Colloidal interactions in two-dimensional nematic emulsions

We review theoretical and experimental work on colloidal interactions in two-dimensional (2D) nematic emulsions. We pay particular attention to the effects of (i) the nematic elastic constants, (ii) the size of the colloids, and (iii) the boundary conditions at the particles and the container. We consider the interactions between colloids and fluid (deformable) interfaces and the shape of fluid colloids in smectic-C films.     

Orientational coupling amplification in ferroelectric nematic colloids

We investigated the physical properties of low concentration ferroelectric nematic colloids, using calorimetry, optical methods, infrared spectroscopy, and capacitance studies. The resulting homogeneous colloids possess a significantly amplified nematic orientational coupling. We find that the nematic orientation coupling increases by approximately 10% for particle concentrations of 0.2%. A manifestation of the increased orientational order is that the clearing temperature of a nematic colloid increases by up to 40 degrees C compared to the pure liquid crystal host. A theoretical model is proposed in which the ferroelectric particles induce local dipoles whose effective interaction is proportional to the square of the orientational order parameter.     

Micro-wires self-assembled and 3D-connected with the help of a nematic liquid crystal

We discuss a method for producing automatic 3D connections at right places between substrates in front of one another. The idea is based on the materialization of disclination lines working as templates. The lines are first created in the nematic liquid crystal (5CB) at the very place where microwires have to be synthesized. Due to their anchoring properties, colloids dispersed into the nematic phase produce orientational distortions around them. These distortions, which may be considered as due to topological charges, result in a nematic force, able to attract the colloids towards the disclinations. Ultimately, the particles get trapped onto them, forming micro- or nano-necklaces. Before being introduced in the nematic phase, the colloids are covered with an adhering and conducting polypyrrole film directly synthesized at the surface of the particles (heterogeneous polymerization). In this manner, the particles become conductive so that we may finally perform an electropolymerization of pyrrole monomers solved in 5CB, and definitely stick the whole necklace. The electric connection thus synthesized is analyzed by AFM, and its strength is checked by means of hydrodynamic tests. This wiring method could allow Moore's law to overcome the limitations that arise when down-sizing the electronic circuits to nanometer scale.     

Entangled nematic colloidal dimers and wires

It has been predicted, but never confirmed, that colloidal particles in a nematic liquid crystal could be self-assembled by delocalized topological defects and entangled disclinations. We show experimentally and theoretically that colloidal dimers and 1D structures bound by entangled topological defect loops can indeed be created by locally thermally quenching a thin layer of the nematic liquid crystal around selected colloidal particles. The topological entanglement provides a strong stringlike binding, which is ten thousand times stronger compared to water-based colloids. This unique binding mechanism could be used to assemble resonator optical waveguides and robust chiral and achiral structures of topologically entangled colloids that we call colloidal wires.     

Colloids in external electric and magnetic fields: Colloidal crystals, pinning, chain formation, and electrokinetics

The motion of dilute and concentrated dispersions of colloids by external electric or magnetic fields is discussed. Electrokinetics is studied for colloids in confinement, where the confining walls can be flat or rough. As an example for a rough wall superhydrophobic surfaces are chosen. It is shown that the reduced friction at the water-air interface is insufficient to enhance electro-osmosis. Magnetic particles are pulled through a crystalline matrix formed by nonmagnetic colloids to investigate local melting and recrystallization of a crystalline matrix. The average strain field is calculated and the reorganization processes are compared to those induced by shear fields. Using single domain, magnetically blocked particles of different shape and surface characteristics, the interplay between particles, their environment and an external field is investigated.     

Inelastic collisions and anisotropic aggregation of particles in a nematic collider driven by backflow

We design a nematic collider for controlled out-of-equilibrium anisotropic aggregation of spherical colloidal particles. The nematic surrounding imparts dipolar interactions among the spheres. A bidirectional backflow of the nematic liquid crystal in a periodic electric field forces the spheres to collide with each other. The inelastic collisions are of two types, head to tail and head to head. Head-to-tail collisions of dipoles result in longitudinal aggregation while head-to-head collisions promote aggregation in the transversal direction. The frequency of head-to-head collisions is set by the impact parameter that controls the resulting shape of aggregates, their anisotropy, and fractal dimension.     

Electrically driven multiaxis rotational dynamics of colloidal platelets in nematic liquid crystals

We describe field-induced multiaxis rotations of colloids in a nematic liquid crystal. Anchoring of the nematic director to the colloidal platelet's surface and interplay of dielectric and elastic energies enable robust control over colloid orientation that cannot be achieved in isotropic liquids. Because of the anisotropy of the fluid and the platelike shape of particles, the colloids can be forced to rotate about four different rotational axes even for a fixed direction of the applied field. The time scale of these unexpected voltage-dependent dynamics varies over four orders of magnitude (10?2-102 s) and promises a number of novel electro-optic, photonic, and display 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.     

