Equilibrium state of a cylindrical particle with flat ends in nematic liquid crystals

A continuum theory is employed to numerically study the equilibrium orientation and defect structures of a circular cylindrical particle with flat ends under a homeotropic anchoring condition in a uniform nematic medium. Different aspect ratios of this colloidal geometry from thin discotic to long rodlike shapes and several colloidal length scales ranging from mesoscale to nanoscale are investigated. We show that the equilibrium state of this colloidal geometry is sensitive to the two geometrical parameters: aspect ratio and length scale of the particle. For a large enough mesoscopic particle, there is a specific asymptotic equilibrium angle associated to each aspect ratio. Upon reducing the particle size to nanoscale, the equilibrium angle follows a descending or ascending trend in such a way that the equilibrium angle of a particle with the aspect ratio bigger than 1:1 (a discotic particle) goes to a parallel alignment with respect to the far-field nematic, whereas the equilibrium angle for a particle with the aspect ratio 1:1 and smaller (a rodlike particle) tends toward a perpendicular alignment to the uniform nematic direction. The discrepancy between the equilibrium angles of the mesoscopic and nanoscopic particles originates from the significant differences between their defect structures. The possible defect structures related to mesoscopic and nanoscopic colloidal particles of this geometry are also introduced.

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

We describe formation of defect-colloidal superstructures induced by microspheres with normal surface anchoring dispersed in chiral nematic liquid crystals in confinement-unwound homeotropic cells. Using three-dimensional nonlinear optical imaging of the director field, we demonstrate that some of the induced defects have nonsingular solitonic nature while others are singular point and line topological defects. The common director structures induced by individual microspheres have dipolar symmetry. These topological dipoles are formed by the particle and a hyperbolic point defect (or small disclination loop) of elementary hedgehog charge opposite to that of a sphere with perpendicular boundary conditions, which in cells with thickness over equilibrium cholesteric pitch ratio approaching unity are additionally interspaced by a looped double-twist cylinder of continuous director deformations. The long-range elastic interactions are probed by holographic optical tweezers and videomicroscopy, providing insights to the physical underpinnings behind self-assembled colloidal structures entangled by twisted solitons. Computer-simulated field and defect configurations induced by the colloidal particles and their assemblies, which are obtained by numerically minimizing the Landau-de Gennes free energy, are in agreement with the experimental findings.

Multiscale models of colloidal dispersion of particles in nematic liquid crystals

We use homogenization theory to develop a multiscale model of colloidal dispersion of particles in nematic liquid crystals under weak-anchoring conditions. We validate the model by comparing it with simulations by using the Landau-de Gennes free energy and show that the agreement is excellent. We then use the multiscale model to study the effect that particle anisotropy has on the liquid crystal: spherically symmetric particles always reduce the effective elastic constant. Asymmetric particles introduce an effective alignment field that can increase the Fredericks threshold and decrease the switch-off time.

Elastic multipoles in the field of the nematic director distortions

Theory of the interaction between all types of elastic dipoles and quadrupoles and distortions of the nematic director is presented. If a particle is small relative to the characteristic distortion length, the interaction is determined by the director derivatives at the particle location. We consider a spherical particle since, even under the standard assumptions of the multipole theory (weak deformations, one constant approximation), the problem can be solved analytically only in this case. Different dipoles interact with different distortion modes (e.g., isotropic dipole interacts with the splay, chiral dipole with the twist, and so on). In the main order, the interaction of a dipole is linear in the director derivatives, and the interaction of a quadrupole is linear in the second-order director derivatives. The theory goes beyond the main-order terms and predicts an effective distortion-induced dipolar component on a particle. This effect is described by the free energy term quadratic in the director derivatives and has contributions both of a bulk and surface origin. The bulk effect takes place even if the director at the particle surface is fixed, whereas the surface effect appears if the surface director is perturbed by the distortions due to a weak surface anchoring. The theory is illustrated by simple examples of the interaction of elastic dipoles with a disclination line, with cholesteric spiral, and with the director distortions in a hybrid cell.

Orientationally ordered colloidal co-dispersions of gold nanorods and cellulose nanocrystals

Nematic-like and helicoidally orientational self-assemblies of gold nanorods co-dispersed with cellulose nanocrystals to form liquid crystalline phases are developed. Polarization-sensitive extinction spectra and two-photon luminescence imaging are used to characterize orientations and spatial distributions of gold nanorods. Cholesteric-isotropic phase coexistence and continuous domains of single-phase regions are observed and qualitatively discussed on the basis of entropic and electrostatic interactions in co-dispersions of rigid rods of different aspect ratios. Potential applications include biologically compatible plasmonic composite nanomaterials for solar biofuel production and polarization-sensitive plasmonic papers and fabrics.

