Topology and self-assembly of defect-colloidal superstructure in confined chiral nematic liquid crystals

Quasi-one- and quasi-two-dimensional symbiotic solitons bound by dipolar interaction

We study the formation of quasi-one- (quasi-1D) and quasi-two-dimensional (quasi-2D) symbiotic solitons bound by an interspecies dipolar interaction in a binary dipolar Bose-Einstein condensate. These binary solitons have a repulsive intraspecies contact interaction stronger than the intraspecies dipolar interaction, so that they can not be bound in isolation in the absence of an interspecies dipolar interaction. These symbiotic solitons are bound in the presence of an interspecies dipolar interaction and zero interspecies contact interaction. The quasi-1D solitons are free to move along the polarization z direction of the dipolar atoms, whereas the quasi-2D solitons move in the x-z plane. To illustrate these, we consider a ^{164}Er-^{166}Er mixture with scattering lengths a(^{164}Er)=81a_{0} and a(^{166}Er)=68a_{0} and with dipolar lengths a_{dd}(^{164}Er)≈a_{dd}(^{166}Er)≈65a_{0}, where a_{0} is the Bohr radius. In each of the two components a>a_{dd}, which stops the binding of solitons in each component in isolation, whereas a binary quasi-1D or a quasi-2D ^{164}Er-^{166}Er soliton is bound in the presence of an interspecies dipolar interaction. The stationary states were obtained by imaginary-time propagation of the underlying mean-field model; dynamical stability of the solitons was established by real-time propagation over a long period of time.

Design and Preparation of Nematic Colloidal Particles

Colloidal systems are abundant in technology, in biomedical settings, and in our daily life. The so-called "colloidal atoms" paradigm exploits interparticle interactions to self-assemble colloidal analogs of atomic and molecular crystals, liquid crystal glasses, and other types of condensed matter from nanometer- or micrometer-sized colloidal building blocks. Nematic colloids, which comprise colloidal particles dispersed within an anisotropic nematic fluid host medium, provide a particularly rich variety of physical behaviors at the mesoscale, not only matching but even exceeding the diversity of structural and phase behavior in conventional atomic and molecular systems. This feature article, using primarily examples of works from our own group, highlights recent developments in the design, fabrication, and self-assembly of nematic colloidal particles, including the capabilities of preprogramming their behavior by controlling the particle's surface boundary conditions for liquid crystal molecules at the colloidal surfaces as well as by defining the shape and topology of the colloidal particles. Recent progress in defining particle-induced defects, elastic multipoles, self-assembly, and dynamics is discussed along with open issues and challenges within this research field.

Topological solitons, cholesteric fingers and singular defect lines in Janus liquid crystal shells

Topological solitons are non-singular but topologically nontrivial structures in fields, which have fundamental significance across various areas of physics, similar to singular defects. Production and observation of singular and solitonic topological structures remain a complex undertaking in most branches of science - but in soft matter physics, they can be realized within the director field of a liquid crystal. Additionally, it has been shown that confining liquid crystals to spherical shells using microfluidics resulted in a versatile experimental platform for the dynamical study of topological transformations between director configurations. In this work, we demonstrate the triggered formation of topological solitons, cholesteric fingers, singular defect lines and related structures in liquid crystal shells. We show that to accommodate these objects, shells must possess a Janus nature, featuring both twisted and untwisted domains. We report the formation of linear and axisymmetric objects, which we identify as cholesteric fingers and skyrmions or elementary torons, respectively. We then take advantage of the sensitivity of shells to numerous external stimuli to induce dynamical transitions between various types of structures, allowing for a richer phenomenology than traditional liquid crystal cells with solid flat walls. Using gradually more refined experimental techniques, we induce the targeted transformation of cholesteric twist walls and fingers into skyrmions and elementary torons. We capture the different stages of these director transformations using numerical simulations. Finally, we uncover an experimental mechanism to nucleate arrays of axisymmetric structures on shells, thereby creating a system of potential interest for tackling crystallography studies on curved spaces.

Cuboidal liquid crystal phases under multiaxial geometrical frustration

Cuboidal liquid crystal phases - the so-called blue phases - consist of a network of topological defects arranged into a cubic symmetry. They exhibit striking optical properties, including Bragg reflection in the visible range and fast response times. Confining surfaces can interfere with the packing of such a network, leading to structures that have not been explored before. In this work, a Landau-de Gennes free energy formalism for the tensor alignment field Q is used to investigate the behavior of chiral liquid crystals under non-isotropic confinement. The underlying free energy functional is solved by relying on a Monte Carlo method that facilitates efficient exploration of configuration space. The results of simulations are expressed in terms of phase diagrams as a function of chirality and temperature for three families of spheroids: oblate, spherical, and prolate. Upon deformation, blue phases adapt and transform to accommodate the geometrical constraints, thereby resulting in a wider range of thermal stability. For oblate spheroids, confinement interferes with the development of a full blue phase structure, resulting on a combination of half skyrmions. For prolate spheroids, the blue phases are hybridized and exhibit features of blue phases I and II. More generally, it is shown that mechanical deformation provides an effective means to control, manipulate and stabilize blue phases and cholesterics confined in tactoids.

