Director Field Configurations Research Articles

Chiral, Topological, and Knotted Colloids in Liquid Crystals

The geometric shape, symmetry, and topology of colloidal particles often allow for controlling colloidal phase behavior and physical properties of these soft matter systems. In liquid crystalline dispersions, colloidal particles with low symmetry and nontrivial topology of surface confinement are of particular interest, including surfaces shaped as handlebodies, spirals, knots, multi-component links, and so on. These types of colloidal surfaces induce topologically nontrivial three-dimensional director field configurations and topological defects. Director switching by electric fields, laser tweezing of defects, and local photo-thermal melting of the liquid crystal host medium promote transformations among many stable and metastable particle-induced director configurations that can be revealed by means of direct label-free three-dimensional nonlinear optical imaging. The interplay between topologies of colloidal surfaces, director fields, and defects is found to show a number of unexpected features, such as knotting and linking of line defects, often uniquely arising from the nonpolar nature of the nematic director field. This review article highlights fascinating examples of new physical behavior arising from the interplay of nematic molecular order and both chiral symmetry and topology of colloidal inclusions within the nematic host. Furthermore, the article concludes with a brief discussion of how these findings may lay the groundwork for new types of topology-dictated self-assembly in soft condensed matter leading to novel mesostructured composite materials, as well as for experimental insights into the pure-math aspects of low-dimensional topology.

Flow-induced order\u2013order transitions in amyloid fibril liquid crystalline tactoids

Liquid crystalline droplets, also known as tactoids, forming by nucleation and growth within the phase diagram region where isotropic and nematic phases coexist, challenge our understanding of liquid crystals under confinement due to anisotropic surface boundaries at vanishingly small interfacial tension, resulting in complex, non-spherical shapes. Little is known about their dynamical properties, since they are mostly studied under quiescent, quasi-equilibrium conditions. Here we show that different classes of amyloid based nematic and cholesteric tactoids undergo order–order transitions by flow-induced deformations of their shape. Tactoids align under extensional flow, undergoing extreme deformation into highly elongated prolate shapes, with the cholesteric pitch decreasing as an inverse power-law of the tactoids aspect ratio. Free energy functional theory and experimental measurements are combined to rationalize the critical elongation above which the director-field configuration of tactoids transforms from bipolar and uniaxial cholesteric to homogenous and to debate on the thermodynamic nature of these transitions.

Suppressed twist in droplets of cholesteric rod-like virus as identified by single particle imaging

ABSTRACT The director field configuration of a colloidal chiral nematic liquid crystal confined in droplets is studied in this work. We employ microfluidics to produce monodisperse droplets containing nematic dispersions of fd virus surrounded by a carrier oil phase, while we vary the size of the droplet as well as the concentration of the virus. The resulting director fields within the droplets are studied at the single-molecule level, using confocal microscopy. The 3-D structures are linked to polarisation microscopy observations of bright rings, which can be attributed to a cholesteric twist of the director field. We identify boundaries of concentration and size where one and two rings are observed, suggesting suppression of the cholesteric twist by confinement. Single particle confocal observations confirm that indeed the twist in the director field underlies the ring formation, but they also show that the twist is non-monotonous throughout the droplet and much smaller than observed in bulk.

Stable and Metastable Patterns in Chromonic Nematic Liquid Crystal Droplets Forced with Static and Dynamic Magnetic Fields

Spherical confinement of nematic liquid crystals leads to the formation of equilibrium director field configurations that include point and line defects. Driving these materials with flows or dynamic fields often results in the formation of alternative metastable states. In this article, we study the effect of magnetic field alignment, both under static and dynamic conditions, of nematic gems (nematic droplets in coexistence with the isotropic phase) and emulsified nematic droplets of a lyotropic chromonic liquid crystal. We use a custom polarizing optical microscopy assembly that incorporates a permanent magnet whose strength and orientation can be dynamically changed. By comparing simulated optical patterns with microscopy images, we measure an equilibrium twisted bipolar pattern within nematic gems that is only marginally different from the one reported for emulsified droplets. Both systems evolve to concentric configurations upon application of a static magnetic field, but behave very differently when the field is rotated. While the concentric texture within the emulsified droplets is preserved and only displays asynchronous oscillations for high rotating speeds, the nematic gems transform into a metastable untwisted bipolar configuration that is memorized by the system when the field is removed. Our results demonstrate the importance of boundary conditions in determining the dynamic behavior of confined liquid crystals even for configurations that share similar equilibrium bulk structures.