Topology and dynamics of active nematic vesicles

Engineering synthetic materials that mimic the remarkable complexity of living organisms is a fundamental challenge in science and technology. We studied the spatiotemporal patterns that emerge when an active nematic film of microtubules and molecular motors is encapsulated within a shape-changing lipid vesicle. Unlike in equilibrium systems, where defects are largely static structures, in active nematics defects move spontaneously and can be described as self-propelled particles. The combination of activity, topological constraints, and vesicle deformability produces a myriad of dynamical states. We highlight two dynamical modes: a tunable periodic state that oscillates between two defect configurations, and shape-changing vesicles with streaming filopodia-like protrusions. These results demonstrate how biomimetic materials can be obtained when topological constraints are used to control the non-equilibrium dynamics of active matter.

Magnetically responsive gourd-shaped colloidal particles in cholesteric liquid crystals

Particle shape and medium chirality are two key features recently used to control anisotropic colloidal self-assembly and dynamics in liquid crystals. Here, we study magnetically responsive gourd-shaped colloidal particles dispersed in cholesteric liquid crystals with periodicity comparable or smaller than the particle's dimensions. Using magnetic manipulation and optical tweezers, which allow one to position colloids near the confining walls, we measured the elastic repulsive interactions of these particles with confining surfaces and found that separation-dependent particle-wall interaction force is a non-monotonic function of separation and shows oscillatory behavior. We show that gourd-shaped particles in cholesterics reside not on a single sedimentation level, but on multiple long-lived metastable levels separated by a distance comparable to cholesteric periodicity. Finally, we demonstrate three-dimensional laser tweezers assisted assembly of gourd-shaped particles taking advantage of both orientational order and twist periodicity of cholesterics, potentially allowing new forms of orientationally and positionally ordered colloidal organization in these media.

Optical manipulation of the nematic director field around microspheres covered with an azo-dendrimer monolayer

We report here the optical manipulation of the director and topological defect structures of nematic liquid crystals around a silica microparticle with azobenzene-containing dendrimers (azo-dendrimers) on its surface. We successfully demonstrate the successive switching processes from hedgehog, to boojum, and further to Saturn ring configurations by ultraviolet (UV) light irradiation and termination. The switching time between these defect structures depends on the UV light intensity and attains about 50 ms. Since the pretreatment of microparticles is not necessary and the surface modification is spontaneously performed just by dissolving the azo-dendrimers in liquid crystals, this dendrimer supplies us with a variety of possible applications.

Decoding the superlattice and interface structure of truncate PbS nanocrystal-assembled supercrystal and associated interaction forces

Large scale three-dimensional supercrystals were grown by controlling evaporation of truncate PbS nanocrystal (NC) dispersed hexane suspensions. Electron microscopy analysis confirmed the nature of single supercrystal with a face-centered cubic (fcc) lattice. Synchrotron small/wide angle scattering (SAXS/WAXS) images from three typical crystallographic projections allowed ultimate reconstruction of shape orientations of NCs at different crystallographic sites. Position exchange of distinctly oriented NCs between crystallographic sites produces two nondegeneration shape-related pseudo-polymorphs of superlattice that accordingly reduce symmetry from Oh to C4h and C2h with various facet-to-facet arrangements, respectively. In situ SAXS measurements of NC-assembled supercrystal and lead oleate and oleic acid upon pressurization provide additional insights into surface ligand density and the nature of ligand-NC interactions and resulting interface structure. These results allow for feasible evaluation of both NC shape and ligand conformation enabled effects that govern the formation and stability of truncate NC assemblies with various superlattice polymorphs and associated NC-ligand interactions in solvent-mediated assembled processes.

Electrically and optically tunable plasmonic guest-host liquid crystals with long-range ordered nanoparticles

Practical guest-host devices in which dichroic dye molecules follow electrical switching of a liquid crystal host remain elusive for decades despite promising efficient displays and emergent applications such as smart windows. This is mainly because of poor stability, surface precipitation, and limited means for property engineering of the dyes. To overcome these challenges, we develop plasmonic metal nanoparticle analogues of dichroic guest-host liquid crystals. Nematic dispersions of aligned anisotropic gold nanoparticles are obtained by polymer passivation of their surfaces to impose weak tangential boundary conditions for orientation of anisotropic host molecules. Control of the ensuing surface interactions leads to long-range ordered colloidal dispersions, allowing for collective optical and electrical switching of rod- and platelet-like nanoparticles. This facile control of mesostructured plasmonic medium's optical properties in visible and infrared spectral ranges is of interest for many applications.

Using nanoscale and mesoscale anisotropy to engineer the optical response of three-dimensional plasmonic metamaterials

The a priori ability to design electromagnetic wave propagation is crucial for the development of novel metamaterials. Incorporating plasmonic building blocks is of particular interest due to their ability to confine visible light. Here we explore the use of anisotropy in nanoscale and mesoscale plasmonic array architectures to produce noble metal-based metamaterials with unusual optical properties. We find that the combination of nanoscale and mesoscale anisotropy leads to rich opportunities for metamaterials throughout the visible and near-infrared. The low volume fraction (<5%) plasmonic metamaterials explored herein exhibit birefringence, a skin depth approaching that of pure metals for selected wavelengths, and directionally confined waves similar to those found in optical fibres. These data provide design principles with which the electromagnetic behaviour of plasmonic metamaterials can be tailored using high aspect ratio nanostructures that are accessible via a variety of synthesis and assembly methods.

