Lassoing saddle splay and the geometrical control of topological defects

Abstract

Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4′-pentylbiphenyl (5CB): Both point and ring topological defects can occur within each hole and around the system while conserving the system's overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives . Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create defect structures, including an array of disclination lines, reminiscent of those found in liquid-crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability.liquid crystals | topological defects | saddle splay | disclinations T he investigation of mechanisms, both chemical and geometrical, to control and manipulate defects in liquid crystals (LCs) is essential for the use of these defects in the hierarchical self-assembly (1-3) of photonic and metamaterials (4, 5), as well as for studies in low-dimensional topology (3, 6-10). For instance, the disclination line networks characteristic of blue phases (11, 12) have been proposed to organize colloidal inclusions (4, 13). But, can similar 3D disclination line networks be designed in the simpler nematic LC? The ubiquitous use of nematic LCs (NLCs) in the display industry is a testament to their efficacy in applications. Wide-ranging studies on the role of nematic elasticity in designing tailored defect structures have focused primarily on the familiar splay, twist, and bend deformations. Recently, however, there has been a renewed interest in exploiting saddle-splay deformations (8,14,15). By confining nematics in cells with properly designed boundary conditions, we demonstrate an array of controlled, defect-riddled minimum energy states that form as a result of saddle-splay distortions, excitable by the system's surfaces. Energy ConsiderationsWe begin with the Frank free energy for a nematic (16, 17):where n ≡ nðxÞ is the (unit) nematic director and K 1 , K 2 , and K 3 are elastic constants that measure the energy cost for splay, twist, and bend deformations, respectively. The final term with the elastic constant K 24 is the saddle splay and, as a total derivative, is absent from the corresponding Euler-Lagrange equation. However, it contributes to the energy when there are defects, potentially stabilizing them by balancing the energy cost of creating a...

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