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.     

Two-dimensional director configurations in a nematic-filled cylindrical capillary with the hybrid director alignment on its surface

ABSTRACT

We analytically calculate two-dimensional equilibrium configurations of the nematic liquid crystal (NLC) director in a right cylindrical capillary with the hybrid director alignment on its inner surface. A part of this surface is treated to impose the strong homeotropic alignment, while on the remaining part the strong circular alignment, perpendicular to the capillary axis, is imposed. Owing to the system homogeneity along the capillary axis, a disclination line emerges in the bulk of the NLC, which runs parallel to the axis. It is shown that there exist either one or two equilibrium locations of the disclination line depending on the ratio of capillary surface parts with homeotropic and circular alignment. The technique that allows to obtain an analytical expression for the system free energy as a function of a disclination line location is presented. It considerably simplifies calculations and can be used while solving a variety of problems in which a defect location is sought.     

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.     

Effect of an electric field on defects in a nematic liquid crystal with variable surface anchoring

We report experimental studies on defects in a nematic liquid crystal with negative dielectric anisotropy mounted in a cell with perfluoropolymer-coated surfaces. The sample exhibits a discontinuous anchoring transition from planar to homeotropic on cooling at zero or a small electric field, and above a cross-over voltage a continuous ‘inverse Freedericksz transition’, at which the director starts tilting in opposite directions at the two surfaces. Defects of strength ±1/2 are either annihilated or expelled when the director tilts. On the other hand, disclination lines of ±1 which end in partial point defects (boojums) at the surfaces in the planar alignment regime acquire point defects of strength ±1 at the midplane of the cell when the director tilts. At a low enough temperature, the homeotropic anchoring becomes strong, and an electric field above the Freedericksz threshold generates the usual umbilic defects, which follow the dynamic scaling laws found in earlier studies.     

Model of a disclination core in nematics

The core structure of a disclination line of strength 1 in uniaxial nematics is determined by using a space-dependent mean-field approach somehow based on the rod-like molecular model. It is shown that, due to distortion, biaxiality arises at all points of the defect core, except at the centre line where symmetry dictates uniaxiality; the orientational distribution of the rod-like molecules is there 'oblate', however. Although, as is well known, the configuration of a 1 defect is stable only under limiting conditions (as compared with either escaping in the axial direction or splitting into two 1/2 lines), the simple example developed here is indicative of a method which can readily be extended to more realistic, if mathematically more complex, situations such as 1/2 lines, layers close to solid boundaries, etc.     

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.     

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．     

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.     

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.     

Forming process and stability of bubble domains in dielectrically positive cholesteric liquid crystals

The nucleation of bubble domains in homeotropic samples of a dielectrically positive cholesteric liquid crystal is described. These domains are found to be more stable in an electric field than the rectilinear double-twisted fingers. The electric field-induced transformation of a looped finger into a bubble domain is described in detail: it is discontinuous and irreversible, and operates only at a large enough confinement ratio C = d/p, where d is the sample thickness and p the quiescent cholesteric pitch. Finally, in contrast with Stieb's model [4], we propose that there are two point defects along the bubble axis and not a disclination line.     

Surface microcracks decoration and disclination defects of wholly aromatic liquid crystalline copolyesters

An intensive study has been conducted to map the director fields of disclination of nematic liquid crystalline copolyesters. In this study, films of two wholly aromatic main-chain polyesters containing para- (ABA/MH/TFTA) and meta-linkages (ABA/MH/TFIA) (ABA, p-acetoxybenzoic acid; MH, maleic hydrazine; TFTA, tetrafluoroterephthalic acid; TFIA, tetrafluoroisophthalic acid) were synthesized to investigate the effects of kinks on liquid crystallinity, disclination strength (S), and surface microcracks decoration. These two copolyesters were prepared by in-situ thin film polymerization and characterized by polarizing light microscope, wide-angle X-ray diffraction, as well as "rotational isomeric states" (RIS) Metropolis Monte Carlo (RMMC) simulation. An optical microscope shows that the surface microcracks forms in the nematic-mosaic texture during a rapid quenching. The ABA/MH/TFTA film exhibits disclination strength with S = +1 and S = -(1)/(2); however, disclination strengths with S = +/-1 have been observed in the ABA/MH/TFIA system. To our best knowledge, this is the first paper reporting the effects and evidence of kink (meta and para moieties) on topological defect of disclination. In addition, the RMMC analysis supports the liquid crystal formation in both polyester films with a persistence ratio greater than 6.42.     

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.     

Interaction between a disclination and a uniaxial-isotropic phase interface in a nematic liquid crystal

We consider the interaction between a disclination line of strength +/-1/2 and an interface between the uniaxial and isotropic phases of a nematic liquid crystal. We apply a recently developed set of interface conditions including a configurational force balance which generalizes the Gibbs-Thomson equation to account for the curvature elasticity of the uniaxial phase and the orientation dependence of the interfacial free-energy density. We consider a rectangular vessel containing both phases and a disclination. We formulate a relevant free-boundary problem and use numerical methods to determine equilibrium shapes of the interface. When the interfacial free-energy is constant, the shape of the interface is insensitive to whether the strength of the defect is +1/2 or -1/2 and to rotations of the director field consistent with the boundary conditions. Accounting for the dependence of the interfacial free-energy density on the angle between the interfacial unit normal field and the director field eliminates these degeneracies. In particular, when such dependence is taken into account, different solution branches are found, indicating the presence of a bifurcation. We find also that, depending on the magnitude of the anisotropic contribution to the interfacial free-energy density, the interaction between the disclination and the interface may be repulsive or attractive. When the interaction is repulsive, the disclination line positions itself at an energetically optimal distance adjacent to the interface. Otherwise, the uniaxial phase expels the disclination to the interface where a cusp forms.     