Self-assembly of skyrmion-dressed chiral nematic colloids with tangential anchoring

We describe dipolar nematic colloids comprising mutually bound solid microspheres, three-dimensional skyrmions, and point defects in a molecular alignment field of chiral nematic liquid crystals. Nonlinear optical imaging and numerical modeling based on minimization of Landau-de Gennes free energy reveal that the particle-induced skyrmions resemble torons and hopfions, while matching surface boundary conditions at the interfaces of liquid crystal and colloidal spheres. Laser tweezers and videomicroscopy reveal that the skyrmion-colloidal hybrids exhibit purely repulsive elastic pair interactions in the case of parallel dipoles and an unexpected reversal of interaction forces from repulsive to attractive as the center-to-center distance decreases for antiparallel dipoles. The ensuing elastic self-assembly gives rise to colloidal chains of antiparallel dipoles with particles entangled by skyrmions.

Shape-dependent dispersion and alignment of nonaggregating plasmonic gold nanoparticles in lyotropic and thermotropic liquid crystals

We use both lyotropic liquid crystals composed of prolate micelles and thermotropic liquid crystals made of rod-like molecules to uniformly disperse and unidirectionally align relatively large gold nanorods and other complex-shaped nanoparticles at high concentrations. We show that some of these ensuing self-assembled orientationally ordered soft matter systems exhibit polarization-dependent plasmonic properties with strongly pronounced molar extinction exceeding that previously achieved in self-assembled composites. The long-range unidirectional alignment of gold nanorods is mediated mainly by anisotropic surface anchoring interactions at the surfaces of gold nanoparticles. Polarization-sensitive absorption, scattering, and extinction are used to characterize orientations of nanorods and other nanoparticles. The experimentally measured unique optical properties of these composites, which stem from the collective plasmonic effect of the gold nanorods with long-range order in a liquid crystal matrix, are reproduced in computer simulations. A simple phenomenological model based on anisotropic surface interaction explains the alignment of gold nanorods dispersed in liquid crystals and the physical underpinnings behind our observations.

Electric-field modulation of liquid crystal structures in contact with structured surfactant monolayers

We present experiments in which we use an electric field to switch between different configurations in the cellular patterns induced in a confined nematic liquid crystal by the contact with a surfactant monolayer that features lateral order and surface defects. By using different combinations of far-field alignment and mesogen dielectric anisotropy, we unravel the nature and stability of point defects and disclinations resulting from the hybrid boundary conditions.

The interaction of colloidal particles with weak homeotropic anchoring energy in homogeneous nematic liquid crystal cells

We have investigated interactions of colloidal particles with weak homeotropic anchoring energy in homogeneous nematic liquid crystal cells. Particle-wall and inter-particle interactions were observed experimentally and analyzed using typical dipole-dipole and quadrupole-quadrupole interactions, including substrate effects as the image charges. Both experimental results matched well with the calculated results for the effective particle radius reflecting the weak anchoring. The effective radius is reduced by the amount of extrapolation length than the actual particle radius. The effective radii of polyethylene micro-particles were reduced to a coefficient ζ (0.78 ≥ ζ ≥ 0.52) times the actual radius with anchoring coefficients in the range of 3.8 × 10(-6) to 1.4 × 10(-6) J m(-2). The anchoring energy of the particles is, therefore, a key component for explaining liquid crystal colloidal systems.

Dispersions of ellipsoidal particles in a nematic liquid crystal

Colloidal particles dispersed in a partially ordered medium, such as a liquid crystal (LC) phase, disturb its alignment and are subject to elastic forces. These forces are long-ranged, anisotropic and tunable through temperature or external fields, making them a valuable asset to control colloidal assembly. The latter is very sensitive to the particle geometry since it alters the interactions between the colloids. We here present a detailed numerical analysis of the energetics of elongated objects, namely prolate ellipsoids, immersed in a nematic host. The results, complemented with qualitative experiments, reveal novel LC configurations with peculiar topological properties around the ellipsoids, depending on their aspect ratio and the boundary conditions imposed on the nematic order parameter. The latter also determine the preferred orientation of ellipsoids in the nematic field, because of elastic torques, as well as the morphology of particle aggregates.

Transport of particles in liquid crystals

Colloidal particles in a liquid crystal (LC) behave very differently from their counterparts in isotropic fluids. Elastic nature of the orientational order and surface anchoring of the director cause long-range anisotropic interactions and lead to the phenomenon of levitation. The LC environment enables new mechanisms of particle transport that are reviewed in this work. Among them the motion of particles caused by gradients of the director, and effects in the electric field: backflow powered by director reorientations, dielectrophoresis in LC with varying dielectric permittivity and LC-enabled nonlinear electrophoresis with velocity that depends on the square of the applied electric field and can be directed differently from the field direction.

