Reconfigurable knots and links in chiral nematic colloids

Tying knots and linking microscopic loops of polymers, macromolecules, or defect lines in complex materials is a challenging task for material scientists. We demonstrate the knotting of microscopic topological defect lines in chiral nematic liquid crystal colloids into knots and links of arbitrary complexity by using laser tweezers as a micromanipulation tool. All knots and links with up to six crossings, including the Hopf link, the Star of David and the Borromean rings are demonstrated, stabilizing colloidal particles into an unusual soft matter. The knots in chiral nematic colloids are classified by the quantized self-linking number, a direct measure of the geometric, or Berry's, phase. Forming arbitrary microscopic knots and links in chiral nematic colloids is a demonstration of how relevant the topology can be for the material engineering of soft matter.Comment: 6 pages, 3 figure

Comparison of Non-stationary Sinusoid Estimation Methods Using Reassignment and Derivatives

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Flexoelectricity and piezoelectricity - reason for rich variety of phases in antiferroelectric liquid crystals

The free energy of antiferroelectric liquid crystal which takes into account polar order explicitly is presented. Steric, van der Waals, piezoelectric and flexoelectric interactions to the nearest layers and dipolar electrostatic interactions to the nearest and to the next nearest layers induce indirect tilt interactions with chiral and achiral properties, which extend to the third and to the fourth nearest layers. Chiral indirect interactions between tilts can be large and induce helicoidal modulations even in systems with negligible chiral van der Waals interactions. If indirect chiral interactions compete with chiral van der Waals interactions, the helix unwinding is possible. Although strength of microscopic interactions change monotonically with decreasing temperature, effective interlayer interactions change nonmonotonically and give rise to nonmonotouous change of modulation period through various phases. Increased enatiomeric excess i.e. increased chirality changes the phase sequence.Comment: 4 pages, 1 figur

Vector beams generated by microlasers based on topological liquid-crystal structures

Structured light with designable intensity, polarization and phase fields is today of high relevance, with application ranging from imaging, metrology, optical trapping, ultracold atoms, classical and quantum communications and memory. Specifically, vortex and vector beams can be generated directly in the laser cavity, however, a controllable, geometrically simple and easy to manufacture laser microcavity that generates structured light on demand, especially tailored polarization, is still an open challenge. Here we show that tunable laser vector beams can be generated from self-assembled liquid-crystal (LC) micro-structures with topological defects inside a thin Fabry-P\'erot microcavity. The LC superstructure provides complex three dimensional birefringent refractive index profiles with order parameter singularities. The topology of the LC structures is transferred into the topology of the light polarization. The oriented fluorescent dye emission dipoles enable the selection of optical modes with a particular polarization, as enabled by the birefringence profile in the laser cavity. The proposed lasers have no principal limitation for realizing structured light with arbitrarily tailored intensity and polarization fields

Generation of Multiple Circular Walls on a Thin Film of Nematic Liquid Crystal by Laser Scanning

We found that multiple circular walls (MCW) can be generated on a thin film of a nematic liquid crystal through a spiral scanning of a focused IR laser. The ratios between radii of adjacent rings of MCW were almost constant. These constant ratios can be explained theoretically by minimization of the Frank elastic free energy of nematic medium. The director field on a MCW exhibits chiral symmetry-breaking although the elastic free energies of both chiral MCWs are degenerated, i.e., the director on a MCW can rotate clockwise or counterclockwise along the radial direction.Comment: 10 pages, 5 figures. Submitted to Chemical Physics Letters 2nd Editio

Switching dynamics of surface stabilized ferroelectric liquid crystal cells: effects of anchoring energy asymmetry

We study both theoretically and experimentally switching dynamics in surface stabilized ferroelectric liquid crystal cells with asymmetric boundary conditions. In these cells the bounding surfaces are treated differently to produce asymmetry in their anchoring properties. Our electro-optic measurements of the switching voltage thresholds that are determined by the peaks of the reversal polarization current reveal the frequency dependent shift of the hysteresis loop. We examine the predictions of the uniform dynamical model with the anchoring energy taken into account. It is found that the asymmetry effects are dominated by the polar contribution to the anchoring energy. Frequency dependence of the voltage thresholds is studied by analyzing the properties of time-periodic solutions to the dynamical equation (cycles). For this purpose, we apply the method that uses the parameterized half-period mappings for the approximate model and relate the cycles to the fixed points of the composition of two half-period mappings. The cycles are found to be unstable and can only be formed when the driving frequency is lower than its critical value. The polar anchoring parameter is estimated by making a comparison between the results of modelling and the experimental data for the shift vs frequency curve. For a double-well potential considered as a deformation of the Rapini-Papoular potential, the branch of stable cycles emerges in the low frequency region separated by the gap from the high frequency interval for unstable cycles.Comment: 35 pages, 15 figure

Morphology of polymer networks formed in the chiral and non chiral phases of an anti-ferroelectric liquid crystal

We introduced photo-polymer networks into the various liquid crystalline phases of the antiferroelectric liquid crystal AS612 and studied the effects of these networks by measuring the temperature dependence of the Bragg wavelengths selectively reflected. After polymerization, the decrease in Bragg wavelengths with respect to the original values is consistent with a shorter helical pitch due to polymer network shrinkage. Also, by removing the liquid crystalline material, we are able to image the residual polymer network using scanning electron microscopy and polarized light microscopy. The polymer strands are a few microns thick and the networks show both chiral and non-chiral features

Front propagation into unstable and metastable states in Smectic C* liquid crystals: linear and nonlinear marginal stability analysis

We discuss the front propagation in ferroelectric chiral smectics (SmC*) subjected to electric and magnetic fields applied parallel to smectic layers. The reversal of the electric field induces the motion of domain walls or fronts that propagate into either an unstable or a metastable state. In both regimes, the front velocity is calculated exactly. Depending on the field, the speed of a front propagating into the unstable state is given either by the so-called linear marginal stability velocity or by the nonlinear marginal stability expression. The cross-over between these two regimes can be tuned by a magnetic field. The influence of initial conditions on the velocity selection problem can also be studied in such experiments. SmC$^*$ therefore offers a unique opportunity to study different aspects of front propagation in an experimental system

Melting of 2D liquid crystal colloidal structure

Using video microscopy, we investigated melting of a two-dimensional colloidal system, formed by glycerol droplets at the free surface of a nematic liquid crystalline layer. Analyzing different structure correlation functions, we conclude that melting occurs through an intermediate hexatic phase, as predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young(KTHNY) theory. However, the temperature range of the intermediate phase is rather narrow, <1°C, and the characteristic critical power law decays of the correlation functions are not fully developed. We conclude that the melting of our 2D systems qualitatively occurs according to KTHNY, although quantitative details of the transition scenario may partly depend on the details of interparticle interaction