Nematic Colloids Research Articles

Nematic Liquid Crystals and Nematic Colloids in Microfluidic Environment

We study nematic LCs and nematic colloids flowing through microchannels using polarizing transmission microscopy and fluorescence confocal polarizing microscopy. Depending on the channel dimensions, the anchoring conditions on the channel walls, and the flow rate, the formation of different textures and defect structures is observed: π-walls, disclination lines (DL) pinned to the channel walls, DL with one pinned and one freely floating end, and DL and loops freely floating in a chaotic-like manner. Preliminary observations of nematic LCs containing colloidal particles indicate that textures and defects of the nematic matrix can be used to guide the transport of the particles through the microchannels.

Reconfigurable Knots and Links in Chiral Nematic Colloids

Tying knots and linking microscopic loops of polymers, macromolecules, or defect lines in complex materials is a challenging task for material scientists. We demonstrate the knotting of microscopic topological defect lines in chiral nematic liquid-crystal colloids into knots and links of arbitrary complexity by using laser tweezers as a micromanipulation tool. All knots and links with up to six crossings, including the Hopf link, the Star of David, and the Borromean rings, are demonstrated, stabilizing colloidal particles into an unusual soft matter. The knots in chiral nematic colloids are classified by the quantized self-linking number, a direct measure of the geometric, or Berry's, phase. Forming arbitrary microscopic knots and links in chiral nematic colloids is a demonstration of how relevant the topology can be for the material engineering of soft matter.

Nematic Braids: Topological Invariants and Rewiring of Disclinations

The conventional topological description given by the fundamental group of nematic order parameter does not adequately explain the entangled defect line structures that have been observed in nematic colloids. We introduce a new topological invariant, the self-linking number, that enables a complete classification of entangled defect line structures in general nematics, even without particles, and demonstrate our formalism using colloidal dimers, for which entangled structures have been previously observed. We also unveil a simple rewiring scheme for the orthogonal crossing of two -1/2 disclinations, based on a tetrahedral rotation of two relevant disclination segments, that allows us to predict possible nematic braids and calculate their self-linking numbers.

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.

Spatially modulated structures in nematic colloids: Statistical thermodynamics and kinetics

We examine the spatial distribution of rigid-sphere-like particles in a nematic host. Using a continuum model we analyse the conditions necessary for the appearance of a modulated lamellar structure. There is a long-range effective interaction between the particles, which can lead to the formation of superstructures. In general, this interaction includes several contributions: van der Waals-type direct interaction and indirect interaction via the director field distortions. The latter depends on the temperature of the sample, the coupling energy between a colloidal particle and a nematic host, and the particle concentration. This effective interaction controls the spatial structure and the kinetic properties of the system. We obtained the analytical expression for the temperature when the system loses the stability with respect to the modulated structure formation. Typical contours of the diffuse light scattering are presented.

Ordered structures of nematic colloids in crystals of liquid crystal dimers

Ordered structures of nano- or micro-particles consisting of SiO2, Fe2O3, TiO2, CuO, Al2O3, Ag, Co, Mo, and SiC in liquid crystal dimers were investigated by means of microscopy both with and without a polarizer. Self-assemblies of the colloidal particles were found in crystals of the liquid crystal dimers as stripes or spots.

Dependence of interparticle force on temperature and cell thickness in nematic colloids

We have experimentally studied the interparticle force between two particles accompanied by hyperbolic hedgehog defects in a nematic liquid crystal. The force F was measured with dual-beam optical tweezers at various temperatures and in cells with various thicknesses. In a thick cell, the dependence of F on the interparticle distance R obtained at different temperatures can be scaled to a universal curve of F∝R^(-4) for R>3a , where a is the radius of a particle. The effective elastic constant evaluated from F is found to be in good agreement with splay constant of the nematic liquid crystal. In a thin cell, the magnitude of F decreases and the dependence of F on R becomes short-ranged as the thickness of a cell, L , decreases. The reduced force curves, FL(4) against R/L , at different L are found to be scaled to a single theoretical curve which has been proposed recently.