Quasicrystalline tilings with nematic colloidal platelets

Complex nematic fluids have the remarkable capability for self-assembling regular colloidal structures of various symmetries and dimensionality according to their micromolecular orientational order. Colloidal chains, clusters, and crystals were demonstrated recently, exhibiting soft-matter functionalities of robust binding, spontaneous chiral symmetry breaking, entanglement, shape-driven and topological driven assembly, and even memory imprinting. However, no quasicrystalline structures were found. Here, we show with numerical modeling that quasicrystalline colloidal lattices can be achieved in the form of original Penrose P1 tiling by using pentagonal colloidal platelets in layers of nematic liquid crystals. The tilings are energetically stabilized with binding energies up to 2500 kBT for micrometer-sized platelets and further allow for hierarchical substitution tiling, i.e., hierarchical pentagulation. Quasicrystalline structures are constructed bottom-up by assembling the boat, rhombus, and star maximum density clusters, thus avoiding other (nonquasicrystalline) stable or metastable configurations of platelets. Central to our design of the quasicrystalline tilings is the symmetry breaking imposed by the platelet shape and the surface anchoring conditions at the colloidal platelets, which are misaligning and asymmetric over two perpendicular mirror planes. Finally, the design of the quasicrystalline tilings as platelets in nematic liquid crystals is inherently capable of a continuous variety of length scales of the tiling, ranging over three orders of magnitude in the typical length (from ~ 10 nm to ~ 10 μm), which could allow for the design of quasicrystalline photonics at multiple frequency ranges.

Design of Functional Materials based on Liquid Crystalline Droplets

This brief perspective focuses on recent advances in the design of functional soft materials that are based on confinement of low molecular weight liquid crystals (LCs) within micrometer-sized droplets. While the ordering of LCs within micrometer-sized domains has been explored extensively in polymer-dispersed LC materials, recent studies performed with LC domains with precisely defined size and interfacial chemistry have unmasked observations of confinement-induced ordering of LCs that do not follow previously reported theoretical predictions. These new findings, which are enabled in part by advances in the preparation of LCs encapsulated in polymeric shells, are opening up new opportunities for the design of soft responsive materials based on surface-induced ordering transitions. These materials are also providing new insights into the self-assembly of biomolecular and colloidal species at defects formed by LCs confined to micrometer-sized domains. The studies presented in this perspective serve additionally to highlight gaps in knowledge regarding the ordering of LCs in confined systems.

Liquid-crystal mediated nanoparticle interactions and gel formation

Colloidal particles embedded within nematic liquid crystals exhibit strong anisotropic interactions arising from preferential orientation of nematogens near the particle surface. Such interactions are conducive to forming branched, gel-like aggregates. Anchoring effects also induce interactions between colloids dispersed in the isotropic liquid phase, through the interactions of the pre-nematic wetting layers. Here we utilize computer simulation using coarse-grained mesogens to perform a molecular-level calculation of the potential of mean force between two embedded nanoparticles as a function of anchoring for a set of solvent conditions straddling the isotropic-nematic transition. We observe that strong, nontrivial interactions can be induced between particles dispersed in mesogenic solvent, and explore how such interactions might be utilized to induce a gel state in the isotropic and nematic phases.

Rotational and translational diffusion of anisotropic gold nanoparticles in liquid crystals controlled by varying surface anchoring

We study translational and rotational diffusion of anisotropic gold nanoparticles (NPs) dispersed in the bulk of a nematic liquid crystal fluid host. Experimental data reveal strong anisotropy of translational diffusion with respect to the uniform far-field director, which is dependent on shape and surface functionalization of colloids as well as on their ground-state alignment. For example, elongated NPs aligned parallel to the far-field director translationally diffuse more rapidly along the director whereas diffusion of NPs oriented normal to the director is faster in the direction perpendicular to it while they are also undergoing elasticity-constrained rotational diffusion. To understand physical origins of these rich diffusion properties of anisotropic nanocolloids in uniaxially anisotropic nematic fluid media, we compare them to diffusion of prolate and oblate ellipsoidal particles in isotropic fluids as well as to diffusion of shape-isotropic particles in nematic fluids. We also show that surface functionalization of NPs with photosensitive azobenzene groups allows for in situ control of their diffusivity through trans-cis isomerization that changes surface anchoring.

Knots and nonorientable surfaces in chiral nematics

Knots and knotted fields enrich physical phenomena ranging from DNA and molecular chemistry to the vortices of fluid flows and textures of ordered media. Liquid crystals provide an ideal setting for exploring such topological phenomena through control of their characteristic defects. The use of colloids in generating defects and knotted configurations in liquid crystals has been demonstrated for spherical and toroidal particles and shows promise for the development of novel photonic devices. Extending this existing work, we describe the full topological implications of colloids representing nonorientable surfaces and use it to construct torus knots and links of type (p,2) around multiply twisted Möbius strips.