The Entangled Structure of Elastic Dipoles and a Twist Disclination Line in a Nematic Phase

The studies concerning 1/2 disclinations started with a focus on the fact that the interactions between the disclination and the microparticle accompanied by topological defects can be explained in a similar manner with electrostatic interactions. Therefore, the interactions in the elastic field have been revealed but the details concerning how the microparticles are entangled with the disclination lines have not been studied. However, because the applications of the entangled structures and the disclination itself are growing in periodic assembling and manipulation of micro- and nanoparticles, further detailed study is necessary. Thus, the detailed entangled structure of the twist disclination line and elastic dipoles is discussed in this work and we were able to conclude that the disclination line through the middle of the bead in the entangled structure acts as a −1/2 disclination line and the hedgehog point defect around the bead disappears because of the change of the director field configuration. In addition, zigzag entangled structures are created in order to lower the elastic energy due to the bend deformation. Based on these results, we will be able to discuss the entangled structure of ±1/2 disclination lines and elastic dipoles.

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.

Six-fold director field configuration in amyloid nematic and cholesteric phases

Chiral liquid crystals, or cholesteric phases, have been widely studied in the last decades, leading to fundamental advances and a multitude of applications and technologies. In general, the rich phenomenology of these systems depends directly on the molecular traits and conditions of the system, imposing precise symmetry to the resulting nematic field. By selecting amyloid fibrils as model filamentous chiral colloids, we report an unprecedented breadth of liquid crystalline morphologies, where up to six distinct configurations of the nematic field are observed under identical conditions. Amyloid-rich droplets show homogeneous, bipolar, radial, uniaxial chiral and radial chiral nematic fields, with additional parabolic focal conics in bulk. Variational and scaling theories allow rationalizing the experimental evidence as a subtle interplay between surface and bulk energies. Our experimental and theoretical findings deepen the understanding of chiral liquid crystals under confinement, opening to a more comprehensive exploitation of these systems in related functional materials.

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.

Edge pinning and transformation of defect lines induced by faceted colloidal rings in nematic liquid crystals.

Nematic colloids exhibit a large diversity of topological defects and structures induced by colloidal particles in the orientationally ordered liquid crystal host fluids. These defects and field configurations define elastic interactions and medium-mediated self-assembly, as well as serve as model systems in exploiting the richness of interactions between topologies and geometries of colloidal surfaces, nematic fields, and topological singularities induced by particles in the nematic bulk and at nematic-colloidal interfaces. Here we demonstrate formation of quarter-strength surface-pinned disclinations, as well as a large variety of director field configurations with splitting and reconnections of singular defect lines, prompted by colloidal particles with sharp edges and size large enough to define strong boundary conditions. Using examples of faceted ring-shaped particles of genus g=1, we explore transformation of defect lines as they migrate between locations in the bulk of the nematic host to edge-pinned locations at the surfaces of particles and vice versa, showing that this behavior is compliant with topological constraints defined by mathematical theorems. We discuss how transformation of bulk and surface defect lines induced by faceted colloids can enrich the diversity of elasticity-mediated colloidal interactions and how these findings may impinge on prospects of their controlled reconfigurable self-assembly in nematic hosts.

Reversal of helicoidal twist handedness near point defects of confined chiral liquid crystals

Handedness of the director twist in cholesteric liquid crystals is commonly assumed to be the same throughout the medium, determined solely by the chirality of constituent molecules or chiral additives, albeit distortions of the ground-state helicoidal configuration often arise due to the effects of confinement and external fields. We directly probe the twist directionality of liquid crystal director structures through experimental three-dimensional imaging and numerical minimization of the elastic free energy and show that spatially localized regions of handedness opposite to that of the chiral liquid crystal ground state can arise in the proximity of twisted-soliton-bound topological point defects. In chiral nematic liquid crystal confined to a film that has a thickness less than the cholesteric pitch and perpendicular surface boundary conditions, twisted solitonic structures embedded in a uniform unwound far-field background with chirality-matched handedness locally relieve confinement-imposed frustration and tend to be accompanied by point defects and smaller geometry-required, energetically costly regions of opposite twist handedness. We also describe a spatially localized structure, dubbed a "twistion," in which a twisted solitonic three-dimensional director configuration is accompanied by four point defects. We discuss how our findings may impinge on the stability of localized particlelike director field configurations in chiral and nonchiral liquid crystals.

