Conservation of disclination strength in two-dimensional lattice models of liquid crystalline textures

Abstract

The disclination strength defined on the boundary of textures generated by recently proposed simple modelling methods appears to be the sum of the strengths of primitive disclinations inside the boundary. In this paper, a rationalization is provided for these observations in two dimensions using an analytical expression for the conservation law for wedge type disclinations.     

A numerical technique for predicting microstructure in liquid crystalline polymers

A numerical technique has been developed to model texture in nematic liquid crystals. The technique differentiates between splay, twist and bend distortions and includes splay-splay compensation. The technique is tested by the simulation of the Freedericksz transition and by the determination of minimum energy director fields for specific boundary conditions. To model the bulk, periodic boundary conditions are imposed. The effect of elastic anisotropy on disclination character has been investigated by terminating simulations before all the defects have been annihilated. With a low twist constant, twist disclinations are observed; with a high twist constant, wedge disclinations are observed. With a low twist constant and high splay constant, realistic for polymeric liquid crystals, features observed experimentally are simulated.     

Identification of disclinations in the structure of strongly deformed materials

The deformation of metallic materials up to large strains leads to the formation of fine grain structures (down to the nanometric scale) with high densities of grain boundaries and grain boundary junctions. Such structures demonstrate significant lattice rotations and the presence of disclination defects at grain boundary junctions. We present the results of transmission electron microscopy (TEM) observations of disclinations in strongly deformed metals and describe the theoretical approaches for their identification.     

String defects connecting pairs of half-integer disclinations and tilting transition of a langmuir monolayer

The static and dynamic string defect textures connecting pairs of half-integer disclinations have been observed by Brewster angle microscopy in the solid phase of pentacosadiynoic acid Langmuir monolayers. The static string defect structures have appeared coexisting with two kinds of point disclinations that have four and two black brushes. The use of local laser heating has allowed one to observe kinetics of creation and annihilation of string defects connecting the two-half-integer disclinations in the splitting process of an s = 1 point disclination into fractional disclinations. These kinetics have been analyzed by studying the competition between the orientational elasticity of the molecules and the line tension of the string and the drag force of the disclinations.     

Grain boundary scars on spherical crystals

We present an experimental system suitable for producing spherical crystals and for observing the distribution of lattice defects (disclinations and dislocations) on a significant fraction (50%) of the sphere. The introduction of fluorescently labeled particles enables us to determine the location and orientation of grain boundary scars. We find that the total number of scars and the number of excess dislocations per scar agree with theoretical predictions and that the geometrical centers of the scars are roughly positioned at the vertices of an icosahedron.     

High strength disclinations in a rigid rod nematic polytolane

Transient disclinations of strength ± 3/2 were observed in the nematic phase of a single-component, thermotropic, rigid rod polytolane. These disclinations were characterized by 6 extinction brushes in textures observed by hot stage transmitted polarized light microscopy. The small number and short lifetime of these disclinations is discussed in terms of their energy per unit line length, and in terms of the force that causes them to be attracted to and annihilated at other disclinations.     

Optical microscopy study for director patterns around disclinations in side-chain liquid crystalline polymer films

Polarizing optical microscopy is employed to study director fields around disclinations in side-chain liquid crystalline polymer films. Optical black brushes together with stripes around disclinations are observed. The stripes run parallel to the local director and thus decorate overall patterns of nematic director around disclinations. Three director patterns involving radial, spiral, and circular microstructures of a positive integer disclination with s = +1 and one hyperbolic pattern of a negative integer disclination with s = -1 are observed in the thin film. It is found that the specific configurations of a pair of (+1, -1) disclinations form during the late stage of annihilation. Increasing the film thickness leads to disclination instability. We observe that black four-brushes of disclinations with s = +/-1 split into black two-brushes, where two types of director patterns of disclinations with half-integer strengths of s = +/- 1/2 produce. Theoretical analysis is presented to explain this instability.     