Liquid crystalline thermotropic and lyotropic nanohybrids

This review is meant to give the reader an insight into hybrids incorporating different types of nanoparticles, e.g. metallic or metal oxides, within different types of lyotropic and thermotropic liquid crystals, from relatively small calamitic molecules to the larger discotics and polymers. In particular, this review highlights the importance of nanoparticle-liquid crystal interactions in accessing hybrid materials that exhibit synergetic properties.

Nematic liquid crystal boojums with handles on colloidal handlebodies

Topological defects that form on surfaces of ordered media, dubbed boojums, are ubiquitous in superfluids, liquid crystals (LCs), Langmuir monolayers, and Bose-Einstein condensates. They determine supercurrents in superfluids, impinge on electrooptical switching in polymer-dispersed LCs, and mediate chemical response at nematic-isotropic fluid interfaces, but the role of surface topology in the appearance, stability, and core structure of these defects remains poorly understood. Here, we demonstrate robust generation of boojums by controlling surface topology of colloidal particles that impose tangential boundary conditions for the alignment of LC molecules. To do this, we design handlebody-shaped polymer particles with different genus g. When introduced into a nematic LC, these particles distort the nematic molecular alignment field while obeying topological constraints and induce at least 2g - 2 boojums that allow for topological charge conservation. We characterize 3D textures of boojums using polarized nonlinear optical imaging of molecular alignment and explain our findings by invoking symmetry considerations and numerical modeling of experiment-matching director fields, order parameter variations, and nontrivial handle-shaped core structure of defects. Finally, we discuss how this interplay between the topologies of colloidal surfaces and boojums may lead to controlled self-assembly of colloidal particles in nematic and paranematic hosts, which, in turn, may enable reconfigurable topological composites.

Active shape-morphing elastomeric colloids in short-pitch cholesteric liquid crystals

Active elastomeric liquid crystal particles with initial cylindrical shapes are obtained by means of soft lithography and polymerization in a strong magnetic field. Gold nanocrystals infiltrated into these particles mediate energy transfer from laser light to heat, so that the inherent coupling between the temperature-dependent order and shape allows for dynamic morphing of these particles and well-controlled stable shapes. Continuous changes of particle shapes are followed by their spontaneous realignment and transformations of director structures in the surrounding cholesteric host, as well as locomotion in the case of a nonreciprocal shape morphing. These findings bridge the fields of liquid crystal solids and active colloids, may enable shape-controlled self-assembly of adaptive composites and light-driven micromachines, and can be understood by employing simple symmetry considerations along with electrostatic analogies.

Liquid crystal-based emulsions for synthesis of spherical and non-spherical particles with chemical patches

We report the use of liquid crystal (LC)-in-water emulsions for the synthesis of either spherical or non-spherical particles with chemically distinct domains located at the poles of the particles. The approach involves the localization of solid colloids at topological defects that form predictably at surfaces of water-dispersed LC droplets. By polymerizing the LC droplets displaying the colloids at their surface defects, we demonstrate formation of both spherical and, upon extraction of the mesogen, anisotropic composite particles with colloids located at either one or both of the poles. Because the colloids protrude from the surfaces of the particles, they also define organized, chemical patches with functionality controlled by the colloid surface.

Electro-induced orientational ordering of anisotropic pigment nanoparticles

The response of anisotropic pigment particle suspensions to externally applied electric fields has been explored for possible application in reflective display technologies. Three different types of pigment particle were suspended in dodecane, using a polymeric stabilizer, and showed Schlieren textures between crossed polarizers at high concentrations (greater than 25-30 wt%), indicating the formation of colloidal nematic phases. Orientational order parameters were determined by X-ray scattering, and the influence of polydispersity on the values is discussed. X-ray scattering measurements also demonstrated a change in the structure factor consistent with the onset of a colloidal nematic phase. In addition, the pigment particles were dispersed into various liquid crystal hosts at low concentrations (less than 5 wt%) with and without the presence of mesogenic mimic stabilizers. However, the influence of these stabilizers on orientational ordering could not be confirmed. The electro-induced ordering determined via scattering was related to the electro-optical response of each suspension using a simple model. The particles in nematic hosts not only showed a high degree of orientational ordering at lower electric field strengths, but also showed a reduction in stability. Although these systems have shown strong orientational ordering, the optical response has been limited by the intrinsic shape of the pigment particles and the distribution of the transition dipoles moments within them. Nevertheless, the feasibility of developing materials for display applications has been demonstrated.

A self-organized anisotropic liquid-crystal plasmonic metamaterial

A composite material that leads to self organization of mesogen-coated gold nanospheres is synthesized and shows enhanced anisotropic optical properties due to synergistic effects of the mesogens intrinsic birefringence and its ability to drive the self-assembly process into highly anisotropic architectures with densely packed nanospheres. Such nanoengineered matter sustains a response beyond that achievable by its individual constituents, i.e., a metamaterial.