Experimental realization of crossover in shape and director field of nematic tactoids

Spindle-shaped nematic droplets (tactoids) form in solutions of rod-like molecules at the onset of the liquid crystalline phase. Their unique shape and internal structure result from the interplay of the elastic deformation of the nematic and anisotropic surface forces. The balance of these forces dictates that tactoids must display a continuous variation in aspect ratio and director-field configuration. Yet, such continuous transition has eluded observation for decades: tactoids have displayed either a bipolar configuration with particles aligned parallel to the droplet interface or a homogeneous configuration with particles aligned parallel to the long axis of the tactoid. Here, we report the first observation of the continuous transition in shape and director-field configuration of tactoids in true solutions of carbon nanotubes in chlorosulfonic acid. This observation is possible because the exceptional length of carbon nanotubes shifts the transition to a size range that can be visualized by optical microscopy. Polarization micrographs yield the interfacial and elastic properties of the system. Absorbance anisotropy measurements provide the highest nematic order parameter (S=0.79) measured to date for a nematic phase of carbon nanotubes at coexistence with its isotropic phase.

Two-dimensional skyrmions and other solitonic structures in confinement-frustrated chiral nematics.

We explore spatially localized solitonic configurations of a director field, generated using optical realignment and laser-induced heating, in frustrated chiral nematic liquid crystals confined between substrates with perpendicular surface anchoring. We demonstrate that, in addition to recently studied torons and Hopf-fibration solitonic structures (hopfions), one can generate a host of other axially symmetric stable and metastable director field configurations where local twist is matched to the surface boundary conditions through introduction of point defects and loops of singular and nonsingular disclinations. The experimentally demonstrated structures include the so-called "baby-skyrmions" in the form of double twist cylinders oriented perpendicular to the confining substrates where their double twist field configuration is matched to the perpendicular boundary conditions by loops of twist disclinations. We also generate complex textures with arbitrarily large skyrmion numbers. A simple back-of-the-envelope theoretical analysis based on free energy considerations and the nonpolar nature of chiral nematics provides insights into the long-term stability and diversity of these inter-related solitonic field configurations, including different types of torons, cholestric-finger loops, two-dimensional skyrmions, and more complex structures comprised of torons, hopfions, and various disclination loops that are experimentally observed in a confinement-frustrated chiral nematic system.

Backflow-mediated domain switching in nematic liquid crystals.

We study the dynamics of the nematic liquid crystal kickback effect upon removal of a primary electric field and its amplification by a perpendicular secondary electric field resulting in the formation of domains with a reverse director orientation. Using computational fluid dynamics, we show that the domain formation is a robust phenomenon that takes place also in the complex case of multiple irregular random Freedericksz domains in three dimension as they appear in a realistic experimental situation. We propose domain switching by kickback amplification as a tool for self-insertion of shell-like inhomogeneities into an otherwise perfectly uniform director field configuration.

Investigations on the director field around microdisc resonators

The dielectric anisotropy of nematic liquid crystals can be used to achieve electrical tunability of optical whispering-gallery modes in microdisc resonators. In the present study the director field configuration around these microdisc resonators has been investigated using polarising optical microscopy, fluorescence confocal polarising microscopy and theoretical director field calculations. The results show a relationship to the director field around spherical particles with planar anchoring conditions, featuring two boojums and a parallel director orientation along the easy direction of the cell. The influence of electrical fields on the director field is discussed, including its effect on dielectric properties in the vicinity of the disc.

Microfluidic Synthesis of Highly Shape-Anisotropic Particles from Liquid Crystalline Elastomers with Defined Director Field Configurations

In this article, we present the synthesis of highly shape-anisotropic, micrometer-sized particles from liquid crystalline elastomers, which have the ability to reversibly change their shape in response to a certain external stimulus. For their preparation, we utilized a microfluidic setup. We succeeded in preparing sets of particles with differing degrees of shape anisotropy in their ground state including highly anisotropic fiber-like objects. All samples produced movement during the phase transition from the nematic to the isotropic phase of the liquid crystal. Depending on the direction of this shape change, we classified the samples in two groups. One type showed a contraction, while the other showed an expansion during the actuation, generating displacements of 60% and 80%, respectively. Using X-ray diffraction experiments, we could show that the different actuation properties arise from different director patterns of the liquid crystalline moieties in the microparticles. While the weakly shape-anisotropic microparticles possess a concentric director field (director perpendicular to the symmetry axis), the highly anisotropic fiber-like particles show an alignment of the director along the fiber axis. We present an explanation, claiming that this is the result of two different orientation mechanisms involving elongational flow on the one side and "log-rolling" on the other.

