Design of 2D binary colloidal crystals in a nematic liquid crystal

Design and Preparation of Nematic Colloidal Particles

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

Conically degenerate anchoring effect in planar nematic-liquid-crystal shells

We study the defect texture in symmetric and asymmetric states of a nematic-liquid-crystal shell with conic and planar degenerate surface anchorings on the inner and outer spherical boundaries, respectively. To achieve the equilibrium nematic orientation, we numerically minimize the Landau-de Gennes free energy by employing surface potentials on the shell walls. The symmetric nematic shells energetically have stable configurations independent of thickness. In thick shells, the director field satisfies bipolar and hexadecapolar configurations between boundaries. In thin shells, the boojums transform into two stable disclination curves.

Nature-Inspired Emerging Chiral Liquid Crystal Nanostructures: From Molecular Self-Assembly to DNA Mesophase and Nanocolloids

Liquid crystals (LCs) are omnipresent in living matter, whose chirality is an elegant and distinct feature in certain plant tissues, the cuticles of crabs, beetles, arthropods, and beyond. Taking inspiration from nature, researchers have recently devoted extensive efforts toward developing chiral liquid crystalline materials with self-organized nanostructures and exploring their potential applications in diverse fields ranging from dynamic photonics to energy and safety issues. In this review, an account on the state of the art of emerging chiral liquid crystalline nanostructured materials and their technological applications is provided. First, an overview on the significance of chiral liquid crystalline architectures in various living systems is given. Then, the recent significant progress in different chiral liquid crystalline systems including thermotropic LCs (cholesteric LCs, cubic blue phases, achiral bent-core LCs, etc.) and lyotropic LCs (DNA LCs, nanocellulose LCs, and graphene oxide LCs) is showcased. The review concludes with a perspective on the future scope, opportunities, and challenges in these truly advanced functional soft materials and their promising applications.

Identification and sorting of particle chirality using liquid crystallinity

Particles dispersed in liquid crystals (LCs) have been shown to assemble due to the elastic interactions arising from the molecular anisotropy. Studies have shown that the alignment of the particles within LCs were strongly dependent on the surface director of LCs on particles. Different from the past studies involving particles with degenerate planar anchoring of LCs, this study shows that the azimuthal surface director can be used to control and finely tune the positioning of the particles in LCs. Specifically, polymeric particles with two flat surfaces that mediate parallel or non-parallel (chiral) anchoring were synthesized and dispersed in nematic 5CB with spatial variations in the director profile. Besides demonstration of their positioning, it was observed that the particles with same chiral handedness with the LC twist were distributed within the LC film, whereas particles with opposite handedness were repelled from the LC medium due to the elastic energy contributions. In addition, a pronounced effect of the surface anchoring of the particles were present on their orientation during non-equilibrium events such as sedimentation. Overall, the studies presented here will find potential use in sensors, separations, optics or soft robotic applications that will take advantages of chirality or chiral interactions.

Perspectives in Liquid-Crystal-Aided Nanotechnology and Nanoscience

The research field of liquid crystals and their applications is recently changing from being largely focused on display applications and optical shutter elements in various fields, to quite novel and diverse applications in the area of nanotechnology and nanoscience. Functional nanoparticles have recently been used to a significant extent to modify the physical properties of liquid crystals by the addition of ferroelectric and magnetic particles of different shapes, such as arbitrary and spherical, rods, wires and discs. Also, particles influencing optical properties are increasingly popular, such as quantum dots, plasmonic, semiconductors and metamaterials. The self-organization of liquid crystals is exploited to order templates and orient nanoparticles. Similarly, nanoparticles such as rods, nanotubes and graphene oxide are shown to form lyotropic liquid crystal phases in the presence of isotropic host solvents. These effects lead to a wealth of novel applications, many of which will be reviewed in this publication.

