Polarized epifluorescence microscopy and the imaging of nematic liquid crystals in highly curved geometries.

We develop polarized epifluorescence microscopy (PFM), a technique to qualitatively determine a director field, even when refraction effects are too strong to use optical polarized microscopy. We present the basic theory behind the technique and cover in detail the experimental setup. We validate PFM on the well-studied cases of a planar nematic cell, spherical nematic droplets, and a cylindrical capillary filled with nematic liquid crystal. Last, we use nematic capillary bridges to demonstrate that PFM can indeed provide measurements of the director field, even when refraction effects are large.

Geometrical Control of Active Turbulence in Curved Topographies.

We investigate the turbulent dynamics of a two-dimensional active nematic liquid crystal constrained to a curved surface. Using a combination of hydrodynamic and particle-based simulations, we demonstrate that the fundamental structural features of the fluid, such as the topological charge density, the defect number density, the nematic order parameter, and defect creation and annihilation rates, are approximately linear functions of the substrate Gaussian curvature, which then acts as a control parameter for the chaotic flow. Our theoretical predictions are then compared with experiments on microtubule-kinesin suspensions confined on toroidal droplets, finding excellent qualitative agreement.

Curved boundaries and chiral instabilities - two sources of twist in homeotropic nematic tori.

Many liquid crystalline systems display spontaneous breaking of achiral symmetry, as achiral molecules aggregate into large chiral domains. In confined cylinders with homeotropic boundary conditions, chromonic liquid crystals - which have a twist elastic modulus which is at least an order of magnitude less than their splay and bend counter parts - adopt a twisted escaped radial texture (TER) to minimize their free energy, whilst 5CB - which has all three elastic constants roughly comparable - does not. In a recent series of experiments, we have shown that 5CB confined to tori and bent cylindrical capillaries with homeotropic boundary conditions also adopts a TER structure resulting from the curved nature of the confining boundaries [P. W. Ellis et al., Phys. Rev. Lett., 2018, 247803]. We shall call this microscopic twist, as the twisted director organization not only depends on the confinement geometry but also on the values of elastic moduli. Additionally, we demonstrate theoretically that the curved geometry of the boundary induces a twist in the escaped radial (ER) texture. Moving the escaped core of the structure towards the center of the torus not only lowers the splay and bend energies, but lowers the energetic cost of this distinct source for twist that we shall call geometric twist. As the torus becomes more curved, the ideal location for the escaped core approaches the inner radius of the torus.

Defect transitions in nematic liquid-crystal capillary bridges.

We use experiment and computational modeling to understand the defect structure and director configuration in a nematic liquid crystal capillary bridge confined between two parallel plates. We find that tuning of the aspect ratio of the bridge drives a transition between a ring defect and a point defect. This transition exhibits hysteresis, due to the metastability of the point-defect structure. In addition, we see that the shape of the capillary-bridge surface determines whether the defect is hyperbolic or radial, with waistlike bridges containing hyperbolic defects and barrel-like bridges containing radial defects.

Curvature-Induced Twist in Homeotropic Nematic Tori.

We confine a nematic liquid crystal with homeotropic anchoring to stable toroidal droplets and study how geometry affects the equilibrium director configuration. In contrast to the case of cylindrical confinement, we find that the equilibrium state is chiral-a twisted and escaped radial director configuration. Furthermore, we find that the magnitude of the twist distortion increases as the ratio of the ring radius to the tube radius decreases; we confirm this with computer simulations of optically polarized microscopy textures. In addition, numerical calculations also indicate that the local geometry indeed affects the magnitude of the twist distortion. We further confirm this curvature-induced twisting using bent cylindrical capillaries.

Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders.

The presumed ground state of a nematic fluid confined in a cylindrical geometry with planar anchoring corresponds to that of an axial configuration, wherein the director, free of deformations, is along the long axis of the cylinder. However, upon confinement of lyotropic chromonic liquid crystals in cylindrical geometries, here we uncover a surprising ground state corresponding to a doubly twisted director configuration. The stability of this ground state, which involves significant director deformations, can be rationalized by the saddle-splay contribution to the free energy. We show that sufficient anisotropy in the elastic constants drives the transition from a deformation-free ground state to a doubly twisted structure, and results in spontaneous symmetry breaking with equal probability for either handedness. Enabled by the twist angle measurements of the spontaneous twist, we determine the saddle-splay elastic constant for chromonic liquid crystals for the first time.

Stable nematic droplets with handles.

We stabilize nematic droplets with handles against surface tension-driven instabilities, using a yield-stress material as outer fluid, and study the complex nematic textures and defect structures that result from the competition between topological constraints and the elasticity of the nematic liquid crystal. We uncover a surprisingly persistent twisted configuration of the nematic director inside the droplets when tangential anchoring is established at their boundaries, which we explain after considering the influence of saddle splay on the elastic free energy. For toroidal droplets, we find that the saddle-splay energy screens the twisting energy, resulting in a spontaneous breaking of mirror symmetry; the chiral twisted state persists for aspect ratios as large as ∼20. For droplets with additional handles, we observe in experiments and computer simulations that there are two additional -1 surface defects per handle; these are located in regions with local saddle geometry to minimize the nematic distortions and hence the corresponding elastic free energy.