Influence of K24 on the structure of nematic liquid crystal droplets

A phenomenological free energy is used to describe the stable ordering of nematic liquid crystals confined to supramicron spherical cavities. In particular the effects of the saddle splay elastic constant, K₂₄, on the equilibrium structures and phase diagram of droplets with homeotropic surface anchoring are discussed. Some structures are illustrated by the corresponding simulated polarization microscope textures. Possibilities for an experimental determination of the saddle-splay elastic constant and surface anchoring strength by studying the radial-axial structural transition in such droplets are analysed. It is shown that the K₂₄ term in the elastic free energy stabilizes a deformed droplet structure even in the limit of the zero anchoring strength.     

Dielectric and elastic properties of a nematic phase induced by charge transfer interaction in a binary system containing disc-shaped molecules

The dielectric constants and the elastic coefficients for splay (K₁) and bend (K₃) of the charge transfer induced nematic (N_c) phase of tridecyl pentakis(phenylethynyl)phenyl ether (1) doped with different amounts of 2,4,7-trinitrofluorenone (2) were determined by studying the electric field induced bend deformation using the capacitance method. A negative dielectric anisotropy was observed. For the bend elastic constant K₃ values up to 22 × 10^-12 N are found which are one order of magnitude higher than the respective values of discotic nematic (N_D) phases. Values of 0·6-0·8 are obtained for the ratio K₁/K₃; these show a minimum for the equimolar complex.     

Measurements of the ratio of the Frank constants for splay and bend in nematics consisting of disc-like molecules 2, 3, 6, 7, 10, 11-hexakis(p-alkoxybenzoyloxy)triphenylenes

Measurements are reported of the magnetic Frederiks transition in nematics consisting of disc-like molecules; 2, 3, 6, 7, 10,11-hexakis(p-alkoxybenzoyloxy)triphenylenes. In agreement with theoretical predictions [1] and previous measurements on 2, 3, 7, 8, 12, 13-hexa(alkanoyloxy)truxenes [2], we find that the splay elastic constant, K₁, is larger than the bend elastic constant, K₃. The ratio K₁/K₃ is remarkably constant throughout the nematic regime.     

Weak-anchoring effects on a Freedericksz transition in an annulus

This paper investigates the effect of weak anchoring on static orientation patterns in a sample of nematic liquid crystal confined to a cylindrical annular geometry, in the presence of a magnetic field. The particular arrangement considered in detail is that in which a magnetic field is applied in the azimuthal direction to a sample of liquid crystal that is initially uniformly aligned parallel to the cylindrical axis and is weakly anchored at the inner cylinder, but strongly anchored at the outer cylinder. A static solution of the non-linear continuum equations is presented which suggests a possible experiment for evaluating the surface elastic coefficient k₂₄. In addition, a linear stability analysis based on the dynamic theory yields results for critical phenomena in agreement with those derived from the non-linear solution.     

Anomalous anisotropy of the elastic constants in the induced smectic O film

Surface tension is known to induce smectic O (S_O) films at the free surface of isotropic droplets of 1-methylheptyl terephthalylidene-bis-4-aminocinnamate (MHTAC). The S_O film has its molecules disposed in a herringbone fashion, with the layers parallel to the free surface. It constitutes a model of a 2D polar nematic liquid crystal without any contact to solid substrates. The film is oriented uniformly when applying a uniform electric field, except along disclination walls. By measuring the width of the disclination walls in the two configurations with the electric field parallel and perpendicular, we determine the anisotropy of the elastic constants in the induced S_o films. We find the ratio of the 2D bend to splay elastic constants K_b/K_s to be ≃ 0.25 which is anomalously small when compared to the corresponding 3D ratio (K₂ + K₃)/2K₁ usually found for the bulk nematic phase. This experimental result is comparable to measurements performed with 2D suspended S_c films with, however, a different physics.     

