Topologically reconfigurable nematic emulsions.

In emulsions of multicomponent fluids, the dispersed phase forms tiny droplets in the continuous phase. In situ control and manipulation to achieve diversity in emulsion droplets for emerging applications is challenging. In a liquid crystal-based emulsion, the surface anchoring of the molecules at the isotropic fluid-liquid crystal interface introduces elastic distortions that result in anisotropic interparticle interactions, similar to electrostatic interactions between multipoles, which also lends a naming analogy as elastic dipoles, quadrupoles, and higher.

Effect of rotational shear on the dielectric dispersion of a nematic liquid crystal above the Freedericksz threshold field.

Rheo-dielectric studies of soft materials provide important information on the dynamic structure and electric polarization. We study the dielectric dispersion of a nematic liquid crystal by applying a high AC probe field without a DC bias and a low AC probe field with a high DC bias under steady rotational shear. The dielectric anisotropy of the nematic is positive and the applied electric field is parallel to the velocity gradient with a magnitude larger than the Freedericksz threshold field.

Many-defect solutions in planar nematics: interactions, spiral textures and boundary conditions.

From incompressible flows to electrostatics, harmonic functions can provide solutions to many two-dimensional problems and, similarly, the director field of a planar nematic can be determined using complex analysis. We derive a closed-form solution for a quasi-steady state director field induced by an arbitrarily large set of point defects and circular inclusions with or without fixed rotational degrees of freedom, and compute the forces and torques acting on each defect or inclusion. We show that a complete solution must include two types of singularities, generating a defect winding number and its spiral texture, which have a direct effect on defect equilibrium textures and their dynamics.

Magnetocontrollable droplet mobility on liquid crystal-infused porous surfaces.

Unlabelled: Magnetocontrollable droplet mobility on surfaces of both solids and simple fluids have been widely used in a wide range of applications. However, little is understood about the effect of the magnetic field on the wettability and mobility of droplets on structured fluids. Here, we report the manipulation of the dynamic behaviors of water droplets on a film of thermotropic liquid crystals (LCs).

Dense packings of geodesic hard ellipses on a sphere.

Packing problems are abundant in nature and have been researched thoroughly both experimentally and in numerical models. In particular, packings of anisotropic, elliptical particles often emerge in models of liquid crystals, colloids, and granular and jammed matter. While most theoretical studies on anisotropic particles have thus far dealt with packings in Euclidean geometry, there are many experimental systems where anisotropically-shaped particles are confined to a curved surface, such as Pickering emulsions stabilized by ellipsoidal particles or protein adsorbates on lipid vesicles.

Measure of overlap between two arbitrary ellipses on a sphere.

Various packing problems and simulations of hard and soft interacting particles, such as microscopic models of nematic liquid crystals, reduce to calculations of intersections and pair interactions between ellipsoids. When constrained to a spherical surface, curvature and compactness lead to non-trivial behaviour that finds uses in physics, computer science and geometry. A well-known idealized isotropic example is the Tammes problem of finding optimal non-intersecting packings of equal hard disks.

From coffee stains to uniform deposits: Significance of the contact-line mobility.

Hypothesis: Contact-line motion upon drying of a sessile droplet strongly affects the solute transport and solvent evaporation profile. Hence, it should have a strong impact on the deposit formation and might be responsible for volcano-like, dome-like and flat deposit morphologies.

Experiments: A method based on a thin-film interference was used to track the drop height profile and contact line motion during the drying.

Long-range order in quadrupolar systems on spherical surfaces.

The interplay between curvature, confinement and ordering on curved manifolds, with anisotropic interactions between building blocks, takes a central role in many fields of physics. In this paper, we investigate the effects of lattice symmetry and local positional order on orientational ordering in systems of long-range interacting point quadrupoles on a sphere in the zero temperature limit. Locally triangular spherical lattices show long-range ordered quadrupolar configurations only for specific symmetric lattices as strong geometric frustration prevents general global ordering.

Self-shaping liquid crystal droplets by balancing bulk elasticity and interfacial tension.

