高分子液晶向列相的向错结构

高分子液晶态向错结构在正交偏振片下呈现出具有不同数目黑刷子的纹影织构，是由于分子指向矢取向排列上的不连续性所引起的一种光学效应。近年来，高分子液晶态向错结构的研究已取得了较大进展，发展和应用片晶装饰、条带织构装饰和表面裂纹装饰等技术可以在电镜和偏光显微镜下直接观察各种向错结构。本文简要介绍高分子液晶态向列相的向错和反转壁结构的几何学、高强度向错以及近年在实验上观察各类型向错形态的研究进展。     

Critical radius of loop defects in homeotropic nematic liquid crystals

We describe an experimental situation with a looped line defect in nematic liquid crystals observed by polarizing optical microscopy. We measured the critical size of the loop below which it spontaneously shrinks and transforms into a point defect. The experiment was done with 5CB which gives rise to twist disclinations as do most of the usual nematics. For this kind of disclination an in-plane force due to the boundary conditions acts on the line and influences the critical radius. W e have constructed a model which is in good agreement with experimental measurements and deduced the line tension of the disclination.     

Critical radius of loop defects in homeotropic nematic liquid crystals

We describe an experimental situation with a looped line defect in nematic liquid crystals observed by polarizing optical microscopy. We measured the critical size of the loop below which it spontaneously shrinks and transforms into a point defect. The experiment was done with 5CB which gives rise to twist disclinations as do most of the usual nematics. For this kind of disclination an in-plane force due to the boundary conditions acts on the line and influences the critical radius. W e have constructed a model which is in good agreement with experimental measurements and deduced the line tension of the disclination.     

Theory and simulation of ovoidal disclination loops in nematic liquid crystals under conical confinement

We present analysis, scaling and modelling based on a previously presented nonlinear nonlocal nematic elastica equation of disclination loop growth in nematic liquid crystals con?ned to conical geometries with homeotropic anchoring conditions. The +1/2 disclination loops arise during the well-known planar radial to planar polar texture transformation and are attached to +1 singular core disclination at two branch points. The shape of the +1/2 loops is controlled by the axial speed of the branch points and the bending stiffness of the disclination both of which being affected by the confinement gradients (reduction in cross-sectional area) of a conical geometry. Motion towards the cone apex results in faster branch point motions and weaker curvature changes, but motion away from the apex results in slower branch point motion and stronger curvature changes. The simultaneous action of these effects results in novel ovoidal disclination loops. The numerical results are condensed into useful power laws and integrated into a shape/energy analysis that reveals the effects of confinement and its gradient on ovoidal disclination loops. These new findings are useful to characterise the Frank elasticity of new nematic mesophases and to predict novel defect structures under complex confinement.     

Nematodynamics and structures in junctions of cylindrical micropores

ABSTRACT

We explore equilibrium structures and flow-driven deformations of nematic liquid crystals confined to 3D junctions of cylindrical micropores with homeotropic surface anchoring. The topological state of the nematic ordering field in such basic unit of porous networks is controlled by nematic orientation profiles in individual pores, anchoring frustration along the edges of joining pores and coupling to the material flow field. We numerically investigate formation of the flow-aligned configurations in single cylindrical pores and pore junctions. Depending on the arrangement of inlet and outlet flows in the junction, we demonstrate existence of numerous stationary nematic configurations, characterised by specific bulk defects and surface disclinations along joining edges. Observed bulk defects are nonsingular escaped structures, disclinations in the form of loops or disclination lines pinned to the joining edges of the pores. Furthermore, we show examples of defect dynamics during the flow-induced topological transformations.     

Chirality-biased point defects dynamics on a disclination line in a nematic liquid crystal

Chiral additives in the nematic liquid crystal can alter the dynamics of point defects moving on a disclination line. They exert a constant force on defects, leading to the bimodal distribution of distances between them at long times. The evolution of the system of defects in the presence of chiral additives provides a very direct proof of the existence of repulsive forces between the defects at large distances. We find that addition of a sufficient amount of chiral compound removes all point defects from the system. The process is studied in the system of 8CB (4-n-octyl-4'-cyanobiphenyl) doped with the chiral compound S811 (from Merck Co.) and in the computer simulations.     

Simulation of texture evolution for nematic liquid crystalline polymers under shear flow

The development of microstructure in nematic liquid crystalline polymers under shear flow is investigated through computational simulation. By using a tensorial expression for the elastic torque, the nemato-dynamic equation is numerically resolved. The simulation shows that elastic anisotropy has a strong influence on the evolution of the director and that the ‘log-rolling’ orientation of the directors emerges for tumbling nematics if the twist constant is smaller than the splay and the bend constants, even though one starts from a structure in which the directors are aligned within the velocity and velocity gradient plane. The interaction of wedge disclination pairs subject to a shear flow field is also simulated. The generation, multiplication and interaction of inversion wall defects during shearing have been revealed. In general the wall moves to the boundaries and is absorbed by the boundaries. When two walls of opposite orientation meet, a loop may form, then shrink, and finally collapse. Correspondingly, if they have the same orientation, commutation will occur.     

