Chiral structures from achiral liquid crystals in cylindrical capillaries

We study chiral symmetry-broken configurations of nematic liquid crystals (LCs) confined to cylindrical capillaries with homeotropic anchoring on the cylinder walls (i.e., perpendicular surface alignment). Interestingly, achiral nematic LCs with comparatively small twist elastic moduli relieve bend and splay deformations by introducing twist deformations. In the resulting twisted and escaped radial (TER) configuration, LC directors are parallel to the cylindrical axis near the center, but to attain radial orientation near the capillary wall, they escape along the radius through bend and twist distortions. Chiral symmetry-breaking experiments in polymer-coated capillaries are carried out using Sunset Yellow FCF, a lyotropic chromonic LC with a small twist elastic constant. Its director configurations are investigated by polarized optical microscopy and explained theoretically with numerical calculations. A rich phenomenology of defects also arises from the degenerate bend/twist deformations of the TER configuration, including a nonsingular domain wall separating domains of opposite twist handedness but the same escape direction and singular point defects (hedgehogs) separating domains of opposite escape direction. We show the energetic preference for singular defects separating domains of opposite twist handedness compared with those of the same handedness, and we report remarkable chiral configurations with a double helix of disclination lines along the cylindrical axis. These findings show archetypally how simple boundary conditions and elastic anisotropy of confined materials lead to multiple symmetry breaking and how these broken symmetries combine to create a variety of defects.The emergence of chirality from achiral systems poses fundamental questions about which we have limited mechanistic understanding (1–11). When the chiral symmetry of an achiral system is broken, a handedness is established, and materials with different handedness commonly exhibit distinct and useful properties (10–14) relevant for applications ranging from chemical sensors (15, 16) to photonics (17–19). To date, considerable effort has been expended to control handedness in materials (for example, by chiral separation of racemic mixtures or chiral amplification of small enantiomeric imbalances) (1, 8, 20–22). Recently and in a different vein, identification and elucidation of pathways by which achiral building blocks spontaneously organize to create chiral structures have become an area of active study. Examples of these pathways include packing with multiple competing length scales (8–10, 23, 24), reconfiguration through mechanical instabilities of periodic structures (20, 25, 26), and helix formation of flexible cylinders through inter- and intracylinder interactions (27, 28). In addition, the system of a broken chiral symmetry often consists of domains of opposite handedness with defects separating the domains.Liquid crystals (LCs) are soft materials composed of anisotropic mesogens that provide remarkable examples of chiral symmetry breaking arising from elastic anisotropy (29–42). In essence, an LC can minimize elastic free energy by organizing its achiral units into chiral structures, such as helices and chiral layers, that incorporate twist deformation (7, 8). The elastic free energy describing nematic LC deformations depends on so-called splay, twist, bend, and saddle-splay elastic moduli, and when twist deformation is comparatively easy, twisting can relieve strong splay and/or bend deformation and lead to production of equilibrium chiral structures (29, 32, 35–38). Similarly, saddle-splay deformation can stabilize chiral structures (43–46).Elasticity-driven chiral symmetry breaking is perhaps most readily manifested in confined LCs (31–43), wherein surface anchoring imposes a preferred angle for LC mesogens at the interface of the confining boundary. Topological defects enforced by boundary conditions can play a key role in the symmetry breaking as well, because energetically costly deformations are often concentrated in the vicinity of the defects (35–37). A simple example of this phenomenon is found in spherical LC droplets with planar anchoring; here, two surface point defects, called Boojums, cause the director to adopt a twisted bipolar configuration, in which energetically cheap twist deformations relieve strong splay deformation near the Boojums.In this paper, we introduce chiral symmetry-broken configurations of nematic LCs in a cylindrical confinement geometry, and we explore the energetics of the configurations and their defects. This general class of configuration has been investigated in cylinders (47–52). However, this system differs significantly from earlier work. The configurations that we report on have homeotropic boundary conditions, and their chirality is not of molecular origin (i.e., handedness is not derived from chiral mesogens or dopants). Our chiral symmetry-breaking experiments use Sunset Yellow FCF (SSY), a lyotropic chromonic LC (LCLC) with small twist elastic constant, in polymer-coated capillaries. SSY is composed of columnar aggregates of organic, plank-like molecules in water. The conformal polymer coating is prepared through chemical vapor deposition. The coating induces homeotropic anchoring of the aggregates on the cylinder surfaces through noncovalent interactions (53) thereby enabling the experimental studies of LCLCs confined in curved geometries with homeotropic alignment. Other than for their biocompatibility (54, 55), LCLCs are known for their very small twist modulus compared with splay and bend moduli; this property renders LCLCs susceptible to spontaneous chiral symmetry breaking (56, 57).Nematic SSY was found to exhibit two different configurations in the cylinder: one twisted and escaped radial (TER) and one with a double helix of disclinations. The samples also contained a variety of chiral defects originating from symmetry breaking. We investigate their structure and energetics using polarized optical microscopy (POM), numerical calculations of director configurations based on elastic free energies, and Jones matrix-simulated optical textures. The chiral director configurations and defects provide a fascinating example of chiral symmetry breaking arising from elastic anisotropy and show the consequences of a delicate interplay between anisotropic elasticity, boundary conditions, chirality, and topological defects.