Optical manipulation and self-assembly of nematic colloids: colloidal crystals and superstructures

Optical manipulation of colloidal particles in nematic liquid crystals is far more complex than manipulation in water-based colloids. Owing to the long-range nature of the orientational ordering, their elasticity and topological conservation laws, almost any kind of object can be trapped and manipulated in liquid crystals. Furthermore, local heating due to the absorption of light can be used to create microdroplets of the isotropic phase, which interact strongly with colloidal particles. This leads to a broad variety of colloidal assemblies in liquid crystals, which cannot be observed in isotropic solvents: colloidal wires, assembled by entangled topological defects, superstructures in mixtures of large and small colloidal particles and a broad variety of two-dimensional nematic colloidal crystals. In all cases, the colloidal binding energy is several orders of magnitude stronger compared with water-based colloids. The large variety of colloidal superstructures, which can be assembled in nematic colloids, makes them highly interesting for application in photonic materials.

Janus Nematic Colloids driven by light

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

Landau–de Gennes modelling of nematic liquid crystal colloids

Phenomenological Landau–de Gennes modelling based on the free energy of nematic liquid crystal colloids is reviewed. Nematic phase, gradient of order, and surface anchoring contributions to the total free energy are used. The numerical finite difference relaxation technique is explained as an efficient tool for the minimisation of the free energy. Effects of the mesh and mesh allocation are discussed. Various conceptually different colloidal structures are calculated to show the universality of the model. Single particles, dipolar–quadrupolar dimers, entangled dimers, dimers bound by escaped hyperbolic rings, and hierarchically patterned Saturn-ring colloidal superstructures are presented.

Forces in nematic liquid crystals: from nanoscale interfacial forces to long-range forces in nematic colloids

In this paper we give an overview of experiments that provided an insight into the nature of forces between surfaces and objects in a nematic liquid crystal. These forces, also called ‘structural forces’, are the consequence of the long-range orientational order and orientational elasticity of nematic liquid crystals. Owing to their fundamental as well as technological importance, forces between objects in liquid crystals have been a subject of growing interest during the last decade. Experimental observations and studies of structural forces are described from nanoscale interfacial forces, measured by an atomic force microscope, to the micro-scale forces between colloidal particles in nematics, studied by laser tweezers and optical video microscopy.

Janus nematic colloids

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

Confinement Effect on Interparticle Potential in Nematic Colloids

We studied the confinement effect on the interaction force in nematic liquid crystal colloids with spherical particles inducing planar anchoring. Using magneto-optical tweezers, we measured the spatial dependence of the quadrupolar structural interparticle force over 4 orders of magnitude. For small separations, the interparticle potential follows the power law, whereas for separations larger than the sample thickness, it decreases exponentially with the decay length proportional to the sample thickness. Experimental results are reproduced by using the Landau-de Gennes free-energy minimization approach.

Nematic colloids entangled by topological defects

Assembly of colloidal particles in nematic liquid crystals is governed by the symmetry of building blocks and type of defects in the liquid crystalline orientation. Particles in a nematic act as nucleation sites for topological defect structures that are homotopic to point defects. The tendency for a minimal deformation free energy and topological constraints limit possible defect configurations to extended and localized defect loops. Here we report on a recently discovered colloidal binding, where particles are entangled by disclination loops. Nematic braids formed by such disclinations stabilize multi-particle objects and entrap particles in a complex manner. Observed binding potentials are highly anisotropic showing string-like behavior and can be of an order of magnitude stronger compared to non-entangled colloids. Controlling the assembly based on entangled disclination lines one can build multi-particle structures with potentially useful features (shapes, periodic structure, chirality, etc.) for photonic and plasmonic applications.

2D Interactions and Binary Crystals of Dipolar and Quadrupolar Nematic Colloids

In this Letter, we demonstrate that the symmetry of the elastic interaction between the dipolar and quadrupolar colloidal particles in the nematic liquid crystal leads to a novel variety of 2D nematic "binary" colloidal crystals, which have not been observed in any colloidal system. The dipolar-quadrupolar interaction is highly anisotropic and shows a power-law dependence when the particles approach each other along the director field with a pair-binding energy of the order of several thousands of k(B)T for 4 microm diameter colloids.

