Nematic Colloids Research Articles

Enhanced optoelastic interaction range in liquid crystals with negative dielectric anisotropy

We demonstrate that the long-range interaction between surface-functionalized microparticles immersed a nematic liquid crystal—a “nematic colloid”—and a laser-induced “ghost colloid” can be enhanced by a low-voltage quasistatic electric field when the nematic mesophase has a negative dielectric anisotropy. The optoelastic trapping distance is shown to be enhanced by a factor up to 2.5 in presence of an electric field. Experimental data are quantitatively described with a theoretical model accounting for the spatial overlap between the orientational distortions around the microparticle and those induced by the trapping light beam itself.

Hydrodynamic effects in the measurement of interparticle forces in nematic colloids

We propose improved measurement methods of interparticle force between nematic colloids. Although various methods have been utilized for the force measurement, the comparison between the forces obtained by different methods has not been reported. In the frequently used method called the "free-release" method, the hydrodynamic interaction between moving particles has a serious influence on the measurement. In this study we modified those measurement methods by taking the long-ranged hydrodynamic interaction into account. The evaluated forces have been compared with that obtained by the dual beam "optical trap" method, which is free from the hydrodynamic effect. The agreement between them is quantitatively fairly good.

Dynamic arrest of nematic liquid-crystal colloid networks

We report interesting self-assembly structures of nematic liquid-crystal colloid (NLCC) networks, which are arrested during cooling from the isotropic temperature to room temperature. The NLCC is composed of sterically stabilized colloidal particles and a nematic liquid crystal (NLC) with nematic-isotropic transition temperature (T_{NI}) that is much higher than those of previously studied 4-Cyano-4'-pentylbiphenyl and N-(4-Methoxybenzylidene)-4-butylaniline. We find that the structure of NLCCs depends on T(NI), cooling rates, and boundary conditions, varying from cellular network to hierarchical fern structures in different length scales. Our time-lapse study shows that the transition from the cellular network to the fern structure directly corresponds to the transition from a spinodal demixing to a nucleation-and-growth mechanism.

Integrated and topological liquid crystal photonics

This contribution is a personal view of the rapidly developing subfield of nematic colloids, with an emphasis on possible applications of these materials in future photonic microdevices. A brief overview of the most important phenomena, observed in the past decade in nematic colloids is given. It is explained why integrated photonics based on microstructured liquid crystals is feasible and future challenges towards the realisation of integrated liquid crystal microphotonics are discussed.

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.

Interparticle force between different types of nematic colloids

We have studied the interparticle force between colloidal particles with three different types of defects in nematic liquid crystal by dual-beam optical tweezers. The force between a dipole (D)- and a Saturn-ring (S)-type particle at large interparticle distance R is proportional to R(-4.95±0.05). The force between a D- and a planar (P)-type particle and that between an S- and a P-type particle are, respectively, proportional to R(-5.04±0.08) and R(-5.78±0.13). The observed dependence of the interparticle force on R at large R is in agreement with that predicted by electrostatic analogy. The topological quadrupole moments for S and P particles are evaluated from experimental data. We have also studied the force curves in oblique arrangement against the far-field director for respective pairs. The experimental force curves at large R quantitatively agree with those predicted by electrostatic analogy, but they always become attractive at small R due to the reorientation and deformation of defects. The force profiles for the S-P pair are also compared with those obtained by the recent numerical simulation.

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.

Topology of nematic liquid crystal colloids confined to two dimensions

We present a brief overview of recent development in the field of nematic colloids with an emphasis on the topology of colloidal structures and recently discovered topologically nontrivial defect configurations. Nematic colloids are complex soft-matter systems, in which the topology of defects, induced by colloidal inclusions, can be controlled and varied locally by laser tweezers and other external fields. We discuss the role of elasticity driven colloidal interactions and demonstrate the importance of precise optical manipulation of topological defects for a targeted design of entangled structures. We conclude that the interplay between particle and defect topologies in liquid crystals provides an exciting journey to the burgeoning area of applied topology and opens several new directions in advanced engineering of soft materials.

