Tunable three-dimensional architecture of nematic disclination lines

Abstract

Disclination lines play a key role in many physical processes, from the fracture of materials to the formation of the early universe. Achieving versatile control over disclinations is key to developing novel electro-optical devices, programmable origami, directed colloidal assembly, and controlling active matter. Here, we introduce a theoretical framework to tailor three-dimensional disclination architecture in nematic liquid crystals experimentally. We produce quantitative predictions for the connectivity and shape of disclination lines found in nematics confined between two thinly spaced glass substrates with strong patterned planar anchoring. By drawing an analogy between nematic liquid crystals and magnetostatics, we find that i) disclination lines connect defects with the same topological charge on opposite surfaces and ii) disclination lines are attracted to regions of the highest twist. Using polarized light to pattern the in-plane alignment of liquid crystal molecules, we test these predictions experimentally and identify critical parameters that tune the disclination lines’ curvature. We verify our predictions with computer simulations and find nondimensional parameters enabling us to match experiments and simulations at different length scales. Our work provides a powerful method to understand and practically control defect lines in nematic liquid crystals.

Escape into the third dimension in cholesteric liquid crystals

“…Singular lines with a negative winding are associated with higher-genus handlebodies and hence energetically accessible. Additionally, the ability to pattern specific directors on the boundaries of a cell [58] opens up the possibility of realising χ k of arbitrary winding k and studying their properties. Twist solitons could potentially be stabilised in a bulk cholesteric using boundary conditions that impose a χ +1 -line and forcing the director into a single direction of escape via an applied field.…”

“…The region of reversed-handedness takes the form of an oscillating tube, shown in red in figure 7(a). To our knowledge this texture has never been observed in an experiment, but it could be engineered using surface-patterning techniques [58] or an applied field. Since the director is planar away from the original χ +2 -line, on any cross-sectional disc we can associate it with a homotopy class in π 2 (RP 2 , RP 1 ), and this class is independent of z even though the director is not.…”

“…To our knowledge such lines have not been observed in experiments except for k = +1, +2. Negative winding lines could arise naturally inside handlebody droplets [5] or on the complement of handlebody-shaped colloidal particles [65], and it may be possible to generate a general χ k -line using surface-patterning techniques [58]. We have performed numerical simulations of a χ −2 -line, which result in splitting before it escapes into a pair of linked λ −1 -lines, completely analogously to the case of the χ +2 -line.…”

A tensor density measure of topological charge in three-dimensional nematic phases

“…The study of line defects in three-dimensional nematic phases, known as disclinations, has gained considerable interest recently following advances in both experimental diagnostics and computational methods [1][2][3][4][5][6]. Disclinations and their motion have found applications in microfluidics, colloidal self-assembly, surface actuation, optical control and active and biological matter [7][8][9][10][11][12][13][14][15][16].…”

Nematic–isotropic phase transitions in thin slabs of liquid crystals with topological defect arrays

“…33 These techniques have enabled the patterning of liquid crystal molecules into highly designable director fields, 34–40 leading to different ways of programming and creating topological defects in liquid crystals. 41–47 Furthermore, topologically non-trivial colloidal particles can be made and sub-immersed in liquid crystals to induce various types of topological defects, including links, knots and networks of disclinations. 48–50 These methodological advancements have also opened up opportunities for studying the roles of preprogrammed topological defects in phase transitions such as nematic–isotropic 51,52 and nematic-to-smectic transitions.…”