Structure and dynamics of the Frenkel-Kontorova dislocations in electroconvection in liquid crystals

The Frenkel-Kontorova instability is studied in a 1D lattice of domains formed during electroconvection in nematic liquid crystals twisted by π/2. It is found that generation of defects by such instability can be observed in this model medium. Among other things, it is shown that several types of defects with singular and nonsingular cores, as well as with a extended core, are formed in the 1D domain structure above the electroconvective instability threshold. The extended cores of dislocations are dissociated into a line, and the entire structure is isomorphic to two partial dislocations spaced by a certain distance, which are not observed in free form. Defects with a nonsingular core (zero topological index) exist owing to spiral hydrodynamic flows in convective rolls and are not observed in layers with a homogeneous orientation of molecules. It is shown that the formation of both types of defects follows the scenario of decay of dislocations with extended cores via detachment of nonsingular defects (i.e., discretely); as a result, a dislocation with a singular core is left. “Breather” defects, which are the result of periodic creation and annihilation of dislocations with a topological index of ±1, are also observed. The effect of defects on the transition from the 1D to 2D structures is considered.     

Breathers in the one-dimensional roll structure of twisted nematics

The dynamics of nonsingular defects has been studied experimentally and theoretically in the periodic roll structures arising at electroconvection in nematic liquid crystals twisted by π/2. The presence of an axial component of the velocity of the hydrodynamic flow with the opposite direction in the neighboring rolls is characteristic of roll structures in twisted nematics. The quantitative estimates of the critical frequency of the oscillations of structural defects have been obtained on the basis of the nonlinear equation of motion for the roll displacement. It has been found that the periodic creation and annihilation of a pair of edge dislocations with the topological indices +1 and −1 occur in the process of oscillations of a defect with a nonsingular nucleus. It has been demonstrated that oscillating defects with zero topological indices correspond to the solution of the sine-Gordon equation in the form of standing breathers.     

Experimental verification of the theory of electrohydrodynamic instability in nematic liquid crystals

Williams domains threshold voltage are given as functions of dielectric and conductivity anisotropy. Experimental data confirm the theory of electrohydrodynamic (EHD) instability in nematic liquid crystals (NLC) based on Helfrich's model and taking into account the boundary conditions.     

Flexoelectric origin of oblique-roll electrohydrodynamic instability in nematics

We develop the theory of electrohydrodynamic instability in nematic liquid crystals by incorporating the flexoelectric terms. Using a one-dimensional linear analysis of the problem for an applied DC field, we demonstrate that for the usual materials the rolls have an oblique orientation as has been found experimentally. We also provide an experimental evidence for the strong flexoelectric influence on the director profile in the rolls.     

Breatherlike defects and their dynamics in the one-dimensional roll structure of twisted nematics

The dynamics of the nonsingular defects in the periodic structures of the rolls that appear in π/2-twisted nematic liquid crystals during electroconvection is studied experimentally and theoretically. The roll structures in twisted nematics are characterized by the presence of an axial component of the hydrodynamic flow velocity with opposite directions in neighboring rolls. The critical oscillation frequency of structural defects is quantitatively estimated using a nonlinear equation of motion for roll displacements. It is found that a pair of edge dislocations with topological charges of +1 and–1 nucleates and annihilates periodically during the oscillations of a defect with a nonsingular core. Oscillating defects with a zero topological charge is shown to correspond to the solution of the sine-Gordon equation in the form of standing breathers. Asymmetry is detected in the full oscillation cycle of a breather defect, and it is related to the twist symmetry of a twist nematic. This asymmetry is taken into account as effective anisotropic friction. The behavior of a breather on a trap, namely, a classical defect (dislocation), is investigated. Dislocation motion is shown to be anisotropic in the oscillation cycle: in one direction, a dislocation moves regularly; in the second phase, the transition into the initial state proceeds via the decay of the breather into a dipole pair of dislocations of opposite signs followed by their annihilation.     

Self-organization processes and topological defects in nanolayers in a nematic liquid crystal

Atomic force microscopy is used to study the self-organization processes that occur during the formation of topological defects in nanomolecular layers in a nematic liquid crystal with the homeotropic orientation of its molecules with respect to the substrate. In this case, a smectic monolayer with a thickness of one molecule length (about 2.2 nm) forms on the substrate, and a nanomolecular layer of a nematic liquid crystal forms above this monolayer. In such virtually two-dimensional layers, numerous different nanoclusters, namely, hut structures, pyramids, raft structures with symmetry C _nm (where n = 2, 4, 5, 6, 7, …, ∞), cones, and nanopools, form [1]. They have a regular shape close to the geometry of solid crystals. Modulated linear structures and topological point defects appear spontaneously in the nanopools and raft structures.     

