Levitation, lift, and bidirectional motion of colloidal particles in an electrically driven nematic liquid crystal

We study electric-field-induced dynamics of colloids in a nematic cell, experimentally and by computer simulations. Solid particles in the nematic bulk create director distortions of dipolar type. Elastic repulsion from the walls keeps the particles in the middle of cell. The ac electric field reorients the dipoles and lifts them to top or bottom, depending on dipole orientation. Once near the walls, the colloids are carried along two antiparallel horizontal directions by nematic backflow. Computer simulations of the backflow agree with the experiment.     

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     

Energetics of 2D colloids in free-standing smectic-C films

The formation of regular colloid patterns in free-standing smectic films at the transition from the smectic-C to the isotropic or nematic phase is well known experimentally. The self-organization of isotropic or nematic droplets is caused by their mutual interaction, mediated by elastic distortions of the local director in the surrounding liquid crystal. These distortions are related to the anchoring conditions of the director at the droplet border. We describe analytically the energetics of the liquid crystal environment of a single droplet in one-constant approximation. A method of complex analysis, Conformal Mapping, is employed. Following a suggestion of Dolganov et al. (Phys. Rev. E. 73, 041706 (2006)), energetics of chain and grid patterns built from the colloids are investigated numerically in order to explain experimentally observed formations and their director fields.     

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.     

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     

Light-driven oscillations of entangled nematic colloidal chains

Laser tweezers have been used to drive the oscillations of a chain of entangled colloidal particles in the nematic liquid crystal 5CB. The amplitude and phase of light-driven oscillations have been determined for the motion of individual colloidal particles. The collective motion of 4.8μm silica particles is highly damped for a driving frequency above 0.5Hz. The results were compared to an effective bead-spring model, where the motion of elastically coupled particles is hindered by viscous damping and hydrodynamic coupling. Qualitative agreement between theory and experiment was obtained.     

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.     

Anisotropic stokes drag and dynamic lift on cylindrical colloids in a nematic liquid crystal

We have measured the Stokes drag on magnetic nanowires suspended in the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB). The effective drag viscosity for wires moving perpendicular to the nematic director differs from that for motion parallel to the director by factors of 0.88 to 2.4, depending on the orientation of the wires and their surface anchoring. When the force on the wires is applied at an oblique angle to the director, the wires move at an angle to the force, demonstrating the existence of a lift force on particles moving in a nematic. This dynamic lift is significantly larger for wires with homeotropic anchoring than with longitudinal anchoring in the experiments, suggesting the lift force as a mechanism for sorting particles according to their surface properties.     

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.     

High-frequency dielectric spectra from liquid crystals of series nCB and nOCB

The design of a resonant frequency-tunable high-sensitivity microstrip sensor is suggested. The permittivity dispersion of liquid crystals of two homologic series, alkylcyanobiphenyls (7CB and 8CB) and alkyloxycyanobiphenyls (7OCB and 8OCB), is studied at frequencies of 100–900 MHz. The dielectric spectra are shown to be the sum of the Debye relaxation and dielectric resonances observed at f≈160, 280, 360, 450, 550, and 650 MHz. The dielectric resonances are present in the spectra of all the samples in both the nematic and isotropic phase. The substitution of an oxygen atom (series nOCB) for a carbon atom (series nCB) in liquid crystal molecules has a minor effect on the dielectric resonance frequencies but changes the resonance intensities and splits some of the resonance lines.     

基于光子晶体马赫-曾德尔干涉仪的太赫兹开关及强度调制器

通过对二维正方晶格光子晶体线缺陷模色散曲线慢光特性的研究, 利用外电场对液晶分子取向的调控作用, 在填充液晶的正方晶格波导的马赫-曾德尔干涉仪结构中实现了开关和强度调制等功能. 利用平面波展开法计算了光子晶体波导的线缺陷模, 分析了液晶折射率的变化对缺陷模的影响. 计算表明, 液晶折射率仅改变了0.1, 线缺陷模有效折射率改变达0.168, 该特性可以更为有效地实现对相位的控制, 进而实现高消光比开关和强度调制功能, 这种高效的相位调节器件在集成光系统中将有很好的应用前景.     

Liquid-crystalline phase behavior of a colloidal rod-plate mixture

The phase behavior of rod-plate mixtures was investigated using model systems containing unambiguously rod- and plate-shaped colloids. We find that the theoretically disputed biaxial nematic phase is unstable with respect to demixing into an isotropic and two uniaxial nematic phases. The phase behavior at very high densities is exceptionally rich and includes the coexistence of up to four different liquid crystalline phases, which stem from the coupling between the employed particle shapes and polydispersity.     

Orientation-dependent depletion interaction in rodlike colloid-polymer mixtures

Depletion interaction in a suspension of rodlike colloids with added non-adsorbing polymer coils is theoretically studied. We calculate an overlap volume of depletion zone between two rodlike colloids, based on the second virial approximation. We examine nematic-isotropic phase transition (NIT) and two-phase coexistence between an isotropic and a nematic phase at low polymer concentrations. We find that the depletion interaction is dependent on the orientational order parameter of rodlike colloids and leads to a decrease in the NIT concentration on the addition of polymer. The coexistence curves have a leaning-chimney shape and are shifted to lower rod concentrations on increasing the polymer concentration. Received 23 May 2001 and Received in final form 18 July 2001     

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.     

