Dynamics and Topology of Symmetry Breaking with Skyrmions.

We observe that pretransitional order parameter fluctuations of a skyrmion-forming chiral nematic liquid crystal are slowed down for 4 orders of magnitude, if confined to ≲100 nm thin layers. Fluctuating fragments of half-skyrmions are observed in a narrow temperature interval and are explained by thermally activated hopping between the various energy states. Skyrmion fluctuations are accompanied by imbalanced topological charge: positive charges appear at higher temperatures and dominate in the fluctuating region until skyrmions fully condense and negative charges appear at lower temperatures.

Optothermally driven colloidal transport in a confined nematic liquid crystal.

We demonstrate transport of microparticles by rapid movement of a laser spot in a thin layer of a nematic liquid crystal. The transport is achieved by fluid flow, caused by two different mechanisms. The thermoviscous expansion effect induces colloidal transport in the direction opposite to the laser movement, whereas thermally induced local melting of the liquid crystal pulls the particles in the direction of the laser movement. We demonstrate control of colloidal transport by changing the speed of the laser trap movement and the laser power. We anticipate that complex optofluidic colloidal transport could be realized in the nematic liquid crystal using a channel-free optofluidic approach.

Fractal nematic colloids.

Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter.

Dynamics of topological monopoles annihilation on a fibre in a thick and thin nematic layer.

We study topological defect annihilation on a glass fibre with homeotropic surface anchoring of nematic liquid crystal molecules. The fibre is set parallel to the nematic director of a planar cell with variable thickness and we create pairs of Saturn ring and Saturn anti-ring using the laser tweezers. In thick cells we observe in the whole region of defect separation a Coulomb-like pair attraction with no background force, [Formula: see text] with [Formula: see text]. In cells with thickness comparable to glass fibre diameter, we observe the Coulomb-like attraction only at small separations of the defect pair. For separations larger than the fibre diameter, the pair interaction force is independent of separation. This string-like force is attributed to the formation of defect lines, connecting both monopoles and are indeed visible only on extremely confined fibre, where the fibre diameter is practically equal to the nematic layer thickness. Numerical simulations confirm the formation of defect lines connecting both rings.

Annihilation dynamics of topological monopoles on a fiber in nematic liquid crystals.

We use the laser tweezers to create isolated pairs of topological point defects in a form of radial and hyperbolic hedgehogs, located close and attracted to a thin fiber with perpendicular surface orientation of nematic liquid crystal molecules in a thin planar nematic cell. We study the time evolution of the interaction between the two monopoles by monitoring their movement and reconstructing their trajectories and velocities. We find that there is a crossover in the pair interaction force between the radial and hyperbolic hedgehog. At small separation d, the elastic force between the opposite monopoles results in an increase of the attractive force with respect to the far field, and their relative velocity v scales as a v(d)∝d^{-2±0.2} power law. At large separations, the two oppositely charged monopoles can either attract or repel with constant interaction force. We explain this strange far-field behavior by the experimental inaccuracy in setting the fiber exactly perpendicular to the cell director.

Unusual temperature dependence of elastic constants of an ambient-temperature discotic nematic liquid crystal.

We report the first experimental studies on the temperature dependence of viscoelastic properties of a room temperature discotic nematic liquid crystal. The splay elastic constant is greater than the bend elastic constant and both show unusual temperature and order parameter dependence. The rotational viscosity is remarkably larger than conventional calamitic liquid crystals. We provide a simple physical explanation based on the columnar short-range order to account for the the unusual temperature dependence of the elastic constants.

Spherical microparticles with Saturn ring defects and their self-assembly across the nematic to smectic-A phase transition.

We report experimental studies on the Saturn ring defect associated with a spherical microparticle across the nematic (N) to smectic-A (SmA) phase transition. We observe that the director distortion around the microparticle changes rapidly with temperature. The equilibrium interparticle separation and the angle between two quadrupolar particles in the N phase are larger than those of the SmA phase. They are almost independent of the temperature in both phases, except for a discontinuous jump at the transition. We assembled a few particles using a laser tweezer to form a two-dimensional colloidal crystal in the N phase. The lattice structure of the crystal dissolves irreversibly across the N-SmA phase transition. The results on the pretransitional behavior of the defect are supported by the Landau-de Gennes Q-tensor modeling.