The shape diversity and controlled reconfigurability of closed surfaces and filamentous structures, universally found in cellular colonies and living tissues, are challenging to reproduce. Here, we demonstrate a method for the self-shaping of liquid crystal (LC) droplets into anisotropic and three-dimensional superstructures, such as LC fibers, LC helices, and differently shaped LC vesicles. The method is based on two surfactants: one dissolved in the LC dispersed phase and the other in the aqueous continuous phase.

Periodic Arrays of Chiral Domains Generated from the Self-Assembly of Micropatterned Achiral Lyotropic Chromonic Liquid Crystal.

Achiral building blocks forming achiral structures is a common occurrence in nature, while chirality emerging spontaneously from an achiral system is usually associated with important scientific phenomena. We report on the spontaneous chiral symmetry-breaking phenomena upon the topographic confinement of achiral lyotropic chromonic liquid crystals in periodically arranged micrometer scale air pillars. The anisotropic fluid arranges into chiral domains that depend on the arrangement and spacing of the pillars.

Three-Dimensional Active Defect Loops.

We describe the flows and morphological dynamics of topological defect lines and loops in three-dimensional active nematics and show, using theory and numerical modeling, that they are governed by the local profile of the orientational order surrounding the defects. Analyzing a continuous span of defect loop profiles, ranging from radial and tangential twist to wedge ±1/2 profiles, we show that the distinct geometries can drive material flow perpendicular or along the local defect loop segment, whose variation around a closed loop can lead to net loop motion, elongation, or compression of shape, or buckling of the loops. We demonstrate a correlation between local curvature and the local orientational profile of the defect loop, indicating dynamic coupling between geometry and topology.

Microfluidic control over topological states in channel-confined nematic flows.

Compared to isotropic liquids, orientational order of nematic liquid crystals makes their rheological properties more involved, and thus requires fine control of the flow parameters to govern the orientational patterns. In microfluidic channels with perpendicular surface alignment, nematics discontinuously transition from perpendicular structure at low flow rates to flow-aligned structure at high flow rates. Here we show how precise tuning of the driving pressure can be used to stabilize and manipulate a previously unresearched topologically protected chiral intermediate state which arises before the homeotropic to flow-aligned transition.

Spotting plants' microfilament morphologies and nanostructures.

The tracheary system of plant leaves is composed of a cellulose skeleton with diverse hierarchical structures. It is built of polygonally bent helical microfilaments of cellulose-based nanostructures coated by different layers, which provide them high compression resistance, elasticity, and roughness. Their function includes the transport of water and nutrients from the roots to the leaves.

Spherical structure factor and classification of hyperuniformity on the sphere.

Understanding how particles are arranged on the surface of a sphere is not only central to numerous physical, biological, soft matter, and materials systems but also finds applications in computational problems, approximation theory, and analysis of geophysical and meteorological measurements. Objects that lie on a sphere experience constraints that are not present in Euclidean (flat) space and that influence both how the particles can be arranged as well as their statistical properties. These constraints, coupled with the curved geometry, require a careful extension of quantities used for the analysis of particle distributions in Euclidean space to distributions confined to the surface of a sphere.

Sculpting stable structures in pure liquids.

Pure liquids in thermodynamic equilibrium are structurally homogeneous. In liquid crystals, flow and light pulses are used to create reconfigurable domains with polar order. Moreover, through careful engineering of concerted microfluidic flows and localized optothermal fields, it is possible to achieve complete control over the nucleation, growth, and shape of such domains.

Orientation, elastic interaction and magnetic response of asymmetric colloids in a nematic liquid crystal.

Colloidal particles in nematic liquid crystals create elastic distortion and experience long-range forces. The symmetry of elastic distortion and consequently the complexity of interaction strongly depends largely on the liquid crystal anchoring, topology and shape of the particles. Here, we introduce a new nematic colloidal system made of peanut-shaped hematite particles.

Mosaics of topological defects in micropatterned liquid crystal textures.