Anisotropic Stokes drag and dynamic lift on spheres sedimenting in a nematic liquid crystal

The motion of silica spheres with homeotropic anchoring sedimenting within nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) has been studied at low Ericksen number. The magnitude of the spheres' velocity depends on the angle θ between the far-field nematic director and the gravitational force, indicating an anisotropic Stokes drag. When the director is oriented at an oblique angle to the gravitational force, the velocity also acquires a component normal to the force, demonstrating the existence of a lift force generated by the fluid. The magnitude and direction of the velocity as functions of θ quantitatively obey theoretically predicted forms.

Van der Waals interaction in uniaxial anisotropic media

Van der Waals interactions between flat surfaces in uniaxial anisotropic media are investigated in the nonretarded limit. The main focus is the effect of nonzero tilt between the optical axis and the surface normal on the strength of the van der Waals attraction. General expressions for the van der Waals free energy are derived using the surface mode method and the transfer-matrix formalism. To facilitate numerical calculations a temperature-dependent three-band parameterization of the dielectric tensor of the liquid crystal 5CB is developed. A solid slab immersed in a liquid crystal experiences a van der Waals torque that aligns the surface normal relative to the optical axis of the medium. The preferred orientation is different for different materials. Two solid slabs in close proximity experience a van der Waals attraction that is strongest for homeotropic alignment of the intervening liquid crystal for all the materials studied. The results have implications for the stability of plate-like colloids in liquid crystal hosts.

Optical manipulation of self-aligned graphene flakes in liquid crystals

Graphene recently emerged as a new two-dimensional material platform with unique optical, thermal and electronic properties. Single- or few-atom-thick graphene flakes can potentially be utilized to form structured bulk composites that further enrich these properties and enable a broad range of new applications. Here we describe optical manipulation of self-aligned colloidal graphene flakes in thermotropic liquid crystals of nematic and cholesteric types. Three-dimensional rotational and translational manipulation of graphene flakes by means of holographic optical tweezers allows for non-contact spatial patterning of graphene, control of liquid crystal defects, and low-power optical realignment of the liquid crystal director using these flakes. Potential applications include optically- and electrically-controlled reconfigurable liquid crystalline dispersions of spontaneously aligning colloidal graphene flakes and new electro-optic devices with graphene-based interconnected transparent electrodes at surfaces and in the bulk of liquid crystals.

Topological colloids

Smoke, fog, jelly, paints, milk and shaving cream are common everyday examples of colloids, a type of soft matter consisting of tiny particles dispersed in chemically distinct host media. Being abundant in nature, colloids also find increasingly important applications in science and technology, ranging from direct probing of kinetics in crystals and glasses to fabrication of third-generation quantum-dot solar cells. Because naturally occurring colloids have a shape that is typically determined by minimization of interfacial tension (for example, during phase separation) or faceted crystal growth, their surfaces tend to have minimum-area spherical or topologically equivalent shapes such as prisms and irregular grains (all continuously deformable--homeomorphic--to spheres). Although toroidal DNA condensates and vesicles with different numbers of handles can exist and soft matter defects can be shaped as rings and knots, the role of particle topology in colloidal systems remains unexplored. Here we fabricate and study colloidal particles with different numbers of handles and genus g ranging from 1 to 5. When introduced into a nematic liquid crystal--a fluid made of rod-like molecules that spontaneously align along the so-called 'director'--these particles induce three-dimensional director fields and topological defects dictated by colloidal topology. Whereas electric fields, photothermal melting and laser tweezing cause transformations between configurations of particle-induced structures, three-dimensional nonlinear optical imaging reveals that topological charge is conserved and that the total charge of particle-induced defects always obeys predictions of the Gauss-Bonnet and Poincaré-Hopf index theorems. This allows us to establish and experimentally test the procedure for assignment and summation of topological charges in three-dimensional director fields. Our findings lay the groundwork for new applications of colloids and liquid crystals that range from topological memory devices, through new types of self-assembly, to the experimental study of low-dimensional topology.

Spontaneous knotting of self-trapped waves

We describe theory and simulations of a spinning optical soliton whose propagation spontaneously excites knotted and linked optical vortices. The nonlinear phase of the self-trapped light beam breaks the wave front into a sequence of optical vortex loops around the soliton, which, through the soliton's orbital angular momentum and spatial twist, tangle on propagation to form links and knots. We anticipate similar spontaneous knot topology to be a universal feature of waves whose phase front is twisted and nonlinearly modulated, including superfluids and trapped matter waves.