Surface charge and interactions of 20-nm nanocolloids in a nematic liquid crystal.

We studied real-time motion of individual 20-nm silica nanoparticles in a thin layer of a nematic liquid crystal using a dark-field optical videomicroscopy. By tracking the positions of individual nanoparticles we observed that particle pair interactions are not only mediated by strong thermal fluctuations of the nematic liquid crystal, but also with a repulsive force of electric origin. We determined the total electric charge of silanated silica particles in the nematic liquid crystal 5CB by observing the electric-force-driven drift. Surprisingly, the surface electric charge density depends on colloidal size and is ∼4.5×10(-3)C/m(2) for 20-nm nanocolloids, and two orders of magnitude lower, i.e., ∼2.3×10(-5)C/m(2), for 1-µm colloids. We conclude that electrostatic repulsion between like-charged particles prevents the formation of permanent colloidal assemblies of nanometer size. We also observed strong attraction of 20-nm silica nanoparticles to confining polyimide surfaces and larger clusters, which gradually results in complete expulsion of nanoparticles from the nematic liquid crystal to the surfaces of the confining cell.

Topological defect transformation and structural transition of two-dimensional colloidal crystals across the nematic to smectic-A phase transition.

We observe that topological defects in nematic colloids are strongly influenced by the elasticity and onset of smectic layering across the nematic (N) to smectic-A (SmA) phase transition. When approaching the SmA phase from above, the nematic hyperbolic hedgehog defect that accompanies a spherical colloidal inclusion is transformed into a focal conic line in the SmA phase. This phase transformation has a strong influence on the pairwise colloidal interaction and is responsible for a structural transition of two-dimensional colloidal crystals. The pretransitional behavior of the point defect is supported by Landau-de Gennes Q-tensor modeling accounting for the increasing elastic anisotropy.

Topological binding and elastic interactions of microspheres and fibres in a nematic liquid crystal.

We present a detailed analysis of topological binding and elastic interactions between a long, and micrometer-diameter fiber, and a microsphere in a homogeneously aligned nematic liquid crystal. Both objects are surface treated to produce strong perpendicular anchoring of the nematic liquid crystal. We use the opto-thermal micro-quench of the laser tweezers to produce topological defects with prescribed topological charge, such as pairs of a Saturn ring and an anti-ring, hyperbolic and radial hedgehogs on a fiber, as well as zero-charge loops. We study the entanglement and topological charge interaction between the topological defects of the fiber and sphere and we observe a huge variety of different entanglement topologies and defect-mediated elastic bindings. We explain all observed phenomena with simple topological rule: like topological charges repel each other and opposite topological charges attract. These binding mechanisms not only demonstrate the fascinating topology of nematic colloids, but also open a novel route to the assembly of very complex topological networks of fibers, spheres and other objects for applications in liquid crystal photonics.

Chiral bipolar colloids from nonchiral chromonic liquid crystals.

We demonstrate that high anisotropy of elastic constants of chromonic liquid crystals leads to a number of spontaneously twisted nematic director fields around colloidal particles in these non-chiral fluids. For spherical colloidal particles with surface inducing degenerate planar nematic ordering we observe that boojum defects at the particles' poles acquire twisted internal structure, extending up to three particle diameters along the rubbing direction of the cell. The twist handedness of the two boojum defects at the poles of the particle can be either the same or opposite, and we can switch the defects handedness by localized thermal microquenching. Numerical simulations confirm that the transitions into the distorted states are induced by lowering of the twist elastic constant, which results in two (meta)stable chiral configurations of the boojums, separated by an energy barrier much higher than the thermal energy. We show that boojum handedness can change the pairwise elastic interaction between the two particles positioned along the rubbing direction from repulsive to attractive.