Binary colloidal crystals (BCCs): Interactions, fabrication, and applications

The organization of matter into hierarchical structures is a fundamental characteristic of functional materials and living organisms. Binary colloidal crystal (BCC) systems present a diversified range of nanotopographic structures where large and small colloidal particles simultaneously self-assemble into either 2D monolayer or 3D hierarchical crystal lattices. More importantly, understanding how BCCs form opens up the possibility to fabricate more complex systems such as ternary or quaternary colloidal crystals. Monolayer BCCs can also offer the possibility to achieve surface micro- and nano-topographies with heterogeneous chemistries, which can be challenging to achieve with other traditional fabrication tools. A number of fabrication methods have been reported that enable generation of BCC structures offering high accuracy in growth with controllable stoichiometries; however, it is still a challenge to make uniform BCC structures over large surface areas. Therefore, fully understand the mechanism of binary colloidal self-assembly is crucial and new/combinational methods are needed. In this review, we summarize the recent advances in BCC fabrication using particles made of different materials, shapes, and dispersion medium. Depending on the potential application, the degree of order and efficiency of crystal formation has to be determined in order to induce variability in the intended lattice structures. The mechanisms involved in the formation of highly ordered lattice structures from binary colloidal suspensions and applications are discussed. The generation of BCCs can be controlled by manipulation of their extensive phase behavior, which facilitates a wide range potential applications in the fields of both material and biointerfacial sciences including photonics, biosensors, chromatography, antifouling surfaces, biomedical devices, and cell culture tools.

Formation of three-dimensional colloidal crystals in a nematic liquid crystal

We investigate the possible structures of three-dimensional colloidal crystals formed when these spherical particles are dispersed in a liquid crystal. The case of a strong homeotropic boundary condition is considered here. Their corresponding defect structures in the space-filler nematic liquid crystal are induced by the presence of the spherical surface of the colloids and produce an attraction between colloidal particles. Here, a standard Landau-de Gennes free energy model for a spatially inhomogeneous liquid crystal is numerically minimized to yield an optimal configuration of both spherical colloids and the orientational field. The stable and metastable structures obtained in this work are described and analyzed according to the type of periodic liquid-crystal defect lines that couple the colloidal spheres together. A large range of the spherical size is covered in this study, corresponding to a 5CB-liquid-crystal comparison for assembling micron- to nano-sized colloidal spheres. Multiple configurations are found for each given particle size and the most stable state is determined by a comparison of the free energies. From large to small colloidal particles, a sequence of structures, which range from quasi-one-dimensional (columnar), to quasi-two-dimensional (planar), and to truly three-dimensional, are found to exist.

Nematic Liquid-Crystal Colloids

This article provides a concise review of a new state of colloidal matter called nematic liquid-crystal colloids. These colloids are obtained by dispersing microparticles of different shapes in a nematic liquid crystal that acts as a solvent for the dispersed particles. The microparticles induce a local deformation of the liquid crystal, which then generates topological defects and long-range forces between the neighboring particles. The colloidal forces in nematic colloids are much stronger than the forces in ordinary colloids in isotropic solvents, exceeding thousands of kBT per micrometer-sized particle. Of special interest are the topological defects in nematic colloids, which appear in many fascinating forms, such as singular points, closed loops, multitudes of interlinked and knotted loops or soliton-like structures. The richness of the topological phenomena and the possibility to design and control topological defects with laser tweezers make colloids in nematic liquid crystals an excellent playground for testing the basic theorems of topology.

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

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

Equilibrium structures of anisometric, quadrupolar particles confined to a monolayer

We investigate the structural properties of a two-dimensional system of ellipsoidal particles carrying a linear quadrupole moment in their center. These particles represent a simple model for a variety of uncharged, non-polar conjugated organic molecules. Using optimization tools based on ideas of evolutionary algorithms, we first examine the ground state structures as we vary the aspect ratio of the particles and the pressure. Interestingly, we find, besides the intuitively expected T-like configurations, a variety of complex structures, characterized with up to three different particle orientations. In an effort to explore the impact of thermal fluctuations, we perform constant-pressure molecular dynamics simulations within a range of rather low temperatures. We observe that ground state structures formed by particles with a large aspect ratio are in particular suited to withstand fluctuations up to rather high temperatures. Our comprehensive investigations allow for a deeper understanding of molecular or colloidal monolayer arrangements under the influence of a typical electrostatic interaction on a coarse-grained level.

