Dynamic interactions between nematic point defects in the spinning extrusion duct of spiders

Complex Nanowrinkling in Chiral Liquid Crystal Surfaces: From Shaping Mechanisms to Geometric Statistics

Surface wrinkling is closely linked to a significant number of surface functionalities such as wetting, structural colour, tribology, frictions, biological growth and more. Given its ubiquity in nature's surfaces and that most material formation processes are driven by self-assembly and self-organization and many are formed by fibrous composites or analogues of liquid crystals, in this work, we extend our previous theory and modeling work on in silico biomimicking nanowrinkling using chiral liquid crystal surface physics by including higher-order anisotropic surface tension nonlinearities. The modeling is based on a compact liquid crystal shape equation containing anisotropic capillary pressures, whose solution predicts a superposition of uniaxial, equibiaxial and biaxial egg carton surfaces with amplitudes dictated by material anchoring energy parameters and by the symmetry of the liquid crystal orientation field. The numerical solutions are validated by analytical solutions. The blending and interaction of egg carton surfaces create surface reliefs whose amplitudes depend on the highest nonlinearity and whose morphology depends on the anchoring coefficient ratio. Targeting specific wrinkling patterns is realized by selecting trajectories on an appropriate parametric space. Finally, given its importance in surface functionalities and applications, the geometric statistics of the patterns up to the fourth order are characterized and connected to the parametric anchoring energy space. We show how to minimize and/or maximize skewness and kurtosis by specific changes in the surface energy anisotropy. Taken together, this paper presents a theory and simulation platform for the design of nano-wrinkled surfaces with targeted surface roughness metrics generated by internal capillary pressures, of interest in the development of biomimetic multifunctional surfaces.

Mechanisms and shape predictions of nematic disclination branching under conical confinement

Liquid crystals (LCs) are self-organizing anisotropic viscoelastic soft materials that flow like viscous liquids and display anisotropies like crystals. When a nematic liquid crystal is confined to a capillary tube with strong anchoring conditions, disclination defects of higher (+1) and lower (+1/2) topological charges can coexist, connected through a defect branch point. The shape of the +1/2 disclination lines emanating from the branch point are functions of confinement and bulk elasticity. Previous work shows that nematic liquid crystals under cylindrical confinement display a radial (one +1 line)-to-planar polar (two +1/2 lines) defect texture transition through the nucleation and uniform motion of a disclination branch point. Here we present analysis, scaling and modeling based on a non-linear non-local nematic elastic equation that shows that a branch point also can be generated from disclinations in a liquid crystal confined to different conical geometries with homeotropic anchoring conditions. The cone aperture increases the bending stiffness but decreases the curvature of the disclination. These competing effects lead to a decrease in the total disclination curvature, increase in elastic energy and volume of the branching region. The results are summarized into power laws and integrated into a shape/energy diagram that reveals the effects of confinement and its gradient (cone angle) on disclination shape selection. These new findings are useful to assess the Frank elasticity of new nematic liquid crystals and to predict novel defect structures in complex confinement, including biological microfluidics and mesophase fiber spinning.