Defect science and engineering of liquid crystals under geometrical frustration

Spontaneous symmetry breaking while preserving flow ability is a remarkable feature of nematic liquid crystals. When a nematic liquid crystal coexists with a solid, the surface field of the solid tends to anchor the director direction on the surface: anchoring effects. If geometrical frustration between nematic ordering and anchoring is strong enough, stable topological defects are formed. Defects in an ordered state are usually regarded as undesirable features. However, recent studies reveal that defects stabilized by a topological constraint from the solid surfaces are actually quite useful and open up novel possibilities for defect engineering of liquid crystals: self-organization of soft matter by defects, memory effects of topological origin, and control of flow of nematic liquid crystals and colloid motion by defects. For example, defect reconfiguration accompanying the change in the topology costs a very high energy far beyond the thermal energy, which overwhelms a typical energy scale in soft matter. This provides extreme stability for structures assembled by defects and information memorized in defect topology. Furthermore, effects of topological defects can easily be removed perfectly by a nematic-to-isotropic transition, which provides switchable functions. Defects also affect the motion of colloids immersed in a liquid crystal and flow behaviour of a liquid crystal. Here we review recent developments in science and engineering of topological defects in nematic liquid crystals, mainly based on our numerical simulation studies.

Electrically tunable optoelastic interaction range of nematic colloids

We report on the electrical tuning of the interaction range between colloidal particles in nematic liquid crystals. The experimental demonstration relies on the study of the dynamics of a real colloidal particle made of a glass sphere in the presence of an artificial laser-induced colloid that results from the local distortion of the nematic by a Gaussian light beam. The optoelastic interaction range between such a pair of colloids is shown to be fully controlled electrically. Moreover, all the observations are well described by an analytical model that accounts for the field-induced reorientation of the liquid crystal and the overlap between the long-range director distortion around both colloids.

APPROXIMATE TECHNIQUES FOR DISPERSIVE SHOCK WAVES IN NONLINEAR MEDIA

Many optical and other nonlinear media are governed by dispersive, or diffractive, wave equations, for which initial jump discontinuities are resolved into a dispersive shock wave. The dispersive shock wave smooths the initial discontinuity and is a modulated wavetrain consisting of solitary waves at its leading edge and linear waves at its trailing edge. For integrable equations the dispersive shock wave solution can be found using Whitham modulation theory. For nonlinear wave equations which are hyperbolic outside the dispersive shock region, the amplitudes of the solitary waves at the leading edge and the linear waves at the trailing edge of the dispersive shock can be determined. In this paper an approximate method is presented for calculating the amplitude of the lead solitary waves of a dispersive shock for general nonlinear wave equations, even if these equations are not hyperbolic in the dispersionless limit. The approximate method is validated using known dispersive shock solutions and then applied to calculate approximate dispersive shock solutions for equations governing nonlinear optical media, such as nematic liquid crystals, thermal glasses and colloids. These approximate solutions are compared with numerical results and excellent comparisons are obtained.

Nematic Colloids – Interaction between Particles in Anisotropic Liquids

We discuss novel interparticle force between colloids in nematic liquid crystal. The dependence of the interparticle force on the interparticle distance was experimentally measured by optical tweezers for the same and different sized particles. The obtained force curves quantitatively make agreement with the theory based on electrostatic analogy and the numerical calculation. We also present the self-assembling and artificial ways for building colloidal assemblies in nematic liquid crystal.

Interactions of distinct quadrupolar nematic colloids

The effective interaction between spherical colloids in nematic liquid crystals is investigated in the framework of the Landau-de Gennes theory. The colloids differ in their surface interaction with the nematic liquid crystal. The particles induce quadrupolar far-field distortions in the nematic matrix, favouring homeotropic and the other degenerate planar anchoring of the nematic director. In the strong anchoring regime the colloids with homeotropic anchoring are accompanied by an equatorial disclination line defect, known as “Saturn-ring”, while the colloids with degenerate planar anchoring nucleate a pair of antipodal surface defects, called “boojums”. In the linear (large-distance) regime, the colloidal interactions are of the quadrupolar type, with quadrupoles of opposite signs. These are attractive when the colloids are aligned either parallel or perpendicular to the far-field director. At short distances, non-linear effects including “direct” interactions between defects give rise to a repulsion between the particles, which prevents them from touching each other. This finding supports the stability of nematic colloidal square crystallites the assembly of which has been reported recently.

Three-dimensional complex-shaped photopolymerized microparticles at liquid crystal interfaces

Microparticles of arbitrary shapes immersed in the bulk of nematic fluids are known to produce dipolar or quadrupolar elastic distortions that can mediate long-range colloidal interactions. We use two-photon photopolymerization to obtain complex-shaped surface-bound microparticles that are then embedded into a nematic liquid crystal host with a uniform far-field director. By means of three-dimensional imaging with multi-photon excitation fluorescence polarizing microscopy, we demonstrate low-symmetry, long-range elastic distortions induced by the particles in the liquid crystal director field. These director distortions may provide a means for controlling elastic interactions in liquid crystals between custom-designed photopolymerized microparticles attached to confining solid substrates and nematic fluid-borne colloids, thus enabling elasticity-mediated templated self-assembly.

