Xuxia Yao

Theory and modeling of nematic disclination branching under capillary confinement

Defects in nematic liquid crystals under controlled confinement serve as a useful tool to characterize material properties as well as to reveal texture stability and pattern formation mechanisms in anisotropic soft matter. In particular, nematics inside micro-capillaries can exhibit a large variety of textures with point defects, line defects and loop defects, whose stability is dictated by factors such as geometry and temperature. In this paper we present a theoretical model, scaling, and simulation of a texture transition between two commonly observed patterns (planar polar and radial), through the uniform translation of a shape-invariant disclination branch point in generic calamitic nematic liquid crystals under capillary confinement and strong radial anchoring. Using the “nematic elastica” model derived from the Q-tensor Landau–de Gennes and n-vector Frank–Oseen equations, the geometry, stability, and energetics of disclination branching of a straight high order +1 disclination into a pair of curved +1/2 disclinations under capillary confinement are fully characterized, including the branch angle, the curvature and final separation of the +1/2 lines, and the scaling of these quantities with the capillary radius (R). It is found that the branching and disclination shapes adjust to the capillary confinement by regulating their tension-to-bending stiffness ratio in such a way that the resulting branch angle is close to π/3, the branch curvature is 3/R and the final disclination distance is . These new findings based on the “nematic elastica” are also useful to predict other novel structures that arise in conical and toroidal geometries of current interest and can be used to assess the Frank elasticity of nematic liquid crystals.

Orientational Order of a Lyotropic Chromonic Liquid Crystal Measured by Polarized Raman Spectroscopy

Lyotropic chromonic liquid crystals are distinct from thermotropic nematics from a fundamental standpoint as the structure of the aggregating columns is a function of both the temperature and concentration. We report on the thermal evolution of orientational order parameters, both the second (=scalar) (⟨P200⟩ (=S)) and fourth (⟨P400⟩) order, of sunset yellow FCF aqueous solutions, measured using polarized Raman spectroscopy for different concentrations. The order parameter increases with the concentration, and their values are high in comparison with those of thermotropic liquid crystals. On the basis of Raman spectroscopy, we provide the strongest evidence yet that the hydrozone tautomer of SSY is the predominant form in aqueous solutions in the isotropic, nematic, and columnar phases, as well as what we believe to be the first measurements of (⟨P400⟩) for this system.

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 confined 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.

Nematic Liquid Crystals under Conical Capillary Confinement: Theoretical Study of Geometry Effects on Disclination Lines

When a nematic liquid crystal is confined to a capillary tube with strong homeotropic anchoring conditions, unstable +1 disclinations lines can branch into a pair of +1/2 lines forming loops attached to the +1 axial line through branch points. The shape of the +1/2 disclination lines is a function of the confinement and the Frank elasticity. Our previous work shows that nematic liquid crystals under cylindrical confinement display a radial-to-planar polar defect texture transition through the nucleation and uniform motion of a disclination branch point that separates a high charge disclination from two lower charge ones. Here, we present the existence of a branch point for a nematic LC confined to different conical geometries with homeotropic anchoring. Determination of the defect geometry in conjunction with our model provides a means of characterizing the elasticity of LCs. Our results show that a larger conical angle reduces the length at which disclination curvature relaxes to zero and it also leads to less bending energy. These new findings are useful to assess the Frank elasticity of the nematic LCs and predict novel defect structures under confinement.