Coarse-grained treatment of the self-assembly of colloids suspended in a nematic host phase

The complex interplay of molecular scale effects, nonlinearities in the orientational field and long-range elastic forces makes liquid-crystal physics very challenging. A consistent way to extract information from the microscopic, molecular scale up to the meso- and macroscopic scale is still missing. Here, we develop a hybrid procedure that bridges this gap by combining extensive Monte Carlo (MC) simulations, a local Landau-de Gennes theory, classical density functional theory, and finite-size scaling theory. As a test case to demonstrate the power and validity of our novel approach we study the effective interaction among colloids with Boojum defect topology immersed in a nematic liquid crystal. In particular, at sufficiently small separations colloids attract each other if the angle between their center-of-mass distance vector and the far-field nematic director is about 30°. Using the effective potential in coarse-grained two-dimensional MC simulations we show that self-assembled structures formed by the colloids are in excellent agreement with experimental data.

Reconfigurable multi-scale colloidal assembly on excluded volume patterns

The ability to create multi-scale, periodic colloidal assemblies with unique properties is important to emerging applications. Dynamically manipulating colloidal structures via tunable kT-scale attraction can provide the opportunity to create particle-based nano- and microstructured materials that are reconfigurable. Here, we report a novel tactic to obtain reconfigurable, multi-scale, periodic colloidal assemblies by combining thermoresponsive depletant particles and patterned topographical features that, together, reversibly mediate local kT-scale depletion interactions. This method is demonstrated in optical microscopy experiments to produce colloidal microstructures that reconfigure between well-defined ordered structures and disordered fluid states as a function of temperature and pattern feature depth. These results are well described by Monte Carlo simulations using theoretical depletion potentials that include patterned excluded volume. Ultimately, the approach reported here can be extended to control the size, shape, orientation, and microstructure of colloidal assemblies on multiple lengths scales and on arbitrary pre-defined pattern templates.

Elastocapillary interactions on nematic films

Rod-like colloids distort fluid interfaces and interact by capillarity. We explore this interaction at the free surface of aligned nematic liquid crystal films. Naive comparison of capillary and elastic energies suggests that particle assembly would be determined solely by surface tension. Here, we demonstrate that, under certain circumstances, the capillary and elastic effects are complementary and each plays an important role. Particles assemble end-to-end, as dictated by capillarity, and align along the easy axis of the director field, as dictated by elasticity. On curved fluid interfaces, however, curvature capillary energies can overcome the elastic orientations and drive particle migration along curvature gradients. Domains of dominant interaction and their transition are investigated.

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.

Disclination lines at homogeneous and heterogeneous colloids immersed in a chiral liquid crystal

In the present work we perform Monte Carlo simulations in the isothermal-isobaric ensemble to study defect topologies formed in a cholesteric liquid crystal due to the presence of a spherical colloidal particle. Topological defects arise because of the competition between anchoring at the colloidal surface and the local director. We consider homogeneous colloids with either local homeotropic or planar anchoring to validate our model by comparison with earlier lattice Boltzmann studies. Furthermore, we perform simulations of a colloid in a twisted nematic cell and discuss the difference between induced and intrinsic chirality on the formation of topological defects. We present a simple geometrical argument capable of describing the complex three-dimensional topology of disclination lines evolving near the surface of the colloid. The presence of a Janus colloid in a cholesteric host fluid reveals a rich variety of defect structures. Using the Frank free energy we analyze these defects quantitatively indicating a preferred orientation of the Janus colloid relative to the cholesteric helix.

Chiral bipolar colloids from nonchiral chromonic liquid crystals

We demonstrate that high anisotropy of elastic constants of chromonic liquid crystals leads to a number of spontaneously twisted nematic director fields around colloidal particles in these non-chiral fluids. For spherical colloidal particles with surface inducing degenerate planar nematic ordering we observe that boojum defects at the particles' poles acquire twisted internal structure, extending up to three particle diameters along the rubbing direction of the cell. The twist handedness of the two boojum defects at the poles of the particle can be either the same or opposite, and we can switch the defects handedness by localized thermal microquenching. Numerical simulations confirm that the transitions into the distorted states are induced by lowering of the twist elastic constant, which results in two (meta)stable chiral configurations of the boojums, separated by an energy barrier much higher than the thermal energy. We show that boojum handedness can change the pairwise elastic interaction between the two particles positioned along the rubbing direction from repulsive to attractive.