Cellular solid behaviour of liquid crystal colloids 2. Mechanical properties

This paper presents the results of a rheological study of thermotropic nematic colloids aggregated into cellular structures. Small sterically stabilised PMMA particles dispersed in a liquid crystal matrix densely pack on cell interfaces, but reversibly mix with the matrix when the system is heated above . We obtain a remarkably high elastic modulus, , which is a nearly linear function of particle concentration. A characteristic yield stress is required to disrupt the continuity of cellular structure and liquify the response. The colloid aggregation in a “poor nematic” MBBA has the same cellular morphology as in the “good nematic” 5CB, but the elastic strength is at least an order of magnitude lower. These findings are supported by theoretical arguments based on the high surface tension interfaces of a foam-like cellular system, taking into account the local melting of nematic liquid and the depletion locking of packed particles on interfaces. Received 13 March 2000 and Received in final form 6 June 2000     

Direct optical quantification of backflow in a 90 degrees twisted nematic cell

Optical guided mode observations of the transient director profile (optical tensor distribution) during the relaxation of a 90 degrees twisted nematic cell directly reveals backflow. In the first 6 ms of the relaxation process, after a voltage across the cell is removed, the midplane tilt of the director increases, reaching a maximum value of 101 degrees at 1.4 ms. This increase in midplane tilt is attributed to coupling between fluid flow (backflow) and director reorientation. A 270 degrees twisted state of the opposite handedness to the 90 degrees twisted state found at equilibrium is shown to exist during the backflow period. Good fits of theoretical models with experimentally determined time dependent director profiles yield the viscosity coefficients.     

Cellular solid behaviour of liquid crystal colloids 1. Phase separation and morphology

We study the phase ordering colloids suspended in a thermotropic nematic liquid crystal below the clearing point and the resulting aggregated structure. Small () PMMA particles are dispersed in a classical liquid crystal matrix, 5CB or MBBA. With the help of confocal microscopy we show that small colloid particles densely aggregate on thin interfaces surrounding large volumes of clean nematic liquid, thus forming an open cellular structure, with the characteristic size of inversely proportional to the colloid concentration. A simple theoretical model, based on the Landau mean-field treatment, is developed to describe the continuous phase separation and the mechanism of cellular structure formation. Received 13 March 2000 and Received in final form 6 June 2000     

Elastic charge density representation of the interaction via the nematic director field

The interaction between particle-like sources of the nematic director distortions (e.g., colloids, point defects, macromolecules in nematic emulsions) allows for a useful analogy with the electrostatic multipole interaction between charged bodies. In this paper we develop this analogy to the level corresponding to the charge density and consider the general status of the pairwise approach to the nematic emulsions with finite-size colloids. It is shown that the elastic analog of the surface electric charge density is represented by the two transverse director components on the surface imposing the director distortions. The elastic multipoles of a particle are expressed as integrals over the charge density distribution on this surface. Because of the difference between the scalar electrostatics and vector nematostatics, the number of elastic multipoles of each order is doubled compared to that in the electrostatics: there are two elastic charges, two vectors of dipole moments, two quadrupolar tensors, and so on. The two-component elastic charge is expressed via the vector of external mechanical torque applied on the particle. As a result, the elastic Coulomb-like coupling between two particles is found to be proportional to the scalar product of the two external torques and does not directly depend on the particles' form and anchoring. The real-space Green function method is used to develop the pairwise approach to nematic emulsions and determine its form and restrictions. The pairwise potentials are obtained in the familiar form, but, in contrast to the electrostatics, they describe the interaction between pairs (dyads) of the elastic multipole moments. The multipole moments are shown to be uniquely determined by the single-particle director field, unperturbed by other particles. The pairwise approximation is applicable only in the leading order in the small ratio particle size-to-interparticle distance as the next order contains irreducible three-body terms.     

Theoretical analysis of the influence of flexoelectric effect on the defect site in nematic inversion walls

Based on the experimental phenomena of flexoelectric response at defect sites in nematic inversion walls conducted by Kumar et al., we gave the theoretical analysis using the Frank elastic theory. When a direct-current electric field normal to the plane of the substrate is applied to the parallel aligned nematic liquid crystal cell with weak anchoring, the rotation of ± 1 defects in the narrow inversion walls can be exhibited. The free energy of liquid crystal molecules around the +1 and-1 defect sites in the nematic inversion walls under the electric field was formulated and the electric-field-driven structural changes at the defect site characterized by polar and azimuthal angles of the local director were simulated. The results reveal that the deviation of azimuthal angle induced by flexoelectric effect are consistent with the switching of extinction brushes at the +1 and-1 defects obtained in the experiment conducted by Kumar et al.     