Healing of defects at the interface of nematic liquid crystals and structured Langmuir-Blodgett monolayers

We use Langmuir-Blodgett molecular monolayers and nematic liquid crystals as model two- and three-dimensional orientationally ordered systems to study the stability and healing of topological defects at their contact interfaces. Integer-strength defects at the monolayer induce disclinations of similar strength in the nematic that, however, do not propagate deep into the bulk, but rather form single- or double-split arch-shaped loops pinned to the interface. This behavior is qualitatively independent of the far-field director orientation and involves either half-integer singular or twist-escaped unity-strength nonsingular nematic disclinations. These two defect configurations can be selected by varying sample preparation given their comparable free energy, consistently with direct probing by use of laser tweezers.     

Asymmetry of the time dynamics of breathers in the electroconvection twist structure of a nematic

Dynamics of breather defects in the periodic structures of rolls arising at electroconvection in nematic liquid crystals twisted by π/2 has been studied experimentally and theoretically. The axial components of the velocity of a hydrodynamic flow in the twist structures of nematics are opposite in the neighboring rolls. Dynamics of the breather defect is the periodic creation and annihilation of a pair of classical dislocations with the topological indices “+1” and “-1.” The annihilation occurs faster than the creation. It has been shown that the asymmetric time dynamics of the breather defect is described well by the solution of the perturbed sine-Gordon equation in the form of an interacting soliton and antisoliton.     

Localized electromagnetic modes and the transmission spectrum of a one-dimensional photonic crystal with lattice defects

The properties of localized electromagnetic modes in a one-dimensional photonic crystal with a structural defect layer were studied. The role of the defect was played by an anisotropic nematic liquid crystal layer. The frequency and the damping factor of defect modes were shown to substantially depend on the defect layer thickness and the orientation of the optical axis of the nematic. The transmission spectra of photonic crystals with one and two lattice defects were studied. Taking into account the special feature of nematic liquid crystals distinguishing them from usual crystals, namely, large permittivity anisotropy, it was shown that the transmission spectrum of the photonic crystal could be controlled by varying the orientation of the optical axis of the nematic, for instance, under the action of an external electric field.     

Liquid-crystal defects and confinement in Yang-Mills theory

It has been shown that, in the Landau gauge of the SU(2) Yang-Mills theory, the residual global symmetry supports the existence of topological vortices which resemble disclination defects in nematic liquid crystals and Alice (half-quantum) vortices in superfluid ³He in the A-phase. The theory also possesses half-integer and integer-charged monopoles, which are analogous to the point-like defects in nematic crystal and in liquid helium. We argue that the deconfinement phase transition in the Yang-Mills theory in the Landau gauge is associated with the proliferation of these vortices and/or monopoles. The text was submitted by the author in English.     

Structure changes induced by external multiplicative noise in the electrohydrodynamic instability of nematic liquid crystals

We study the influence of external multiplicative noise on the electrohydrodynamic instability (EHD) in nematic liquid crystals. It turns out that the correlation time _n and the intensityQ of the noise are the crucial parameters to control the system. Different types of noise lead to minor quantitative changes when compared to Gaussian white noise, leaving the qualitative aspects unchanged. With increasing noise intensity the threshold for the onset of the first instability changes drastically. We observe that the curvature arising when the threshold of the various instabilities is plotted as a function of the noise intensity changes as one is going, e.g., from the onset of Williams domains (WD) to the onset of the grid pattern (GP). This result reflects the transition in the flow structure from two-dimensional (WD) to three-dimensional (GP, DSM) flow patterns. As the intensity of the noise is increased further, the onset of the first instability becomes more complex. The measurement of the nonlinear onset time shows a strong dependence on the noise intensityQ, which is linear for WD and GP well above onset. The linear onset time shows an unexpected dependence on the noise intensity close to the onset of the first instability. For sufficiently long correlation times of the noise, a destabilization by noise is obtained.     

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.     

Molecular orientations and photorefractive effects in C60-doped liquid crystals with capillary-flow-induced alignment

Molecular orientations and photorefractive effects of C₆₀-doped nematic liquid crystals were investigated with layer-structured liquid crystal cells where a nematic phase was injected. Regardless of the surface treatments of the layers, liquid crystals injected with nematic phase showed a higher degree of director orientation and photorefractivity than those injected with an isotropic phase. The nematic alignment of liquid crystals in an untreated cell is generated by a capillary flow of liquid crystal during the nematic injection. However, it was observed that the grating formation was delayed a little longer with injection of nematic phase than with injection of isotropic phase. Received: 11 March 2002 / Revised version: 22 April 2002 / Published online: 12 July 2002     

Nematic liquid crystal around a spherical particle: Investigation of the defect structure and its stability using adaptive mesh refinement