Thermo-Optical Generation of Particle-Like Structures in Frustrated Chiral Nematic Film

The creation of metastable particle-like structures in frustrated (unwound) chiral nematic film containing light-absorbing additive is studied. It is shown that such localized structures can be generated by the thermo-optical action of a focused laser beam or arise spontaneously at a phase transition from an isotropic to a liquid crystal state. Observed axisymmetric patterns resemble cholesteric spherulites with toroidal double-twisted director-field configuration.

Silica aerogel films via ambient pressure drying for broadband reflectors

This manuscript demonstrates the advantages of silica aerogel films over nanoparticles in broadening the reflection bandwidth of cholesteric liquid crystals.

A ferroelectric liquid crystal confined in cylindrical nanopores: reversible smectic layer buckling, enhanced light rotation and extremely fast electro-optically active Goldstone excitations

The orientational and translational order of a thermotropic ferroelectric liquid crystal (2MBOCBC) imbibed in self-organized, parallel, cylindrical pores with radii of 10, 15, or 20 nm in anodic aluminium oxide monoliths (AAO) are explored by high-resolution linear and circular optical birefringence as well as neutron diffraction texture analysis. The results are compared to experiments on the bulk system. The native oxidic pore walls do not provide a stable smectogen wall anchoring. By contrast, a polymeric wall grafting enforcing planar molecular anchoring results in a thermal-history independent formation of smectic C* helices and a reversible chevron-like layer buckling. An enhancement of the optical rotatory power by up to one order of magnitude of the confined compared to the bulk liquid crystal is traced to the pretransitional formation of helical structures at the smectic-A*-to-smectic-C* transformation. A linear electro-optical birefringence effect evidences collective fluctuations in the molecular tilt vector direction along the confined helical superstructures, i.e. the Goldstone phason excitations typical of the para-to-ferroelectric transition. Their relaxation frequencies increase with the square of the inverse pore radii as characteristic of plane-wave excitations and are two orders of magnitude larger than in the bulk, evidencing an exceptionally fast electro-optical functionality of the liquid-crystalline-AAO nanohybrids.

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. The control of macroscopic optical density and diffraction efficiency of the BD texture is demonstrated by a selection of a confinement ratio of the CLC. Experimentally reconstructed CLC director profile reveals the topology of BD torons allowing consideration of naturally occurring BD texture for applications in optical and photonic devices, which are bistably switchable between active and transparent optical states.

Bipolar configuration with twisted loop defect in chiral nematic droplets under homeotropic surface anchoring

Optical textures and appropriate orientational structures have been studied within droplets of chiral nematic dispersed in polymer assigning the homeotropic anchoring. The helix axis of the chiral structure inside droplets forms the bipolar configuration. The optical droplet textures were analysed in the unpolarised light, analyser switching-off scheme and in crossed polarisers. The twisted loop defect reveals itself convincingly in all schemes. Its appearance at the optical patterns of the chiral nematic droplets has been examined depending on their size and the aspect direction. The existence of the defect has been verified by the structural and optical calculations. The effect of an electric field on both the defect line shape and the orientational structure of chiral nematic has been studied.

Nonsingular defects and self-assembly of colloidal particles in cholesteric liquid crystals

Cholesteric liquid crystals can potentially provide a means for tunable self-organization of colloidal particles. However, the structures of particle-induced defects and the ensuing elasticity-mediated colloidal interactions in these media remain much less explored and understood as compared to their nematic liquid crystal counterparts. Here we demonstrate how colloidal microspheres of varying diameter relative to the helicoidal pitch can induce dipolelike director field configurations in cholesteric liquid crystals, where these particles are accompanied by point defects and a diverse variety of nonsingular line defects forming closed loops. Using laser tweezers and nonlinear optical microscopy, we characterize the ensuing medium-mediated elastic interactions and three-dimensional colloidal assemblies. Experimental findings show a good agreement with numerical modeling based on minimization of the Landau-de Gennes free energy and promise both practical applications in the realization of colloidal composite materials and a means of controlling nonsingular topological defects that attract a great deal of fundamental interest.

