects of free charges are small. Then the electrostatic interaction leads to elimination of disclinations from the sample. When there is a high concentration of free charges in the sample (smaller value of depolarisation factor), the electrostatic interaction energy is of the order of the elastic interaction energy of disclinations what influences the equilibrium of disclination arrays in the sample. Two disclination configurations are considered. In the Brunet-Williams configuration the disclinations of opposite topological charge have also the opposite electrostatic charge so their attraction is augmented. This attraction can be balanced by the helical structure in the central part of the sample when the sample thickness is rather high.On the contrary, in the Glogarová-Pavel configuration the disclinations of opposite topological charge have the electrostatic charge of the same sign. The equilibrium in this configuration is either a balance of elastic attraction and electrostatic repulsion if elastic and Coulomb forces are of the same order or it is governed by the value of the anchoring energy when electrostatic interaction prevails over the elastic one.     

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.     

Twist disclination system in a planar sample of chiral smectic C* liquid crystal

In thick samples of Sm C^* liquid crystals the helicoidal structure in the sample centre is connected to the unwound structure near sample surfaces by a regular system of (?2π) and (+2π)-twist disclinations associated in rows near the upper and lower sample surfaces. The geometry and stability of such a disclination system in a high electric field is investigated and the critical electric field causing the disclination annihilation is estimated. The mutual disclination annihilation is the proposed mechanism for the field induced transition from helicoidal Sm C^* structure to unwound Sm C^* structure with the twist along the sample thickness.     

Interaction of an inclusion and (±1)-wedge disclination in smectic C free standing films

The interaction between an inclusion and (±1)-disclination situated near it in smectic C free standing films is investigated. The inclusion is modelled by the simplified model of an inclusion represented by (+1)-wedge disclination in the inclusion centre and two (−1/2)-wedge disclinations at opposite positions on the inclusion surface. New positions of (−1/2)-wedge disclinations due to the elastic interaction with (±1)-disclination were determined.     

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.     

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.     

Twist disclination loops in chiral smectic C liquid crystals

The notion of an infinitesimal twist disclination loop known from solids is introduced into a chiral smectic C liquid crystal with parallel layers. Finite rectangular and straight twist disclinations are described as a synthesis of a planar distribution of infinitesimal loops. Then a small impurity which disturbs only the molecular arrangement in one smectic layer is modelled by a pair of infinitesimal twist disclination loops. The interaction between a 2π-twist disclination and a small impurity is estimated using the interaction energy between a straight 2π-twist disclination and an infinitesimal twist disclination loop.     

Electronic structure of carbon nanoparticles

The electronic structure of graphitic nanoparticles is investigated within a gauge field-theory model. The local and total densities of states (DOS) near the pentagonal defects (disclinations) are calculated for three geometries: sphere, cone, and hyperboloid. It is found that the low-energy electron states have a rather specific dependence on both the energy and the distance from a disclination line. In particular, the low-energy total DOS has a cusp that drops to zero at the Fermi energy for disclinations with the Frank index v<1/2, while a region of a nonzero DOS across the Fermi level is formed for v=1/2. The true zero-mode fermion state is found for the graphitic hyperboloid. The appearance of an enhanced charge density near the Fermi level for nanocones with a 60° opening angle (180° disclination) is predicted.     

Dislocation and disclination loops in the virtual-defect method

A method of virtual circular defect loops is developed for determining the elastic fields produced by defects in a bounded medium in the case of an axially symmetric geometry. In this method, continuously distributed virtual circular Volterra and Somigliana dislocation loops are adjusted in such a way as to satisfy the boundary conditions imposed at free surfaces and interfaces. Original calculations of the elastic fields of circular defect loops of different types are carried out. The elastic fields are found for the case of straight dislocations and disclinations in a plate that are perpendicular to the plate plane and for the case of circular disclination loops parallel to the plate plane or to an interface.     

Misfit dislocations in thin films on plastically deformed substrates

A theoretical model describing the nucleation of misfit dislocations (MD) in interfaces between films and plastically deformed substrates with disclinations is proposed. The ranges of the parameters (disclination strength, density of the disclination ensemble, film thickness, and degree of misfit) within which MD nucleation is energetically favorable are found. It is shown that at certain strengths of disclinations and densities of their ensemble the critical thickness of the film on a plastically deformed substrate with disclinations can exceed that on an undeformed defect-free substrate by a few times.     

Charged ±2π-twist Disclinations in Ferroelectric Liquid Crystals

The electrostatic charge of (±2)-twist disclinations in ferroelectric chiral smectic C liquid crystals is introduced as an approximation in order to simplify the evaluation of the electrostatic self-energy of disclination. As an example, electrostatic charges of (±2)-twist disclinations in an infinite sample are evaluated. Screening effects of free charges in a material and of the ferroelectric structure surrounding the disclination are taken into account by introducing a phenomenological depolarization factor.     

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     

Simulation of the dynamics of a two-dimensional dislocation-disclination ensemble

A computer code for simulating the dynamics of an arbitrary 2D dislocation-disclination ensemble is developed. The code is constructed according to the molecular-dynamics principles; individual interacting particles are taken to be edge dislocations and dipoles of partial wedge disclinations. Pure copper is considered as an example for simulating the glide of one dislocation near an immobile dipole for various orientations of the dipole and under various initial conditions of the problem. The dislocation dynamics is shown to be mainly determined by the distribution of the elastic field of the disclination dipole rather than by the initial velocity of the dislocation.     

On the annealing of junction disclinations in deformed polycrystals

The kinetics of relaxation of disclination quadrupoles formed within triple junctions of grains during plastic deformation are studied. The calculations are made using the discrete dislocation model for disclinations by simulating the climb of dislocations. Exponential relationships are obtained for the relaxation of the strength and elastic energy of disclination quadrupoles with a characteristic time proportional to the cube of grain size. The distribution of vacancy fluxes along grain boundaries (GBs) during the relaxation of a disclination quadrupole is studied in detail. The relation between continuum and discrete dislocation approaches to a study of the GB recovery process is considered. Characteristics of each relaxation stage are studied. A hierarchy of characteristic relaxation times for dimerent grain size ranges is constructed and it is show that in nanocrystalline materials the spreading time of trapped lattice dislocations can depend on the grain size.     

Hydrodynamics of pair-annihilating disclinations in SmC films

The pair annihilation of smectic c-director defects with winding numbers +/-1 in a freestanding SmC film as a representative of the XY model is studied numerically, considering a full coupling of orientational degrees of freedom and hydrodynamics. A reduction of the annihilation time compared to the nonhydrodynamic treatment is observed. It is demonstrated that the +1 disclination moves considerably faster than the -1 one primarily due to hydrodynamic flow, weakly assisted also by elastic anisotropy. The stress tensor terms and material parameters relevant for this effect are identified.     

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)