Nematic liquid crystals on sinusoidal channels: the zigzag instability

Abstract

Abstract.Substrates which are chemically or topographically patterned induce a variety of liquid crystal textures. The response of the liquid crystal to competing surface orientations, typical of patterned substrates, is determined by the anisotropy of the elastic constants and the interplay of the relevant lengths scales, such as the correlation length and the surface geometrical parameters. Transitions between different textures, usually with different symmetries, may occur under a wide range of conditions. We use the Landau-de Gennes free energy to investigate the texture of nematics in sinusoidal channels with parallel anchoring bounded by nematic-air interfaces that favour perpendicular (hometropic) anchoring. In micron size channels 5CB was observed to exhibit a non-trivial texture characterized by a disclination line, within the channel, which is broken into a zigzag pattern. Our calculations reveal that when the elastic anisotropy of the nematic does not favour twist distortions the defect is a straight disclination line that runs along the channel, which breaks into a zigzag pattern with a characteristic period, when the twist elastic constant becomes sufficiently small when compared to the splay and bend constants. The transition occurs through a twist instability that drives the defect line to rotate from its original position. The interplay between the energetically favourable twist distortions that induce the defect rotation and the liquid crystal anchoring at the surfaces leads to the zigzag pattern. We investigate in detail the dependence of the periodicity of the zigzag pattern on the geometrical parameters of the sinusoidal channels, which in line with the experimental results is found to be non-linear.

Nematic line defects in microfluidic channels: wedge, twist and zigzag disclinations

“…More recently, zigzag shaped disclinations have been observed also in NLCs confined to microwrinkle grooves 12,37 and were theoretically studied within a Landau-de Gennes model. 38 In these studies 12,[34][35][36][37][38] it was argued that the elastic anisotropy of NLCs is at the origin of the zigzag disclinations: because twist deformations of the director field cost significantly less elastic energy than splay or bend deformations, disclination lines form under the boundary conditions of the above mentioned studies in the twist configuration and release some twist energy by inclining and forming the zigzag pattern.…”

Pattern-induced anchoring transitions in nematic liquid crystals

“…If we assume that the elastic distortions are on the xy plane, the conclusion is that the anchoring transition, which corresponds to moderate values of λ, may be shifted by this contribution, although qualitatively it will be very similar. However, if the twist elastic constant is smaller than K, there is experimental [11] and numerical [48] evidence of a twist instability which breaks the azimuthal symmetry: the disclination line is no longer parallel to the z axis, but exhibits a zig-zag structure which decreases the splay and bending dist ortions. This cannot happen in the sawtooth and crenellated substrates, since the disclination-like singularities are located at the surface cusps.…”

Wetting of Nematic Liquid Crystals on Crenellated Substrates: A Frank–Oseen Approach

“…In addition, the interplay between interfacial configurations (as well as the substrate relief) and the orientational order in the nematic phase generates a plethora of distinct interfacial states, leading to rather complex interfacial phase diagrams [36]. In this context, systematic studies of the wetting for sawtooth [36,37], sinusoidal [38,39] and crenellated substrates [40,41] have been reported within the Landau-de Gennes theory. These studies revealed complex phase diagrams which differ considerably from their simple fluids counterparts.…”