Resonant transport of light from planar polymer waveguide into liquid-crystal microcavity.

We demonstrate the resonant transfer of light from a planar waveguide to a nematic liquid-crystal microdroplet immersed in water. A wide spectrum of light from a supercontinuum laser source is coupled into a high-refractive-index polymer waveguide using a prism-film coupler. The waveguide is in contact with a water dispersion of droplets from the nematic liquid-crystal 5CB. The evanescent field of the light in the waveguide is resonantly coupled to the whispering-gallery mode resonances, sustained by 5 - 20 µm-sized nematic liquid-crystal droplets, which are in close proximity to the waveguide. The resonant transfer of light is tuned by the temperature-induced shifting of the WGM resonances due to the temperature dependence of the refractive index of the nematic liquid crystal. The measurements are compared to the calculations of the coupled-mode theory.

Light-induced rewiring and winding of Saturn ring defects in photosensitive chiral nematic colloids.

We study the winding and unwinding of Saturn ring defects around silica microspheres with homeotropic surface anchoring in a cholesteric liquid crystal with a variable pitch. We use mixtures of a nematic liquid crystal 5CB and various photoresponsive chiral dopants to vary the helical pitch and sense of the helical winding by illuminating the mixtures with UV or visible light. Upon illumination, we observe motion of the Grandjean-Cano disclination lines in wedge-like cells. When the line touches the colloidal particle, we observe topological reconstruction of the Grandjean-Cano line and the Saturn ring. The result of this topological reconstruction is either an increase or decrease of the degree of winding of the Saturn ring around the colloidal particle. This phenomenon is similar to topological rewiring of -1/2 disclination lines, observed recently in chiral nematic colloids.

Consolidation trend design based on Young's modulus of clarithromycin single crystals.

The key aim of this study was to determine single mechanical properties of clarithromycin polymorphic forms in order to select some of them as more suitable for the tableting process. For this purpose, AFM single-point nanoindentation was used. The Young's moduli of clarithromycin polymorphs were substantially different, which was consistent with the structural variations in their packing motifs. The presence of the adjacent layers, which can easily slide over each other due to the low energy barrier (the lowest Young's modulus was 0.25 GPa) resulted in better bulk compressibility (the highest Heckel coefficient) of clarithromycin Form I. We also addressed the importance of tip geometry screening because the stress during the force mode often results in tip apex fracture. Even the initial manufacture of the diamond-coated tips can result in defects such as double-apex tips.

Transport of particles by a thermally induced gradient of the order parameter in nematic liquid crystals.

We demonstrate manipulation and transport of microparticles and even fluorescent molecules by the thermally induced gradient of the order parameter in the nematic liquid crystal. We use IR light absorption of the tightly focused beam of laser tweezers to heat locally a thin layer of the nematic liquid crystal by several degrees. This creates a spatial gradient of temperature of the nematic liquid crystal over separations of several tens of micrometers. We show that a dipolar colloidal particle is attracted into the hot spot of the laser tweezers. The depth of the trapping potential scales linearly with particle radius, indicating that the trapping mechanism is due to elastic self-energy of the distorted nematic liquid crystal around the particle and softening of the elasticity with increased temperature of the liquid crystal. We also demonstrate that this thermal trapping mechanism is efficient down to the nanoscale, as fluorescent molecules are also transported into hotter regions of the liquid crystal. This effect is absent in the isotropic phase, which calls into question particle transport due to the Soret effect.

Chirality screening and metastable states in chiral nematic colloids.

We show that forces between two colloidal particles in a thin layer of a chiral nematic liquid crystal strongly depend on the chirality of the liquid crystal. The observed pair potentials are attractive, but are oscillatory functions of colloidal separation. The number and the position of local energy minima increase with increasing chirality. The pair interaction is the strongest for the pitch equal to the colloidal diameter and decreases with increasing chirality. We show that the chirality of the medium is responsible for this oscillatory nature and screening of the colloidal interaction in the far and near field. The measurements are in agreement with numerical calculations using Landau-de Gennes theory.