Simulation of texture evolution for nematic liquid crystalline polymers under shear flow

The development of microstructure in nematic liquid crystalline polymers under shear flow is investigated through computational simulation. By using a tensorial expression for the elastic torque, the nemato-dynamic equation is numerically resolved. The simulation shows that elastic anisotropy has a strong influence on the evolution of the director and that the 'log-rolling' orientation of the directors emerges for tumbling nematics if the twist constant is smaller than the splay and the bend constants, even though one starts from a structure in which the directors are aligned within the velocity and velocity gradient plane. The interaction of wedge disclination pairs subject to a shear flow field is also simulated. The generation, multiplication and interaction of inversion wall defects during shearing have been revealed. In general the wall moves to the boundaries and is absorbed by the boundaries. When two walls of opposite orientation meet, a loop may form, then shrink, and finally collapse. Correspondingly, if they have the same orientation, commutation will occur.     

片晶装饰技术研究高分子液晶向列相的向错

采用片晶装饰技术和四氧化钉染色技术相结合在透射电镜下研究了热致性高分子液晶的向错结构，在一种热致性聚芳酯的冻结液晶态中观察到了向错强度分别为Ｓ＝±１／２和Ｓ＝±１的两类共六种的向错形态，以及每个向错与其相邻向错之间相互联结和相互作用的状态．     

Numerical analysis of the radial-axial structure transition with an applied field in a nematic droplet

In this paper the director configurations and the free energies of a nematic droplet with a surface normal anchoring condition are calculated numerically. For this surface anchoring, a transition occurs between the radial and axial structures with respect to an applied field. In the calculation of the director configurations, the position of a disclination has been fixed. Comparing the free energies for different disclinations, the stable position which gives the minimum free energy is found. In calculating the free energy of a droplet, it is assumed that the free energy density of the nematic phase does not exceed the isotropic free energy density, so that the large distortion in the vicinity of the disclination causes a nematic-isotropic transition and the free energy density of the disclination core becomes equal to the isotropic free energy density. The director configuration in a droplet is calculated as a function of an applied field for different isotropic free energy densities, elastic constant ratios and droplet shapes. The relation between the radial-axial structure transition and these factors are clarified.     

Anisotropy of domain growth in nematic liquid crystals

We have studied domain growth in nematic liquid crystals using a lattice Boltzmann algorithm to solve the full, three-dimensional equations of hydrodynamics. An initially cylindrical V (bend) domain in an H (splay) state grows or shrinks anisotropically in agreement with experiment. A disclination loop forms at the mid-point of the wall surrounding the domain. We argue that different director configurations at different points on the loop lead to velocity anisotropy and show that both elastic effects and backflow are relevant. We discuss the dependence of the domain wall velocity on surface tilt and on the magnitude of an applied electric field.     

Defect controlled dynamics of nematic liquids

The long time dynamical response of a nematic liquid exhibiting banded textures (inversion walls) during the twist Freedericksz transition is presented. A dynamical model of approach to equilibrium through defect interaction and the resulting dissolution of the banded textures is presented. A linear stability analysis shows that splay-bend inversion wall defects are unstable to two dimensional infinitesimal perturbations. A model of inversion wall segment collapse with production of a disclination line pair is given. The energy-momentum tensor gives the force of interaction between inversion walls and disclination lines. A perturbation analysis gives the evolution of the director field in closed form. Entropy production gives the velocity of each line. The growth law governing the wall dissolution is given.     

Anisotropy of domain growth in nematic liquid crystals

We have studied domain growth in nematic liquid crystals using a lattice Boltzmann algorithm to solve the full, three-dimensional equations of hydrodynamics. An initially cylindrical V (bend) domain in an H (splay) state grows or shrinks anisotropically in agreement with experiment. A disclination loop forms at the mid-point of the wall surrounding the domain. We argue that different director configurations at different points on the loop lead to velocity anisotropy and show that both elastic effects and backflow are relevant. We discuss the dependence of the domain wall velocity on surface tilt and on the magnitude of an applied electric field.     

Disclinations dynamics in confined nematic liquid crystals: strong anchoring

We have investigated the dynamics of pair annihilation of disclination lines in strong anchoring. This work is based on the Frank free energy. The director angle, φ(x, y, z), is obtained by the continuous theory. We show that the form of the viscous force in a confined nematic liquid crystal and in strong anchoring is a function of the initial distance between the two disclination lines. The asymptotic velocity, v _asy, is also a function of the initial distance. Our theoretical result on the asymptotic velocity is in good agreement with previous experimental results.     