Atomic force microscopy study for supermolecular microstructures in side-chain liquid crystalline polymer films

Atomic force microscopy (AFM) is employed to study the supermolecular microstructures of disclinations and inversion walls in thin films of a smectic side-chain liquid crystalline polymer. Two-dimensional nanostripes are formed in thin films when the material enters the smectic phase. A possible mechanism for their formation is also suggested. The stripes run parallel to the local director and thus decorate the overall patterns of nematic director around the disclinations and inversion walls. Three patterns involving radial, spiral, and circular supermolecular microstructures of a positive disclination with s = +1 and one hyperbolic pattern of a negative disclination with s = -1 are observed. The cores of all these microstructures exhibit circular dark centers in AFM height images. It is found that the specific configurations of a pair of (+1, -1) disclinations form during the late stage of annihilation and inversion walls always separate a pair of (+1, +1) disclinations. The analysis on the director fields around disclinations and inversion walls shows that the bend and splay elastic constants are of the same order of magnitude in the side-chain liquid crystalline polymer.     

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。     

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.     

Recent advances in the observation of disclinations of main-chain nematic polymers

Experimental observation of disclinations of main-chain nematic polymers is reviewed. The geometry of disclination structure is discussed both from observations of schlieren texture and the theory of curvature elasticity for a two-dimensional case with equal splay and bend moduli. The effects of non-equal elastic moduli, the nature of the disclination core and the observation of inversion wails are briefly mentioned. Examples of experimental observation of disclinations of high topological strengths up to S=4 are given. The main experimental methods to map the director field around disclinations are 1) lamellar decoration, 2) band-texture decoration and 3) surface microcrack decoration. The methods are discussed and compared, and examples illustrated by electron micrographs or photomicrographs are presented.     

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.     

High strength disclinations in the nematic and smectic states of 2,5-bis(4-alkoxybenzoyloxy)- p -benzoquinones

High strength disclinations were observed in both nematic and smectic phases exhibited by members of the 2,5-bis(4-alkoxybenzoyloxy)- p -benzoquinone series, beyond 4- n -pentoxy. The shorter members of the series show only a nematic mesophase, the highest members only a smectic mesophase, while intermediate members exhibit both types of mesophase. These high strength disclinations seen in a single component system are very stable due to energy dispersion and the high viscosity of the smectic state. All the high strength disclinations are negative in sign.     

Elastic constant anisotropy and disclination interaction in nematic polymers II. Effect of disclination interaction

A new tensorial approach introducing unequal elastic constants in a two-dimensional lattice model is applied to simulate the influence of disclination interaction on the structures of half-wedge disclinations, for the understanding of the variation of apparent elastic anisotropy ε_a measured from different disclinations in a texture (see preceding paper, part I [1]). The apparently random variation of ε_a implies that disclination interaction has a strong effect on the structure of disclinations; as elastic anisotropy increases, its impact becomes overpowering. Nevertheless the disclination interaction still acts in the same way as in the case of equal elastic constants. Analysis of the free energy of disclination pairs shows that the structures of both +1/2 and -1/2 disclinations are changed under the influence of a neighbouring disclination, but in different ways. For +1/2 disclination, the splay and bend distortions vary with the relative orientation of its -1/2 neighbour. Meanwhile, for -1/2 disclination, the bend and splay distortions are remarkably insensitive to the relative orientation of its +1/2 disclination neighbour.     

Interstitial fractionalization and spherical crystallography

Finding the ground states of identical particles packed on spheres has relevance for stabilizing emulsions and has a venerable history in the literature of theoretical physics and mathematics. Theory and experiment have confirmed that defects such as disclinations and dislocations are an intrinsic part of the ground state. Here we discuss the remarkable behavior of vacancies and interstitials in spherical crystals. The strain fields of isolated disclinations forced in by the spherical topology literally rip interstitials and vacancies apart, typically into dislocation fragments that combine with the disclinations to create small grain-boundary scars. The fractionalization is often into three charge-neutral dislocations, although dislocation pairs can be created as well. We use a powerful, freely-available computer program to explore interstitial fractionalization in some detail, for a variety of power-law pair potentials. We investigate the dependence on initial conditions and the final state energies, and compare the position dependence of interstitial energies with the predictions of continuum elastic theory on the sphere. The theory predicts that, before fragmentation, interstitials are repelled and vacancies are attracted from 5-fold disclinations. We also use vacancies and interstitials to study low-energy states in the vicinity of "magic numbers" that accommodate regular icosadeltahedral tessellations.     

Textures and defects in lyotropic liquid crystals of ethyl-cyanoethyl cellulose

Textures and defects in ethyl-cyanoethyl cellulose [(E-CE)C]/dichloroacetic acid (DCA) cholesteric liquid crystalline solutions and in (E-CE)C/polyacrylic acid (PAA) composites were observed and studied by polarizing microscopy and electron microscopy. The existence of χ, λ and τ disclinations were observed in the mesophase with disk-like and band-like textures. Pairs of disclinations with different signs were also found in the mesophase with the band-like texture. Domain walls were observed in (E-CE)C/PAA composite films with cholesteric order by TEM. The orientation of polymer chains in the vicinity of the core of the disclinations is discussed.     

