Branching chains and critical clusters of Ising spins

Ising critical clusters are related to the excess of neighbor spins of similar, over anti-similar, orientation. The clusters are approximately described by self-avoiding branching chains. γ, ν andalso a “time” (of growth from the origin) and a “perimeter/bulk” exponent are measured with the help of Monte-Carlo sampling.     

Light-driven oscillations of entangled nematic colloidal chains

Laser tweezers have been used to drive the oscillations of a chain of entangled colloidal particles in the nematic liquid crystal 5CB. The amplitude and phase of light-driven oscillations have been determined for the motion of individual colloidal particles. The collective motion of 4.8μm silica particles is highly damped for a driving frequency above 0.5Hz. The results were compared to an effective bead-spring model, where the motion of elastically coupled particles is hindered by viscous damping and hydrodynamic coupling. Qualitative agreement between theory and experiment was obtained.     

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.     

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.     

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.     

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.     

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     

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.     

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.     

Dispersion and absorption of sound in nematics

The unified hydrodynamic theory for systems with a liquid crystalline phase is generalized to include a frequency dependence of the elastic and dissipative parameters of the system. Application is made to nematics for which the frequency dependent anisotropies of the velocity and absorption of sound are calculated. It is shown that the relaxation approximation for the dispersion leads to reasonable results.     

Disclinations in nematics in the presence of flexoelectricity

The stability problems of wedge disclinations (with pure splay and bend distortions) in nematic liquid crystals (NLC) are considered in the presence of flexoelectricity. We write NLC director equations in the cylindrical coordinate system, taking into account flexoelectricity. These equations allow us to solve many interesting problems on the influence of flexoelectricity on the orientational structures of NLC. In particular, it is shown that the line of disclination with radial distribution of director can be stabilized in the presence of flexoelectricity even far from nematicsmectic phase transition point. For the disclination with azimuthal distribution of director for all physical sizes the line is not stable and escapes in the third dimension.     

Isotropic phase of nematics in porous media

We study the effect of random porous matrices on the isotropic-nematic phase transition. Sufficiently close to the cleaning temperature, both random field and thermal fluctuations are important as disordering agents. A novel random field fixed point of the renormalization group equation was found that controls the transition from isotropic to the replica symmetric phase. Explicit evaluation of the exponents in d = 6 ? ε dimensions yields to a dimensional reduction and three-exponent scaling.     

Optical Freedericksz transitions in twisted planar nematics

Summary We study the propagation of an elliptically polarized light beam normally incident onto a twisted nematic liquid-crystal film. A set of nonlinear differential equations for the molecular director and the polarization of the light beam is derived; it is solved analytically in the limit of small perturbations around the steady-state solutions that represent the nonreoriented sample. We prove that optical Freedericksz transitions are possible only for a particular polarization state of the incident light. The threshold behaviour is studied as a function of the light intensity and of the twist angle between the molecular directors at the sample walls. The results are characteristic of the optical interaction and have no analogue in the molecular reorientation induced on such a system by d.c. fields.

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Riassunto Si è studiata la propagazione di un fascio di luce polarizzata ellitticamente che incide normalmente su un campione di cristallo liquido nematico planare ?twisted?, cioè nel quale l'angolo α fra la direzione delle molecole nel piano di ingresso della luce e quella nel piano di uscita è≠O. è stato derivato un sistema non lineare di equazioni differenziali che governa l'evoluzione del direttore molecolare e dello stato di polarizzazione della luce. Questo sistema è stato risolto analiticamente nel limite di piccole variazioni intorno a soluzioni corrispondenti allo stato imperturbato. Si è dimostrato che transizioni di Freedericksz ottiche sono possibili solo se la luce incidente si trova in un particolare stato di polarizzazione. I risultati ottenuti sono peculiari dell'interazione ottica e non sono riconducibili al fenomeno della riorientazione molecolare indotta su campioni di questo tipo da campi statici, elettrici o magnetici.

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Резюме Мы исследуем распространение эллипчески поляриэованного светового пучка, падаюшего номально на пленку эакрученного нематического жидкого кристалла. Выводится система нелинейных дифференциальиых уравнений для молекулярного директора и поляриэации светового пучка. Полуенная система решается аналитчески в пределе малЫх воэмущений относительно решений для стционарнЫх состояний, которЫе соответствуют не-переориентированному обраэцы. МЫ докаэЫваем, что оптические перехоые фредерикса воэможиы только для частично поляриэованного состояния падаюшего света. Исследуется пороповое поведение как функция интенсвности света и упла эакручивания между молекуляриыми директорами на стенках обраэца. Полученные реэультаты являются характерными для оптического вэаимодействия и не имеют аналога при молекулярной переориентации, индуцрованной в такой системе d.c. полями.