Inversion walls in homeotropic nematic and cholesteric layers

We describe the experimental properties of metastable domains associated with the presence of an Inversion Wall (IW ) and observed with homeotropically anchored nematic and cholesteric liquid crystals sandwiched between parallel glass plates. Such a distorted situation, stabilized by the application of an electric field parallel to the plates as described in reference [1], can also be obtained transiently either when filling a sample cell by capillarity or in some studies of directional solidification at the N-I interface [2]. The application of an electric field perpendicular to the plates with Delta epsilon 0 materials allows control of the reversal region thickness in the bulk of the sample and its associated birefringence. This IW can be stabilized in the particular case of low lateral extension globules in which the line tension of the looped disclination separating the pi wall regions from the homeotropic regions counterbalances the unfavourable bulk free energy. Particular attention is devoted to the defects of these walls, whose appearance using polarizing microscopy is similar to the umbilics of the Freedericksz transition. The structure of these 'four brush' defects is nevertheless here singular, corresponding to point defects of a 3D uniaxial nematic medium. In the case of a chiral nematic, these IW undergo a particular undulation instability which is also observed in 2D simulations.     

Modelling of director equilibrium states in a nematic cell with relief surface

We study two-dimensional equilibrium configurations of nematic liquid crystal (NLC) director in a cell bounded by two parallel surfaces. One surface is planar and the other one is spatially modulated. The relief of the modulated surface is described by a smooth periodic sine-like function. The orientation of NLC director easy axis is assumed to be homeotropic at one cell surface and planar at the other one. The NLC director anchoring with cell surfaces is assumed to be strong. We consider the case where disclination lines occur in the bulk of NLC above the extrema of the modulated surface. These disclination lines run along the crests and troughs of the surface relief. If the orientation of director at both bounding surfaces is of the same type, then NLC director field is continuous. For both configurations mentioned above (with defects and without defects), we obtain analytical expressions for director distribution in the bulk of NLC in the approximation of planar director deformations. Equilibrium distances from disclination lines to the spatially modulated surface are calculated when the defects occur. The dependences of these equilibrium distances on the period and depth of surface relief and the cell thickness are investigated in detail.     

Disclinations dynamics in confined nematic liquid crystals: strong anchoring

We have investigated the dynamics of pair annihilation of disclination lines in strong anchoring. This work is based on the Frank free energy. The director angle, φ(x, y, z), is obtained by the continuous theory. We show that the form of the viscous force in a confined nematic liquid crystal and in strong anchoring is a function of the initial distance between the two disclination lines. The asymptotic velocity, v _asy, is also a function of the initial distance. Our theoretical result on the asymptotic velocity is in good agreement with previous experimental results.     

Chiral nematic liquid crystals in cylindrical cavities. A classification of planar structures and models of non-singular disclination lines

A part of homotopy theory is applied to classify planar structures in chiral nematic liquid crystals confined to cylindrical cavities. The resulting classification is exact in the approximation of undeformed chiral nematic surfaces. Within this approach the relative stability of possible planar structures with surface and bulk disclination lines is discussed. The number and the shape of these disclinations, which in some cases form spiral structures, are predicted. Further approximate analytical expressions for non-singular director fields close to disclination lines with integral strength are introduced. Our predictions, which are also in agreement with some previously suggested pictures of such director fields, are used to improve stability considerations of the confined planar chiral nematic structures in tubes and droplets.     

Chiral nematic liquid crystals in cylindrical cavities. A classification of planar structures and models of non-singular disclination lines

Abstract

A part of homotopy theory is applied to classify planar structures in chiral nematic liquid crystals confined to cylindrical cavities. The resulting classification is exact in the approximation of undeformed chiral nematic surfaces. Within this approach the relative stability of possible planar structures with surface and bulk disclination lines is discussed. The number and the shape of these disclinations, which in some cases form spiral structures, are predicted. Further approximate analytical expressions for non-singular director fields close to disclination lines with integral strength are introduced. Our predictions, which are also in agreement with some previously suggested pictures of such director fields, are used to improve stability considerations of the confined planar chiral nematic structures in tubes and droplets.     

主链型高分子液晶向列相向错观察的进展

综述了主链型高分子液晶向列相向错在实验观察方面的进展。从纹影织构的观察和展曲、弯曲弹性常数相等条件下的二维曲率弹性理论出发探讨了向错结构的几何特征。简要涉及了弹性常数不相等对向错的影响、向错核心的本质和反转墙的观察;给出了拓扑强度s高达4的高阶向错的实验观察结果;归纳出描绘向错周围指向矢场的主要实验方法:1)片晶装饰;2)条带织构装饰;3)表面微裂纹装饰。本文对上述方法进行了讨论和比较,列举了一些电子显微镜和光学显微镜照像的图例。