Elastic and hydrodynamic torques on a colloidal disk within a nematic liquid crystal

The orientationally dependent elastic energy and hydrodynamic behavior of colloidal disks with homeotropic surface anchoring suspended in the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) have been investigated. In the absence of external torques, the disks align with the normal of the disk face â parallel to the nematic director n[over ^]. When a magnetic field is applied, the disks rotate â by an angle θ so that the magnetic torque and the elastic torque caused by distortion of the nematic director field are balanced. Over a broad range of angles, the elastic torque increases linearly with θ in quantitative agreement with a theoretical prediction based on an electrostatic analogy. When the disks are rotated to angles θ>π/2, the resulting large elastic distortion makes the disk orientation unstable, and the director undergoes a topological transition in which θ→π-θ. In the transition, a defect loop is shed from the disk surface, and the disks spin so that â sweeps through π radians as the loop collapses back onto the disk. Additional measurements of the angular relaxation of disks to θ=0 following removal of the external torque show a quasi-exponential time dependence from which an effective drag viscosity for the nematic can be extracted. The scaling of the angular time dependence with disk radius and observations of disks rotating about â indicate that the disk motion affects the director field at surprisingly modest Ericksen numbers.

Template-assisted assembly of the functionalized cubic and spherical microparticles

The patterned template-assisted assembly of the cubic microparticles driven by the competing capillary, Columbic, and van der Waals forces had been studied in comparison with the traditional spherical colloidal microparticles. We observed that the spherical and cubic microparticles assembled with different probability in the channels of the hydrophobic-hydrophilic patterned substrates due to differences in a balance of adhesive and capillary forces. In contrast to highly selective assembly of spherical microparticles, selective deposition of cubic microcrystals with channels is impeded by strong adhesive forces facilitated by large specific interfacial areas between cube facets and substrate. The modification of the patterned substrate by functionalized coatings with oppositely charged topmost layers significantly increases the probability (to 86%) of the cubic microparticles to assemble into chemically modified channels. The introduction of ultrathin LbL shells on cubic microparticles and functionalization of patterned substrates are critical for the directed colloidal assembly of anisotropic microparticles into ordered aggregates.

Interface-induced nucleation, orientational alignment and symmetry transformations in nanocube superlattices

The self-assembly of colloidal nanocrystals into ordered superstructures depends critically on the shape of the nanocrystal building blocks. We investigated the self-assembly of cubic PbSe nanocrystals from colloidal suspensions in real-time using in situ synchrotron-based X-ray scattering. We combined small-angle and wide-angle scattering to investigate the translational ordering of nanocrystals and their orientational ordering in the lattice sites, respectively. We found that cubic PbSe nanocrystals assembled into a face-up (i.e., [100] normal to the interface) configuration at the liquid/substrate interface whereas nanocubes at the liquid/air interface assume a corner-up (i.e., [111] normal to the interface) configuration. The latter nanocrystal superlattice displays polymorphism as a function inter-NC separation distance. We explain the observed superlattice structure polymorphs in terms of the interactions directing the self-assembly. Insights into the directed self-assembly of superlattices gained from this study have important implication on the future development of nanocrystals as building blocks in artificial solids.

Nematic director-induced switching of assemblies of hexagonally packed gold nanorods

Self-assembled disc-shaped clusters of hexagonally packed, thiol-functionalized gold nanorods are prepared and dispersed in thermotropic nematic liquid crystals. The resultant hybrid complex fluids exhibit colloidal anisotropy with very high orientational order and are characterized by SAXS as shown in the figure. Precise, reconfigurable control of the cluster orientation at very low electric field strengths (0.18 V μm(-1) ) is achieved.

Optical generation of crystalline, quasicrystalline, and arbitrary arrays of torons in confined cholesteric liquid crystals for patterning of optical vortices in laser beams

Condensed matter systems with topological defects in the ground states range from the Abrikosov phases in superconductors, to various blue phases and twist grain boundary phases in liquid crystals, and to phases of skyrmion lattices in chiral ferromagnets and Bose-Einstein condensates. In nematic and chiral nematic liquid crystals, which are true fluids with long-range orientational ordering of constituent molecules, point and line defects spontaneously occur as a result of symmetry-breaking phase transitions or due to flow, but they are unstable, hard to control, and typically annihilate with time. Here we describe the optical generation of two-dimensional crystalline, quasicrystalline, and arbitrary ensembles of particlelike structures manifesting both skyrmionlike and Hopf fibration features--dubbed "torons"--composed of looped double twist cylinders and point defects embedded in a uniform director field. In these two-dimensional lattices, we then introduce various dislocations, defects in positional ordering of the torons. We show that the periodic defect lattices with and without dislocation are light- and voltage-tunable reconfigurable two-dimensional diffraction gratings and can be used to generate various controlled phase singularities in the diffracted laser beams. The results of computer simulations of optical images, diffraction patterns, and phase distributions with optical vortices are in a good agreement with the corresponding experimental findings.

Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities

Topological defect lines are ubiquitous and important in a wide variety of fascinating phenomena and theories in many fields ranging from materials science to early-universe cosmology, and to engineering of laser beams. However, they are typically hard to control in a reliable manner. Here we describe facile erasable “optical drawing” of self-assembled defect clusters in liquid crystals. These quadrupolar defect clusters, stabilized by the medium's chirality and the tendency to form twisted configurations, are shaped into arbitrary two-dimensional patterns, including reconfigurable phase gratings capable of generating and controlling optical phase singularities in laser beams. Our findings bridge the studies of defects in condensed matter physics and optics and may enable applications in data storage, singular optics, displays, electro-optic devices, diffraction gratings, as well as in both optically- and electrically-addressed pixel-free spatial light modulators.