Topological defects in the orientational order that appear in thin slabs of a nematic liquid crystal, as seen in the standard schlieren texture, behave as a random quasi-two-dimensional system with strong optical birefringence. We present an approach to creating and controlling the defects using air pillars, trapped by micropatterned holes in the silicon substrate. The defects are stabilized and positioned by the arrayed air pillars into regular two-dimensional lattices.

Topology-commanded optical properties of bistable electric-field-induced torons in cholesteric bubble domains.

Nowadays, complicated topological defects enable many experimental manipulations and configurational simulations of active soft matter for optical and photonic applications. Investigation of topological defects in soft anisotropic materials enables one to better understand three-dimensional orientation fields in cholesteric liquid crystals. Here, we describe optical properties of bistable bubble domain (BD) texture torons in a thin layer of cholesteric liquid crystal (CLC), frustrated by homeotropic anchoring conditions, and reliably switchable by a random process.

Field-controlled structures in ferromagnetic cholesteric liquid crystals.

One of the advantages of anisotropic soft materials is that their structures and, consequently, their properties can be controlled by moderate external fields. Whereas the control of materials with uniform orientational order is straightforward, manipulation of systems with complex orientational order is challenging. We show that a variety of structures of an interesting liquid material, which combine chiral orientational order with ferromagnetic one, can be controlled by a combination of small magnetic and electric fields.

Action of fields on captive disclination loops.

We report on two effects observed in experiments with captive disclination loops on polymeric fibers immersed in nematics and submitted to electric and/or magnetic fields. We show that the magnetic field oblique to a fiber with axial or helicoidal anchoring on its surface induces translation of disclination loops. Fields orthogonal to fibers with helicoidal anchoring make disclination loops rotate around the field direction.

Hidden topological constellations and polyvalent charges in chiral nematic droplets.

Topology has an increasingly important role in the physics of condensed matter, quantum systems, material science, photonics and biology, with spectacular realizations of topological concepts in liquid crystals. Here we report on long-lived hidden topological states in thermally quenched, chiral nematic droplets, formed from string-like, triangular and polyhedral constellations of monovalent and polyvalent singular point defects. These topological defects are regularly packed into a spherical liquid volume and stabilized by the elastic energy barrier due to the helical structure and confinement of the liquid crystal in the micro-sphere.

Hedgehogs in the dowser state.

We show how to easily generate point defects called hedgehogs, in the so-called quasi-planar texture --the dowser state-- of a nematic layer confined between surfaces with homeotropic anchoring conditions. We point out that the dowser texture can be preserved infinitely in spite of its higher energy with respect to the homogeneous homeotropic texture. For topological reasons the dowser state in a squeezed droplet must contain at least one hedgehog.

Persistent quasiplanar nematic texture: Its properties and topological defects.

In the so-called quasiplanar texture of a nematic layer confined between parallel plates with homeotropic anchoring conditions, the director field rotates by π between limit surfaces so that field lines have the shape of a dowsing Y-shaped wooden tool. The orientation of the director field at midheight of the layer is arbitrary for symmetry reasons and is thus very sensitive to perturbations. We point out that contrary to accepted ideas the quasiplanar texture can be preserved infinitely in spite of its metastability with respect to the homogeneous homeotropic texture.

Topological defects in cholesteric liquid crystal shells.

We investigate experimentally and numerically the defect configurations emerging when a cholesteric liquid crystal is confined to a spherical shell. We uncover a rich scenario of defect configurations, some of them non-existent in nematic shells, where new types of defects are stabilized by the helical ordering of the liquid crystal. In contrast to nematic shells, here defects are not simple singular points or lines, but have a large structured core.

Waltzing route toward double-helix formation in cholesteric shells.

Liquid crystals, when confined to a spherical shell, offer fascinating possibilities for producing artificial mesoscopic atoms, which could then self-assemble into materials structured at a nanoscale, such as photonic crystals or metamaterials. The spherical curvature of the shell imposes topological constraints in the molecular ordering of the liquid crystal, resulting in the formation of defects. Controlling the number of defects, that is, the shell valency, and their positions, is a key success factor for the realization of those materials.