Domed Silica Microcylinders Coated with Oleophilic Polypeptides and Their Behavior in Lyotropic Cholesteric Liquid Crystals of the Same Polypeptide

Liquid crystals can organize dispersed particles into useful and exotic structures. In the case of lyotropic cholesteric polypeptide liquid crystals, polypeptide-coated particles are appealing because the surface chemistry matches that of the polymeric mesogen, which permits a tighter focus on factors such as extended particle shape. The colloidal particles developed here consist of a magnetic and fluorescent cylindrically symmetric silica core with one rounded, almost hemispherical end. Functionalized with helical poly(γ-stearyl-l-glutamate) (PSLG), the particles were dispersed at different concentrations in cholesteric liquid crystals (ChLC) of the same polymer in tetrahydrofuran (THF). Defects introduced by the particles to the director field of the bulk PSLG/THF host led to a variety of phases. In fresh mixtures, the cholesteric mesophase of the PSLG matrix was distorted, as reflected in the absence of the characteristic fingerprint pattern. Over time, the fingerprint pattern returned, more quickly when the concentration of the PSLG-coated particles was low. At low particle concentration the particles were "guided" by the PSLG liquid crystal to organize into patterns similar to that of the re-formed bulk chiral nematic phase. When their concentration increased, the well-dispersed PSLG-coated particles seemed to map onto the distortions in the bulk host's local director field. The particles located near the glass vial-ChLC interfaces were stacked lengthwise into architectures with apparent two-dimensional hexagonal symmetry. The size of these "crystalline" structures increased with particle concentration. They displayed remarkable stability toward an external magnetic field; hydrophobic interactions between the PSLG polymers in the shell and those in the bulk LC matrix may be responsible. The results show that bio-inspired LCs can assemble suitable colloidal particles into soft crystalline structures.

Two-dimensional assemblies of nematic colloids in homeotropic cells and their response to electric fields

Micrometer-sized colloidal particles dispersed in nematic liquid crystals interact with each other through anisotropic interactions induced by orientational deformation of the nematic field. In the case of so-called dipole nematic colloids, their interaction is of the dipole-dipole type. Two-dimensional, non-close-packed colloidal assemblies having various characteristics were fabricated using optical tweezers by exploiting the attraction between anti-parallel dipole nematic colloids in homeotropically aligned nematic cells. Structures comprising polygons, squares, and tetrahedra were built using equal-sized particles, and hexagonal structures were built using particles of two sizes. As the nematic field is sensitive to electric fields, the response of the fabricated assemblies toward an alternating electric field was also studied. All assemblies exhibited homogeneous reversible shrinkage, and their shrinkage rates were dependent on the structure. The maximum shrinkage rate in the linear dimension of the assemblies was over 20% at 5 Vrms for a hexagon comprising tetrahedral units.

Elastic response and phase behavior in binary liquid crystal mixtures

Utilizing density-of-states simulations, we perform a full mapping of the phase behavior and elastic responses of binary liquid crystalline mixtures represented by the multicomponent Lebwohl-Lasher model. Our techniques are able to characterize the complete phase diagram, including nematic-nematic phase separation predicted by mean-field theories, but previously not observed in simulations. Mapping this phase diagram permits detailed study of elastic properties across the miscible nematic region. Importantly, we observe for the first time local phase separation and disordering driven by the application of small linear perturbations near the transition temperature and more significantly through nonlinear stresses. These findings are of key importance in systems of blended nematics which contain particulate inclusions, or are otherwise confined.

Frustration and Self-Ordering of Topological Defects in Ferroelectrics

A first-principles-based effective Hamiltonian technique is used to investigate the interplay between geometrical frustration and the ordering of topological defects in a ferroelectric nanocomposite consisting of a square array of BaTiO_{3} nanowires embedded in a Ba_{0.15}Sr_{0.85}TiO_{3} matrix. Different arrangements of the wires' chiralities geometrically frustrate the matrix, which in response exhibits point topological defects featuring self-assembled ordered structures spatially fluctuating down to the lowest temperatures. These fluctuations thereby endow the system with residual configurational entropy from which many properties characteristic of geometric frustration, such as the ground state degeneracy and the broadness of the dielectric response, are further found to originate.

Anisotropic colloidal transport and periodic stick-slip motion in cholesteric finger textures

We have investigated the mobility of discoidal colloidal particles sedimenting within cholesteric finger textures formed by mixtures of the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) and the chiral dopant 4-(2-methylbutyl)-4'-cyanobiphenyl (CB15) with cholesteric pitch p between 24 and 114 μm. The nickel disks, with radius 17 μm and thickness 300 nm, displayed varied transport behavior that depended on the size of the pitch and the orientation of the gravitational force with respect to the cholesteric axis. In textures with small pitch (p < 40 μm), the disks moved perpendicular to the axis irrespective of the orientation of gravity as a result of an elastic retarding force that prevented motion along the axis. In textures with larger pitch, the disks similarly moved perpendicular to the axis when the angle between the force and axis was large. When the angle was small, the disks displayed stick-slip motion caused by periodic yielding of the finger texture. A model considering viscous drag on the particles and the elastic energy cost of deforming the finger texture describes the stick-slip motion accurately. The effective drag viscosities obtained from the disk motion are anomalously large compared with those of pure nematic 5CB indicating a large contribution to the dissipation from the motion of disclinations in the texture in the vicinity of the translating disks.