Direct nanomechanical measurement of an anchoring transition in a nematic liquid crystal subject to hybrid anchoring conditions

We have used a surface forces apparatus to measure the normal force between two solid curved surfaces confining a film of nematic liquid crystal (5CB, 4'-n-pentyl-4-cyanobiphenyl) under hybrid planar-homeotropic anchoring conditions. Upon reduction of the surface separation D, we measured an increasingly repulsive force in the range D = 35-80 nm, reaching a plateau in the range D = 10-35 nm, followed by a short-range oscillatory force at D < 5 nm. The oscillation period was comparable to the cross-sectional diameter of the liquid crystal molecule and characteristic of a configuration with the molecules parallel to the surfaces. These results show that the director field underwent a confinement-induced transition from a splay-bend distorted configuration at large D, which produces elastic repulsive forces, to a uniform planar nondegenerate configuration with broken homeotropic anchoring, which does not produce additional elastic forces as D is decreased. These findings, supported by measurements of the birefringence of the confined film at different film thicknesses, provide the first direct observation of an anchoring transition on the nanometer scale.

Confinement-induced transition of topological defects in smectic liquid crystals: from a point to a line and pearls

We report a study on the confinement-induced transition of the topological defects of liquid crystals (LCs) using smectic-A LCs confined in prolate spheroids with homeotropic anchoring. Upon increasing the aspect ratio of a LC droplet, dispersed in a stretched elastomer film, the topological defect undergoes a transition from a point to a line of which the length is a function of the aspect ratio. Additionally, when the size of a droplet is larger than a certain value, the defect has a pearl-necklace-like texture. We propose a simple model to understand the formation of these defects in terms of the misorientation and undulation instability of the smectic layers.

Detection of diffusion anisotropy due to particle asymmetry from single-particle tracking of Brownian motion by the large-deviation principle

We show that the diffusion anisotropy due to the asymmetry of the particle can be extracted from the trajectory data without the information of the particle orientation. The subject of analysis is typical in single-particle tracking (SPT) experiments, and the analysis is based on the large-deviation principle in mathematics. We consider the model system of Langevin equations in two dimensions where a particle diffusion shows anisotropy depending on a single parameter defined by the two diffusion coefficients in the perpendicular directions of the frame fixed to the particle. We show how the large-deviation quantities depend on this parameter so that it can be used for the detection of the diffusion anisotropy. We also illustrate how the discreteness of the sampling interval in the SPT and the finiteness of the number of samples influence the results of the analysis.

Unconventional structure-assisted optical manipulation of high-index nanowires in liquid crystals

Stable optical trapping and manipulation of high-index particles in low-index host media is often impossible due to the dominance of scattering forces over gradient forces. Here we explore optical manipulation in liquid crystalline structured hosts and show that robust optical manipulation of high-index particles, such as GaN nanowires, is enabled by laser-induced distortions in long-range molecular alignment, via coupling of translational and rotational motions due to helicoidal molecular arrangement, or due to elastic repulsive interactions with confining substrates. Anisotropy of the viscoelastic liquid crystal medium and particle shape give rise to a number of robust unconventional trapping capabilities, which we use to characterize defect structures and study rheological properties of various thermotropic liquid crystals.

Reconfigurable interactions and three-dimensional patterning of colloidal particles and defects in lamellar soft media

Colloidal systems find important applications ranging from fabrication of photonic crystals to direct probing of phenomena typically encountered in atomic crystals and glasses. New applications--such as nanoantennas, plasmonic sensors, and nanocircuits--pose a challenge of achieving sparse colloidal assemblies with tunable interparticle separations that can be controlled at will. We demonstrate reconfigurable multiscale interactions and assembly of colloids mediated by defects in cholesteric liquid crystals that are probed by means of laser manipulation and three-dimensional imaging. We find that colloids attract via distance-independent elastic interactions when pinned to the ends of cholesteric oily streaks, line defects at which one or more layers are interrupted. However, dislocations and oily streaks can also be optically manipulated to induce kinks, allowing one to lock them into the desired configurations that are stabilized by elastic energy barriers for structural transformation of the particle-connecting defects. Under the influence of elastic energy landscape due to these defects, sublamellar-sized colloids self-assemble into structures mimicking the cores of dislocations and oily streaks. Interactions between these defect-embedded colloids can be varied from attractive to repulsive by optically introducing dislocation kinks. The reconfigurable nature of defect-particle interactions allows for patterning of defects by manipulation of colloids and, in turn, patterning of particles by these defects, thus achieving desired colloidal configurations on scales ranging from the size of defect core to the sample size. This defect-colloidal sculpturing may be extended to other lamellar media, providing the means for optically guided self-assembly of mesoscopic composites with predesigned properties.