Twin nematic phenylbenzoates in a.c. electric fields

The orientational behaviour of nematic compounds having twin phenylbenzoate mesogens was examined under a wide range of a.c. electric fields (0-2 V mum-1 and 10Hz-50 kHz). For this study, crossed polarizing optical microscopy (POM) and real-time X-ray diffraction (RTXRD) measurements were employed to investigate optical and orientational response. These nematic compounds have a positive dielectric anisotropy and a relatively low epsilon// relaxation frequency which allowed study in both homeotropic and planar orientations over a controllable frequency range. The optical behaviour and X-ray results corresponded well, providing a tool for understanding the orientational behaviour of these liquid crystals. For homeotropic alignment, an electric field of over 1 V mum-1 was required in order to obtain good orientation. However, homeotropic orientation depended on a delicate balance between thermal fluctuations and dielectric torque imposed by the electric field, which are both strongly related to the elasticity of the LC domains. Due to this effect, the highest orientation parameter achieved for homeotropic orientation was only 0.48, which indicated that this state was still non-equilibrium. On the other hand, for planar orientation, a uniform texture with orientation parameter of 0.65 was easily obtained even at electric fields as low as 0.2 V mum-1. The application of an electric field stronger than 1 V mum-1 induced a distortion in the texture, and reduced the orientation parameter to 0.45 for planar alignment.     

Effect of the elastic constant anisotropy on disclination interaction in the nematic polymers

In this work, disclination interaction behavior in relation to Frank elastic constant anisotropy in nematics has been studied. A large number of (+(1/2), -(1/2)) disclination pairs are revealed by spontaneous band texture in a semiflexible copolyester. The pairs show no preferential relative orientation, with the intervening fields showing intermediate patterns. A two-dimensional tensor lattice model considering unequal elastic constants is applied to simulate the interaction behavior and patterns of disclination pairs in the presence of elastic anisotropy. Scaling laws for disclination density rho(t) as a function of time step t with different elastic anisotropy are obtained as t(-nu). The value of the exponent nu decreases as elastic anisotropy is increased. Obviously, elastic anisotropy slows the texture coarsening. The simulations also show that angular forces arise in the presence of elastic anisotropy and change the patterns of pairs during the texture coarsening. When disclination density is considerably decreased, some +(1/2) disclinations start to rotate to the energetically favored patterns depending on the sign of the elastic anisotropy. As a result of the disclination rotation, the distribution of patterns of pairs continues to change during the annihilation. However, disclination pairs are influenced not only by elastic anisotropy but also by disclination interaction during the whole annihilation. Therefore, in a real system, the dependence of pairs on elastic anisotropy is not as strong as the theoretical prediction for an isolated pair, and the full pattern range of disclination pairs can be observed.     

DNA hybridization-induced reorientation of liquid crystal anchoring at the nematic liquid crystal/aqueous interface

Interactions between DNA and an adsorbed cationic surfactant at the nematic liquid crystal (LC)/aqueous interface were investigated using polarized and fluorescence microscopy. The adsorption of octadecyltrimethylammonium bromide (OTAB) surfactant to the LC/aqueous interface resulted in homeotropic (untilted) LC alignment. Subsequent adsorption of single-stranded DNA (ssDNA) to the surfactant-laden interface modified the interfacial structure, resulting in a reorientation of the LC from homeotropic alignment to an intermediate tilt angle. Exposure of the ssDNA/OTAB interfacial complex to its ssDNA complement induced a second change in the interfacial structure characterized by the nucleation, growth, and coalescence of lateral regions that induced homeotropic LC alignment. Fluorescence microscopy showed explicitly that the complement was colocalized in the same regions as the homeotropic domains. Exposure to noncomplementary ssDNA caused no such response, suggesting that the homeotropic regions were due to DNA hybridization. This hybridization occurred in the vicinity of the interface despite the fact that the conditions in bulk solution were such that hybridization did not occur (high stringency), suggesting that the presence of the cationic surfactant neutralized electrostatic repulsion and allowed for hydrogen bonding between DNA complements. This system has potential for label-less and portable DNA detection. Indeed, LC response to ssDNA target was detected with a lower limit of approximately 50 fmol of complement and was sufficiently selective to differentiate a one-base-pair mismatch in a 16-mer target.     

High strength disclinations induced by hydrogen bond dissociation in the nematic phases of p-alkoxycinnamic acids

Disclinations of high strength ( S 1) in the hydrogen bond-induced nematic phases of p-alkoxycinnamic acids are reported. The existence of the disclinations of high strength is ascribed to the partial dissociation and regeneration of the hydrogen bonds in a mesastable equilibrium state around the clearing point and the core of the high strength disclination is an isotropic area.     

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.     

Alignment and alignment dynamics of nematic liquid crystals on Langmuir-Blodgett mono-layers

Mono-layers of stearic and behenic acids, deposited with the Langmuir-Blodgett technique, were used as aligning films in nematic liquid crystal cells. During the filling process the liquid crystal adopts a deformed quasi-planar alignment with splay-bend deformation and preferred orientation along the filling direction. This state is metastable and transforms with time into a homeotropic state once the flow has ceased. The transition is accompanied by formation of disclination lines which nucleate at the edges of the cell. The lifetime of the metastable splay-bend state was found to depend on the cell thickness. On heating, an anchoring transition from quasi-homeotropic to degenerate tilted alignment in the form of circular domains takes place near the transition to the isotropic phase. The anchoring transition is reversible with a small hysteresis.