We investigate the orientation profile and the structure of topological defects of a nematic liquid crystal around a spherical particle using an adaptive mesh refinement scheme developed by us previously. The previous work [J. Fukuda et al., Phys. Rev. E 65, 041709 (2002)] was devoted to the investigation of the fine structure of a hyperbolic hedgehog defect that the particle accompanies and in this paper we present the equilibrium profile of the Saturn ring configuration. The radius of the Saturn ring r_d in units of the particle radius R₀ increases weakly with the increase of , the ratio of the nematic coherence length to R₀. Next we discuss the energetic stability of a hedgehog and a Saturn ring. The use of adaptive mesh refinement scheme together with a tensor orientational order parameter allows us to calculate the elastic energy of a nematic liquid crystal without any assumption of the structure and the energy of the defect core as in the previous similar studies. The reduced free energy of a nematic liquid crystal, , with L₁ being the elastic constant, is almost independent of in the hedgehog configuration, while it shows a logarithmic dependence in the Saturn ring configuration. This result clearly indicates that the energetic stability of a hedgehog to a Saturn ring for a large particle is definitely attributed to the large defect energy of the Saturn ring with a large radius.Received: 10 December 2003, Published online: 2 March 2004PACS: 61.30.Cz Molecular and microscopic models and theories of liquid crystal structure - 61.30.Jf Defects in liquid crystals - 82.20.Wt Computational modeling; simulation     

The domain structure of a nematic liquid crystal layer in an oscillating poiseuille flow

A spatially periodic structure arising in a nematic liquid crystal layer with planar orientation under the effect of an oscillating Poiseuille flow is described theoretically. The effect is analyzed on the basis of hydrodynamic equations of nematic liquid crystals, from which a self-consistent set of equations for perturbations of hydrodynamic variables is separated. It is demonstrated that the structure type and the threshold parameters of the effect depend on the frequency and the layer thickness through the scaling combination ωh ². The dependence of the configuration of arising distortions on the value of viscosity α₃ is analyzed.     

Phase transition in ellipsoidal droplets of nematic liquid crystals

We developed a simple method for the calculation of the director field distribution in the droplets of nematic liquid crystals (LCs) of any shape, allowing for the interaction of LCs with the droplet surface, as well as the influence of constant electric field. In contrast to different approaches, the approach that is developed in the present paper does not require any simplifying suppositions about the structure of the LC director field. The elastic-continuum theory is used, complemented with the possibility of consideration of point and linear defects. Calculations are performed using the Monte Carlo method on a simple grid. The triangulation technique is used to take the boundary conditions of droplets of a complex shape into account. The developed approach can be used for investigation of the properties of polymer-dispersed liquid crystals (PDLCs). The topological phase transitions in the nematic LC 4-cyano-4′-pentyl-biphenyl (5CB) in spherical and ellipsoidal droplets are investigated in this paper.     

Flexoelectric origin of oblique rolls with helical flow in electroconvective nematics under DC excitation

We present a 3-dimensional, linear analysis of electrohydrodynamic (EHD) roll instability in a nematic liquid crystal under DC excitation. It is shown that the flexoelectric effect leads to a new symmetry of the flow pattern, viz. ahelical flow inoblique rolls. Our experimental observations agree with the theoretical predictions.     

弱锚泊对液晶微波相位调制的影响

液晶对微波的调制取决于外加电压作用下液晶分子的取向, 而基板的锚泊对液晶取向有重要影响, 必然导致微波调制的变化. 本文研究了无手性掺杂的弱锚泊90°扭曲向列相液晶的微波调制特性. 基于液晶弹性理论和变分原理得到了液晶盒系统的平衡态方程和边界条件, 采用差分迭代方法数值模拟了不同锚定强度大小和不同预倾角下单位长度相移随电压的变化. 结果表明: 1)预倾角对微波相移的影响与施加电压有关. 当液晶盒施加电压为0.5–1.6 V之间时, 随预倾角增大, 单位长度微波相移及其与强锚泊0°预倾角90°扭曲液晶相移差均增大, 且相移差达到最大时的电压值也随倾角增大而减小; 1.6–3.0 V之间, 单位长度微波相移及相移差随预倾角增大而减小; 1.6 V附近及3.0 V之后, 相移基本没有变化. 2)表面锚定强度大小对微波相移的影响非常大. 随锚定强度减小, 单位长度微波相移及相移差均会增大, 微波相移的可调范围也增大, 且增加越来越明显. 此研究为液晶微波调制器件的设计提供了理论依据.     

Relaxation of the director field in the form of a traveling wave in twisted nematic cells

The orientational relaxation of the director field toward its equilibrium orientation in the form of a traveling wave is investigated. It is shown that the nonlinear relaxation can occur in the form of a traveling wave in a twisted nematic cell under specific conditions for the external electric field and material parameters characterizing the nematic liquid crystal. The calculations of the relaxation processes in the form of traveling waves have demonstrated that these nonlinear processes in the twisted nematic cell proceed more easily when the initial perturbation of the director is induced in the vicinity of one of the bounding cell surfaces.