Stability and rewiring of nematic braids in chiral nematic colloids

Disclination lines in chiral nematic liquid crystals exhibit larger geometrical diversity than their counterparts in ordinary nematics and form rich entangled structures in systems with dispersed colloidal inclusions. Numerous metastable and stable states separated by low energy barriers allow for simple rewiring of the braids. Introducing a new visualization scheme where variations in splay, bend and twist deformations are followed separately allows us to display the effect of chirality on the director profile of the disclinations, and to uncover the mechanism of their rewiring. We demonstrate the richness of structures by performing a survey of all possible disclination structures that entangle a pair of homeotropic silica microspheres in a π-twisted cholesteric cell using numerical free-energy minimization and laser tweezers assisted microscopy. We analyze their stability against spontaneous rewiring and trace the stability differences to the local effects of chiral environment. We compare the predictions to the experimental results and discuss the differences between both approaches.

Photonic Control of Surface Anchoring on Solid Colloids Dispersed in Liquid Crystals

The anchoring of liquid-crystal (LC) mesogens to the surfaces of colloids is an important factor in determining intercolloidal interactions and the symmetry of the ensuing colloidal assembly in nematic colloids. The dynamic control of surface anchoring could therefore provide a handle to tune the colloidal organization and resulting properties in these systems. In this article, we report our results on the study of thermotropic nematic LC (E7) dispersions of silica and glass microcolloids bearing photosensitive surface azobenzene groups. By the photoinduced modulation of the colloidal-LC interfacial properties, due to the trans-cis isomerization of azobenzene units, we tune the anchoring on silica colloids from homeotropic (trans-azobenzene) to homogeneous planar (cis-azobenzene) reversibly. In tune with the change in surface anchoring, the interparticle interactions were also dictated by dipolar and quadrupolar symmetries for homeotropic and homogeneous planar anchoring, respectively. In our experiments, we find that, in addition to the isomerization state of the surface-bound azobenzene units, the nature of the colloid plays a crucial role in determining the anchoring state obtained on applying photostimuli. We also study the LC anchoring on colloids as a function of the azobenzene surface density and find that beyond a threshold value the anchoring properties remain invariant.

Colloidal entanglement in highly twisted chiral nematic colloids: Twisted loops, Hopf links, and trefoil knots

The topology and geometry of closed defect loops is studied in chiral nematic colloids with variable chirality. The colloidal particles with perpendicular surface anchoring of liquid crystalline molecules are inserted in a twisted nematic cell with the thickness that is only slightly larger than the diameter of the colloidal particle. The total twist of the chiral nematic structure in cells with parallel boundary conditions is set to 0, π, 2π, and 3π, respectively. We use the laser tweezers to discern the number and the topology of the -1/2 defect loops entangling colloidal particles. For a single colloidal particle, we observe that a single defect loop is winding around the particle, with the winding pattern being more complex in cells with higher total twist. We observe that colloidal dimers and colloidal clusters are always entangled by one or several -1/2 defect loops. For colloidal pairs in π-twisted cells, we identify at least 17 different entangled structures, some of them exhibiting linked defect loops-Hopf link. Colloidal entanglement is even richer with a higher number of colloidal particles, where we observe not only linked, but also colloidal clusters knotted into the trefoil knot. The experiments are in good agreement with numerical modeling using Landau-de Gennes theory coupled with geometrical and topological considerations using the method of tetrahedral rotation.

Interparticle force in nematic colloids: Comparison between experiment and theory

We have studied the interparticle force between two colloidal particles in a nematic liquid crystal experimentally and theoretically. The force F was directly measured using dual-beam optical tweezers and was numerically calculated from the equilibrium tensor field around the particles. The dependence of F on the center-to-center distance R between the particles was studied not only for equal-sized particles but also for different-sized ones in various kinds of configurations and arrangements. The magnitude of F between different-sized particles in the dipole configuration depends on their relative arrangement. Both experimental and theoretical force curves are found to be in good agreement with each other. At large R, they also make agreement with those predicted by an electrostatic analogy of nematic field.

Temperature and Confinement Effect on Interparticle Force in Nematic Colloids

We experimentally studied the interparticle force between two colloidal particles with point defects in a nematic liquid crystal. The force F at various temperatures was measured using optical tweezers and with a free release method. The effective elastic constant was evaluated from F using electrostatic analogy of nematic field. At respective temperatures, that is in good agreement with the splay constant obtained by dielectric measurement. The dependence of F on cell thicknesses was also studied in a wedge-type cell. In a thinner cell, the magnitude of F becomes smaller, and F becomes short-ranged.