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.     

Demixing and nematic behaviour of oblate hard spherocylinders and hard spheres mixtures: Monte Carlo simulation and Parsons–Lee theory

Parsons–Lee approach is formulated for the isotropic–nematic transition in a binary mixture of oblate hard spherocylinders and hard spheres. Results for the phase coexistence and for the equation of state in both phases for fluids with different relative size and composition ranges are presented. The predicted behaviour is in agreement with Monte Carlo simulations in a qualitative fashion. The study serves to provide a rational view of how to control key aspects of the behaviour of these binary nematogenic colloidal systems. This behaviour can be tuned with an appropriate choice of the relative size and molar fractions of the depleting particles. In general, the mixture of discotic and spherical particles is stable against demixing up to very high packing fractions. We explore in detail the narrow geometrical range where demixing is predicted to be possible in the isotropic phase. The influence of molecular crowding effects on the stability of the mixture when spherical molecules are added to a system of discotic colloids is also studied.     

The properties of some derivative autocorrelation functions computed with the atom-atom potential

High-resolution quasi-elastic neutron-scattering measurements have been made on two nematogens: DMBCA with a nematic range 108 to 119°C, and 5CB and a tail-deuteriated sample (D5CB), having a nematic range 22·6 to 35·1°C.

Results on 5CB in the crystal phase at ～18°C showed no significant quasielastic broadening, which means that any random motions of the alkyl chain are slower than about 5 × 10⁹ rad s^-1. Measurements were made at a single temperature in the nematic phases on specimens aligned in a magnetic field of 0·25T; for DMBCA with scattering vector Q⊥n (n is the nematic director) and for 5CB and D5CB with Q⊥n and Q∥n and also on the isotropic liquid phase of D5CB at 45°C. Analysis of the coherent scattering from nematic D5CB at Q = 1·2 Å^-1 and 25°C gave an order parameter <P ₂>=0·55, close to the simple mean field value for this temperature. The coherent scattering from DMBCA is too weak to allow this experiment to be performed.

The most remarkable qualitative feature of the results is the close similarity of the scattering law S(Q, ω) for D5CB (and 5CB) with Q⊥n and Q∥n. Analysis of the results in all cases was made using values for the translational diffusion constants measured previously. Corrections for multiple scattering are shown to be important and a single simple model has been devised which fits the line shapes of all the results for D5CB in nematic (Q⊥n and Q∥n) and isotropic liquid phases and DMBCA. The model involves uniaxial rotational diffusion about the long molecular axis m coupled to a displacement along the rotation axis giving a net rotation in a plane whose normal makes an angle ∝ relative to the direction m. Values for the rotational diffusion constant D _rd ns^-1 are as follows: D5CB, 25°C, 6 (∝ ～ 50°); 45°C, 10. DMBCA, 112°C, 16, (all ±10–15 per cent).

The results for D5CB and 5CB are so similar that no additional detailed model fitting was attempted for the fully hydrogenous sample and it is concluded that while the motion of the alkyl tails is freer, the time scale of the motions is not more than about a factor of 2 faster than that of the molecular cores.     

Elastic properties of liquid crystals

The structural and elastic properties of 4-n′-pentyl-4′-cyanobiphenyl (5CB) in the nematic liquid-crystal phase are investigated in the framework of the statistical-mechanical theory and the molecular dynamics method.     

Phase Conjugation by Degenerate Four-wave Mixing in Nematic Liquid Crystals

1.IntroductionOpticalphaseconjugationhasbeeninvestigatedextensivelybecauseofitswideapplicationsinimagingtechnology,phase--conjugationlasers,andopticalassociativememorysystems.Notedfortheirlargeopticalreorientationnonlinearities[IJ,nematicliquidcrystals(NLC)havebecomepromisingopticalmediaforapplicationsinthefieldofnonlinearopticsincludingnonlinearphaseconjugation.In1980,Feketectal.[2)firstrealizedphase--conjugationbydegeneratefour--wavemixing(DFWM)inNLCintheisotropicphase.Sincethen,thefie…     

Local measurement of the zenithal anchoring strength

We present an electro-optic method for measuring the zenithal anchoring strength of nematic liquid crystals, based on the determination of the distortion produced by a small electric field. This method yields the zenithal anchoring strength at small applied torques, and remarkably, only needs local measurements (optical path difference versus applied voltage, sample thickness), in contrast to the classical methods that use measurements integrated over the entire sample. We determine the zenithal anchoring strength for two nematic liquid crystals (5 CB and 5 OCB) with positive dielectric anisotropy, onto poly(tetrafluoroethylene) (PTFE) treated surfaces, that yield planar liquid crystal cells. We find that the anchoring at the PTFE-5 CB interface is strong, with an extrapolation length approximately 30 nm, and independent of temperature far enough from the isotropic transition. We observe a pretransitional weakening of the anchoring strength near the nematic-isotropic transition, due to the reduction of the orientational order parameter at the interface. With 5 OCB, we measure a stronger anchoring, with an extrapolation length approximately 15 nm. This result may be explained by the increase of the van der Waals interactions between the liquid crystal molecules and the surface, due to the presence of the oxygen atom.