Bridging the gap between phenomenology and microscopic theory: Asymptotes in nematic colloids

The Ornstein-Zernike equation is applied to nematic colloids with up-down symmetry to determine how the electrostatic analogy and other phenomenological results appear in molecular theory. In contrast to phenomenological approaches, the molecular theory does not assume particular boundary conditions (anchoring) at colloidal surfaces. For our molecular parameters the resulting anchoring appears to be realistic, neither rigid nor infinitely weak. For this case, the effective force between a colloidal pair at large separation remains essentially constant over the entire region of nematic stability. We show that a simple van der Waals approximation gives a potential of mean force that in some important aspects is similar to the phenomenological results obtained in the limit of weak anchoring; at large separations the potential varies as Sigma8, where Sigma is the colloidal diameter. In contrast, the more sophisticated mean spherical approximation yields a Sigma6 dependence consistent with phenomenological calculations employing rigid boundary conditions. We show that taking proper account of the correlation (or magnetic coherence) length xi inherent in the nematic sample is essential in an analysis of the Sigma dependence. At infinite xi the leading Sigma dependence is Sigma6, but this shifts to Sigma8 when xi is finite. The correlation length also influences the orientational behavior of the effective interaction. The so-called quadrupole interaction that determines the long-range behavior at infinite xi transforms into a superposition of screened "multipoles" when xi is finite. The basic approach employed in this paper can be readily applied to a broad range of physically interesting systems. These include patterned and nonspherical colloids, colloids trapped at interfaces, and nematic fluids in confined geometries such as droplets.

Interactions of quadrupolar nematic colloids

We present experimental and theoretical study of colloidal interactions in quadrupolar nematic liquid crystal colloids, confined to a thin planar nematic cell. Using the laser tweezers, the particles have been positioned in the vicinity of other colloidal particles and their interactions have been determined using particle tracking video microscopy. Several types of interactions have been analyzed: (i) quadrupolar pair interaction, (ii) the interaction of an isolated quadrupole with a quadrupolar chain, and (iii) the interaction of an isolated quadrupolar colloidal particle with a two-dimensional (2D) quadrupolar crystallite. In all cases, the interactions are of the order of several 100k(B)T for 2 microm particles, which gives rise to relatively stable 2D colloidal crystals. The experimental results are compared to the predictions of Landau-de Gennes theory and we find a relatively good qualitative agreement.

Self-assembly of nematic colloids.

Dispersions of colloidal particles in nematic liquid crystals show new classes of interparticle forces, which are anisotropic, long range, and several thousand times stronger than van der Waals forces in water-based colloids. These forces are responsible for a variety of new self-assembled colloidal microstructures, which cannot be observed in isotropic solvents, such as chains of microspheres and cellular soft solid materials. Basic principles of particle self-assembly in 2D nematic colloids are discussed, showing this is a novel paradigm in colloid science, which could lead to new approaches of colloidal self-assembly for photonic devices.

Improved ansatz for the direct correlation function in dilute nematic colloids

We present an improved analytical ansatz for the colloid-nematic direct correlation function. This ansatz is more accurate than our earlier version, and yields numerical results that are very close to the true mean spherical approximation for dilute nematic colloids. Furthermore, the improved ansatz is valid for external fields of any strength. We examine the zero-field behavior of t he colloid-colloid potential of mean force in light of the improved ansatz, and show that at zero field and large separations this function decays as R 5

Colloidal Interactions and Transport in Nematic Liquid Crystals

We describe a new nematic liquid-crystal colloid system which is characterized by both charge stabilization of the particles and an interaction force. We estimate the effective charge of the particles by electrophoretic measurements and find that in such systems the director anchoring energy W is very low and the particles have little director distortion around them. The interaction force is created by producing a radial distribution of the nematic order parameter around a locally isotropic region created by ir laser heating. We theoretically describe this as being due to the induced flexoelectric polarization, the quadrupolar symmetry of which provides the required long-range force acting on charged particles.