Magnetic field effects on tactoids of plate-like colloids

We investigate the effect of a magnetic field on the shape and director field of nematic droplets in dispersions of sterically stabilized and charge-stabilized colloidal gibbsite platelets with a negative diamagnetic anisotropy. Depending on the magnetic field strength and tactoid size, we observe with polarized light microscopy several interesting structures, with different shapes and director fields both with and without defects. In particular, our findings provide the first experimental evidence for the existence of the split-core defect structure predicted ten years ago by Mkaddem and Gartland [Phys. Rev. E 62, 6694 (2000)]. The split-core structure is a metastable director-field configuration that can be stabilized by a sufficiently strong externally applied magnetic field but only if the diamagnetic anisotropy of the particles is negative. To account for our observations, we present a calculation of the stability regions of different shapes and director-field structures as a function of tactoid size, anchoring conditions, surface tension, elastic constants, and magnetic field strength. By fitting the experimental data to the theoretically predicted structures, we are able to extract values for the splay elastic constant, interfacial tension, and anchoring strength. Remarkably, we find significant differences between the two systems studied: for sterically stabilized gibbsite in bromotoluene the anchoring strength is one order of magnitude larger than that of aqueous gibbsite, with the latter exhibiting weak and the former strong anchoring of the director field to the interface. The splay elastic constants that we obtain are in agreement with earlier experiments, simulations, and theory, while the interfacial tension and anchoring strength are considerably larger than what was found in earlier experiments.

Janus Nematic Colloids driven by light

We present an experimental analysis of different equilibrium orientations and light driven transformations of Janus particles in the nematic liquid crystal 5CB. Depending on the preparation technique of homeotropic (DMOAP) and planar (Au) hemispheres we have observed two types of director field configurations: dipolar-like in the case of Au/DMOAP capped colloids and boojum-like in the case of DMOAP/Au capped colloids. Using the manipulation of Au/DMOAP capped colloids with laser tweezers we report on light driven irreversible orientational transformations into Saturn-ring and a novel, boojum-ring configuration. On the contrary, boojum-like DMOAP/Au capped colloids can act as rotators when exposed to the laser filed. Observed rotation is continuous around an axis perpendicular to the laser beam axis, with the frequency increasing linearly with the laser power.

Control of mesogen configuration in colloids of liquid crystalline polymers

We report on a method to chemically predetermine the surface anchoring of mesogens in liquid crystalline colloids formed by different types of dispersion polymerization, and hence to achieve control over the mesogen configuration in such colloids. The surface anchoring is controlled by the chemical linkage of the polymers forming the colloids to the surfactants stabilizing the colloids towards the dispergent. We find that the hydroxypropyl cellulose used in conventional dispersion poylmerization induces parallel mesogen surface anchoring that in turn leads to bipolar director-field configurations, while a methacrylate terminated polysiloxane stabilizer, which is used in nonpolar dispersion polymerization, induces perpendicular anchoring and because of that to radial or axial configurations, depending on the size of the synthesized colloid. These differences in surface anchoring tendencies are due to differences in the molecular structure of the LC/non-LC block copolymers formed by the mesogens and the stabilizers. Based on these observations we synthesized a novel macroinitiator able to induce bipolar director-field configurations in the nonpolar dispersion polymerization.

Janus nematic colloids

We study the behavior of Janus colloidal particles in the nematic liquid crystal 5CB using polarizing optical microscopy and Landau-de Gennes (LdG) modeling. Different equilibrium orientations of Janus particles and different director field configurations around them are observed, depending on the preparation technique of homeotropic (DMOAP) and planar (Au) hemispheres. Using laser tweezers we measure the interactions between different orientations of Janus nematic colloids, showing a boojum type of interaction in the case of DMOAP/Au capped colloids and dipolar-like attraction for Au/DMOAP capped colloids. We observe a novel type of nematic colloidal particle, called a boojum-ring, characteristic of Au/DMOAP Janus nematic colloids, that is also predicted within the LdG theory for patterned colloidal particles with competing homeotropic and planar surfaces.

Planar photonic crystals infiltrated with liquid crystals: optical characterization of molecule orientation

Nematic liquid crystals are infiltrated into InP-based planar photonic crystals. Optical measurements as a function of temperature and polarization are used to study the average director field configuration in the nanometer-size holes: a planar equilibrium state is found.