Elastic constant anisotropy and disclination interaction in nematic polymers I. Apparent variation in anisotropy

This work presents the effect of elastic anisotropy and disclination interaction on wedge disclinations in the nematic phase of thermotropic polymers, by combining experimental measurements, (this paper part I), with numerical simulation (part II [1]). In part I, the decoration provided by spontaneous banded texture gives much information about the defect structure of polymeric nematics. Working with a semi-rigid polyester, the optical images of +1/2 disclinations revealed by banding enable the distortion to be determined as a function of polar coordinates from the cores. Continuum theory allows the apparent elastic anisotropy, ε_a, of bend and splay constants of the copolyester to be determined from the distortion measurement. The values of ε_a, are seen to vary greatly in the range -1 to +1 between different +1/2 disclinations in the same sample. The statistics of the measurement indicate that the distribution of the values of ε_a is random. The implication of these observations is that the curvature of wedge disclinations is affected not only by the elastic anisotropy of the material, but also by other factors. The possible reasons are discussed: the interaction of neighbouring disclinations has been numerically analysed to be the predominant factor in [1]. This work also implies that values of the intrinsic elastic anisotropy obtained by measuring the distortion of individual wedge disclinations must be viewed with some circumspection.     

Schlieren textures in free-standing nematic films: evidence of biaxiality

Conoscopic studies reveal that the nematic phase of 4,4-( p -terphenyl)-bis\[2,3,4-tri(dodecyloxy)benzal]imine is biaxial, the biaxial angle increasing with schlieren textures exhibited by the nematic phase have been between glass plates, as well as free-standing consisting entirely of s or 2-brush disclinations, confirming an earlier suggestion that the absence of 4-brush disclinations is evidence of biaxiality. decreasing temperature. The examined. Films sandwiched films, exhibit a nematic schlieren texture     

Direct observation of director fields of disclinations in the nematic mesophase of a main chain thermotropic aromatic polyester by surface microcrack decoration

For a main chain thermotropic aromatic polyester with a flexible spacer, Cr 194 N 245 I (°C), the director fields around disclinations in the nematic mesophase can be decorated by both the solidification-induced band texture and surface microcracks. Director fields of various types of disclinations, including inversion walls, in the nematic mesophase of this semi-rigid polyester have been observed directly by polarizing optical microscopy. It was found that when the polymer was pre-sheared in the nematic state and then quenched to room temperature, a shear-induced band texture was observed, which relaxed slowly during annealing at 200°C, and then on quenching the solidification-induced band texture and surface microcracks appeared, displaying the pattern of the disclination fields. Pre-shearing is a necessary condition for the appearance of microcracks. On annealing, disclinations of various types were generated, quite often connected by inversion walls in the direction of pre-shearing. In some areas of the specimen where the shear-induced bands had not been completely relaxed during annealing, the shear-induced band texture was shown by the birefringence and surface microcracks to have a supermolecular structure of sinusoidal chain fibrils.     

Direct observation of director fields of disclinations in the nematic mesophase of a main chain thermotropic aromatic polyester by surface microcrack decoration

For a main chain thermotropic aromatic polyester with a flexible spacer, Cr 194 N 245 I (°C), the director fields around disclinations in the nematic mesophase can be decorated by both the solidification-induced band texture and surface microcracks. Director fields of various types of disclinations, including inversion walls, in the nematic mesophase of this semi-rigid polyester have been observed directly by polarizing optical microscopy. It was found that when the polymer was pre-sheared in the nematic state and then quenched to room temperature, a shear-induced band texture was observed, which relaxed slowly during annealing at 200°C, and then on quenching the solidification-induced band texture and surface microcracks appeared, displaying the pattern of the disclination fields. Pre-shearing is a necessary condition for the appearance of microcracks. On annealing, disclinations of various types were generated, quite often connected by inversion walls in the direction of pre-shearing. In some areas of the specimen where the shear-induced bands had not been completely relaxed during annealing, the shear-induced band texture was shown by the birefringence and surface microcracks to have a supermolecular structure of sinusoidal chain fibrils.