Nematic colloids, topology and photonics.

We review and discuss recent progress in the field of nematic colloids, with an emphasis on possible future applications in photonics. The role of the topology is described, based on experimental manipulations of the topological defects in nematic colloids. The topology of the ordering field in nematics provides the forces between colloidal particles that are unique to these materials. We also discuss recent progress in the new field of active microphotonic devices based on liquid crystals (LCs), where chiral nematic microlasers and tuneable nematic microresonators are just two of the recently discovered examples. We conclude that the combination of topology and microphotonic devices based on LCs provides an interesting platform for future progress in the field of LCs.

Laser-driven microflow-induced bistable orientation of a nematic liquid crystal in perfluoropolymer-treated unrubbed cells.

We demonstrate laser-driven microflow-induced orientational change (homeotropic to planar) in a dye-doped nematic liquid crystal. The homeotropic to planar director alignment is achieved in unrubbed cells in the thermal hysteresis range of a discontinuous anchoring reorientation transition due to the local heating by light absorption in dye-doped sample. Various bistable patterns were recorded in the cell by a programmable laser tweezers. The width of the patterns depend on the scanning speed of the tightly focussed laser beam and the minimum width obtained is approximately equal to 0.57µm which is about 35 times smaller than the earlier report in the rubbed cells. We show that the motion of the microbeam spot causes local flow as a result the liquid crystal director is aligned along that direction.

Assembly and control of 3D nematic dipolar colloidal crystals.

Topology has long been considered as an abstract mathematical discipline with little connection to material science. Here we demonstrate that control over spatial and temporal positioning of topological defects allows for the design and assembly of three-dimensional nematic colloidal crystals, giving some unexpected material properties, such as giant electrostriction and collective electro-rotation. Using laser tweezers, we have assembled three-dimensional colloidal crystals made up of 4 µm microspheres in a bulk nematic liquid crystal, implementing a step-by-step protocol, dictated by the orientation of point defects. The three-dimensional colloidal crystals have tetragonal symmetry with antiparallel topological dipoles and exhibit giant electrostriction, shrinking by 25-30% at 0.37 V µm(-1). An external electric field induces a reversible and controllable electro-rotation of the crystal as a whole, with the angle of rotation being ~30° at 0.14 V µm(-1), when using liquid crystal with negative dielectric anisotropy. This demonstrates a new class of electrically highly responsive soft materials.

Viscoelasticity of ambient-temperature nematic binary mixtures of bent-core and rodlike molecules.

We report measurements of the temperature variations of physical parameters in ambient-temperature nematic liquid crystal mixtures of bent-core (BC) and rodlike molecules (5CB): birefringence Δn; static dielectric constants ε(||) and ε(⊥); splay K(11) and bend K(33) elastic constants; rotational viscosity γ(1); and diffusion coefficients D(||) and D(⊥) of a microsphere. Both Δn and ε(||) decreases rapidly with increasing BC concentration, whereas ε(⊥) remains almost constant. At a shifted temperature (e.g., T-T(NI)=-10 °C), K(11) increases by ~50% and K(33) decreases by ~80% compared to pure 5CB when the BC concentration is increased to ~43 mol % in the mixture. Viscosities parallel and perpendicular to the director, η(||), η(⊥), which are nearly equal to the Miesowicz viscosities η(2) and η(3), respectively, were obtained by D(||) and D(⊥) using the Stokes-Einstein relation. Both the viscosities at room temperature increase by 60 and 50 times, respectively, whereas γ(1) increases by 180 times (at ~43 mol %) compared to the corresponding values of pure 5CB. The stiffening of K(11) and exorbitantly large enhancement in all the viscosities at a higher mol % of BC indicate that the viscoelastic properties are highly impacted by the presence of smectic clusters of BC molecules that results from the restricted free rotation of the molecules along the bow axis in the nematic phase. A possible attachment model of smectic type clusters of BC molecules surrounding the microparticle is presented.