Turbiscan多重光散射法研究纳米银溶胶的分散稳定性

以硝酸银为银源、间苯二酚为还原剂、聚乙烯吡咯烷酮为保护剂通过化学还原法制得纳米银颗粒,通过离心洗涤等操作洗掉多余的反应物,将其分别超声分散于水、无水乙醇和乙二醇中获得0.2 Wt%不同体系的纳米银溶胶。利用激光粒度分析仪、透射电子显微镜、扫描电子显微镜和同步热分析仪对纳米银颗粒进行表征并测定纳米银溶胶中的银含量。激光粒度分析仪的粒度分析结果表明,实验制得的纳米银颗粒的粒径在100 nm左右,且粒径分布均一。透射电子显微镜和扫描电子显微镜的结果进一步证实纳米银颗粒的粒径在纳米尺度范围且粒径均匀。采用Turbiscan多重光散射法研究了不同体系纳米银溶胶的分散稳定性,分析了导致纳米银溶胶不稳定的主要因素。研究发现：影响纳米银溶胶分散稳定性的主要因素包括颗粒粒径的变化和颗粒的迁移。对于水相体系,样品池中间部分背散射光强度随时间变化不大,样品池底部和顶部背散射光强度有较大变化,说明其稳定性的主要影响因素是纳米银颗粒的迁移,颗粒粒径变化影响不大;对于乙醇和乙二醇体系,样品池中间部分、底部和顶部的背散射光强度均有明显变化,说明颗粒粒径的变化和颗粒的迁移对体系稳定性均有一定程度的影响;最后通过比较三个体系的稳定性动力学指数,得到体系稳定性由高到低依次为乙二醇、水和乙醇。     

Effective interactions of colloids on nematic films

The elastic and capillary interactions between a pair of colloidal particles trapped on top of a nematic film are studied theoretically for large separations d. The elastic interaction is repulsive and of quadrupolar type, varying as d^-5. For macroscopically thick films, the capillary interaction is likewise repulsive and proportional to d^-5 as a consequence of mechanical isolation of the system comprised of the colloids and the interface. A finite film thickness introduces a nonvanishing force on the system (exerted by the substrate supporting the film) leading to logarithmically varying capillary attractions. However, their strength turns out to be too small to be of importance for the recently observed pattern formation of colloidal droplets on nematic films.     

Topology and geometry of nematic braids

Topological analysis of disclinations in nematic liquid crystals is an interesting and diverse topic that goes from strict mathematical theorems to applications in elaborate systems found in experiments and numerical simulations. The theory of nematic disclinations is shown from both the geometric and topological perspectives. Entangled disclination line networks are analyzed based on their shape and the behavior of their cross section. Methods of differential geometry are applied to derive topological results from reduced geometric information. For nematic braids, systems of −1/2 disclination loops, created by inclusion of homeotropic colloidal particles, a formalism of rewiring is constructed, allowing comparison and construction of an entire set of different conformations. The disclination lines are described as ribbons and a new topological invariant, the self-linking number, is introduced. The analysis is generalized from a constant −1/2 profile to general profile variations, while retaining the geometric treatment. The workings of presented topological statements are demonstrated on simple models of entangled nematic colloids, estimating the margins of theoretical assumptions made in the formal derivations, and reviewing the behavior of the disclinations not only under topological, but also under free-energy driven constraints.     

Dynamical properties of ions confined within dense dispersions of charged anisotropic colloids : A <Superscript>23</Superscript>Na quadrupolar NMR study

We used ²³Na quadrupolar NMR spectroscopy and relaxation measurements to determine the mobility of the sodium counterions confined within dense aqueous dispersions of synthetic Laponite clays as a model of charged anisotropic nano-composite colloids. The lineshape analysis of the ²³Na spectra and the measurements of the Hahn echo attenuation are used to determine the critical clay concentration corresponding to the nematic organisation of the dispersion. As validated by numerical simulations of the ion diffusion within partially oriented nematic dispersion of the anisotropic colloids, the angular variation of the apparent relaxation rates is interpreted as an indice of degree of ordering of the dispersion.     

Control of two-dimensional motion of microparticles in nematic liquid crystal

The possibility of controlling two-dimensional motion of dielectric microparticles in the channel filledwith nematic liquid crystalwas experimentally shown. It was found that particle motion along the electric field occurs by means of the electrophoresis phenomenon. Particle motion along electrodes perpendicularly to the electric field is caused by the combination of two effects, i.e., the backflow and Quincke rotation.     

Silicon oxides as alignment surfaces for vertically-aligned nematics in photonic devices

A comparative study on alignment performance and microstructure of inorganic layers used for liquid crystal cell conditioning has been carried out. The study has focused on two specific materials, SiO_x and SiO₂, deposited under different conditions. The purpose was to establish a relationship between layer microstructure and liquid crystal alignment. The surface morphology has been studied by FESEM and AFM. An analysis on liquid crystal alignment, pretilt angle, response time, contrast ratio and the conditions to develop backflow effect (significant rise time increase due to pure homeotropic alignment) on vertically-aligned nematic cells has been carried out. A technique to overcome the presence of backflow has been identified. The full comparative study of SiO_x and SiO₂ layer properties and their influence over liquid crystal alignment and electrooptic response is presented.