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.

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.

Bonded boojum-colloids in nematic liquid crystals

We investigate bonded boojum-colloids in nematic liquid crystals, configurations where two colloids with planar degenerate anchoring are double-bonded through line defects connecting their surfaces. This bonded structure promotes the formation of linear chains aligned with the nematic director. We show that the bonded configuration is the global minimum in systems that favor twist deformations. In addition, we investigate the influence of confinement on the stability of bonded boojum-colloids. Although the unbonded colloid configuration, where the colloids bundle at oblique angles, is favored by confinement, the bonded configuration is again the global minimum for liquid crystals with sufficiently small twist elastic constants.

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.

Defect topologies in a nematic liquid crystal near a patchy colloid

Using isothermal-isobaric Monte Carlo simulations we investigate defect topologies due to a spherical colloidal particle immersed in a nematic liquid crystal. Defects arise because of the competition between the preferential orientation at the colloid's surface and the far-field director ̂n(0). Considering a chemically homogeneous colloid as a special case we observe the well-known surface and saturn ring defect topologies for weak and strong perpendicular anchoring, respectively; for homogeneous, strong parallel anchoring we find a boojum defect topology that has been seen experimentally [see P. Poulin and D. A. Weitz, Phys. Rev. E 57, 626 (1998)] but not in computer simulations. We also consider a heterogeneous, patchy colloid where the liquid-crystal molecules anchor either preferentially planar or perpendicular at the surface of the colloid. For a patchy colloid we observe a boojum ring defect topology in agreement with recent experimental studies [see M. Conradi, M. Ravnik, M. Bele, M. Zorko, S. Žumer, and I. Muševič, Soft Matter 5, 3905 (2009)]. We also observe two other novel defect topologies that have not been reported thus far neither experimentally nor theoretically.

Nonequilibrium condensation and coarsening of field-driven dipolar colloids

In colloidal suspensions, self-organization processes can be easily fueled by external fields. Here we consider monolayers of particles with permanent dipole moments that are driven by rotating external fields. In recent experiments, it has been shown that the particles in such systems self-organize into two-dimensional clusters. Here we report results from a computer simulation study of these pattern forming systems. Specifically, we employ Langevin dynamics simulations, Brownian dynamics simulations that include hydrodynamic interactions, and Wang-Landau Monte Carlo simulations of soft spheres interacting via dipolar potentials. We investigate at which field strengths and frequencies clusters form and explore the influence of hydrodynamic interactions. We also examine the phase behavior of the equilibrium system resulting from a time average of the colloidal interactions in the rotating field. In this way we demonstrate that the clustering described in the driven system arises from a first-order phase transition between a vapor and a condensed phase.

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.

Nematic disclinations as twisted ribbons

The disclination loops entangling colloidal structures in nematics are geometrically stabilized and restricted according to topological rules. We focus on colloidal dimers and show how the writhe and twist, which are constrained to sum to a constant value, are affected by changing the intercolloidal spacing, the twist angle of the cell, and the cholesteric pitch. We analyze the geometric properties of disclination loops using finite difference numerical simulations of colloidal dimers. The observed trends are explained and correlated to the symmetry properties and effects of liquid crystal elasticity.

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.

Direct and inverted nematic dispersions for soft matter photonics

General properties and recent developments in the field of nematic colloids and emulsions are discussed. The origin and nature of pair colloidal interactions in the nematic colloids are explained and an overview of the stable colloidal 2D crystalline structures and superstructures discovered so far is given. The nature and role of topological defects in the nematic colloids is discussed, with an emphasis on recently discovered entangled colloidal structures. Applications of inverted nematic emulsions and binding force mechanisms in nematic colloids for soft matter photonic devices are discussed.

Square colloidal lattices and pair interaction in a binary system of quadrupolar nematic colloids

Spherical colloidal particles with normal and tangential surface director alignment in a nematic liquid crystal induce elastic quadrupoles of opposite signs that attract one another along and perpendicular to the director. We utilize this unique angular profile of the mixed quadrupolar interaction to build 2D crystals with square lattices by laser tweezers.