Elastic constants of uniaxial nematic liquid crystals: A comparison between theory and experiment

Using the unified molecular theory developed in our earlier paper (1992, Phys. Rev. A, 45, 974) we study in detail the influence of molecular interactions on the fundamental elastic properties of uniaxial nematic liquid crystals composed of molecules of cylindrical symmetry. The expressions for the elastic moduli associated with 'splay', 'twist' and 'bend' modes of deformations are written in terms of order parameters characterizing the nature and amount of ordering in the phase and the structural parameters which involve the generalized spherical harmonic coefficients of the direct pair correlation function of an effective isotropic liquid. Numerical calculations are done for a model system, the molecules of which have prolate ellipsoid of revolution symmetry and interact via a pair potential having both repulsive and attractive parts. The repulsive interaction is represented by a repulsion between hard ellipsoids of revolution. The attractive potential is represented by the dispersion and electrostatic interactions. Results for the elastic constants are reported for a range of molecular length-width ratio, temperature, density and molecular parameters and are compared with the experimental values of p-azoxyanisole (PAA) and 4'-n-octyloxy-4-cyanobiphenyl (8OCB). It is found that the inclusion of electrostatic interactions reduces the values of the ratios K₂/K₁ and K₃/K₁. The absolute values of the elastic constants and their ratios are in good agreement with the experimental and computer simulation values. The temperature dependence of the elastic constants and their ratios is studied. It is observed that the twist elastic constant has a weak temperature dependence but a pronounced influence is observed on the bend moduli. We also observed a pronounced increase in the values of the twist and bend elastic constants on approaching the nematic-smectic A transition temperature.     

Splay elasticity in an oligomeric liquid crystal

A magnetically-induced Freedericksz transition was used in conjunction with capacitance techniques to determine the splay elastic constant of the 4,4'-dialkoxyphenylbenzoate monomer '5OO5rsquo; [C₅H₁₁OC₆H₄COOC₆H₄OC₅H₁₁] and its dimer. As a function of reduced temperature in the nematic phase, it was found that K₁₁ of the dimer is only about 20 per cent larger than that of the monomer. Moreover, the values of K₁₁/S² versus reduced temperature, where S is the scalar order parameter, are equal to within experimental noise. These results suggest that for short oligomers Meyer's entropic model for splay elasticity in polymer liquid crystals is not applicable. A lowest order correction to the entropic model is suggested, which partially accounts for excluded volume and dispersive effects.     

Observation of textures of nematic polymers and estimation of the elastic constants

The texture of a copolyesteramide, Vectra® B950, has been studied by optical microscopy. At rest, the defects are typical of a biaxial nematic phase, but under the influence of a magnetic field or under shear, the nematic transforms into a uniaxial phase. The Freedericksz geometry yields a K₁ elastic constant of the order of 10^-8 N. The diffusivities K_III/_n and K_II/_n are obtained by measuring the light intensity transmitted through a sample during shear start-up and relaxation, and from this we estimate K_III ≅ 10 ^-9N and K_II ≅ 10 ^-10N. Since the biaxiality is small, these uniaxial constants adequately describe the phase at rest.     

Light scattering from a nematic monodomain in an electric field Twist elastic constant and viscosity coefficient of nematic polymer-solvent mixtures

The light scattering technique was used to investigate the viscoelastic parameters characterizing director twist distortions in miscible nematic mixtures of 5CB (pentacyanobiphenyl) with two side chain liquid crystal polymers and a main chain liquid crystal polymer. By applying an AC electric field to homeotropically-aligned nematic monodomains of the mixtures, the field-dependent scattering intensities and director orientation fluctuation relaxation rates yield, respectively, the twist elastic constant K₂₂ and viscosity coefficient γ₁. The results directly demonstrate that the addition of liquid crystal polymers causes substantial decreases of the relaxation rates for dynamic light scattering from the twist mode and these changes are due to small decreases in K₂₂ coupled with large increases in γ₁. The decrements in K₂₂ are comparable for both side chain and main chain liquid crystal polymers. The relative increase in the twist viscosity for the side chain liquid crystal polymers is much smaller than those of main chain polymers. A theoretical model is used to qualitatively interpret the difference between the viscous behaviour of the twist mode for both side chain and main chain liquid crystal polymers in a nematic solvent.     

Director orientation of a ferroelectric liquid crystal on substrates with rubbing treatment: The effect of surface anchoring strength

One of the most important problems with ferroelectric liquid crystals is obtaining homogeneous as well as bistable alignment, not only to study their physical characteristics but also for their application to optical devices. In this connection it was predicted that the formation of homogeneous alignment requires strong surface anchoring, whereas bistability requires weak anchoring. We have therefore developed a method to determine the surface anchoring strength, and have tried to clarify whether there is a suitable anchoring range. It was found that A/K₂₂ (A is the surface anchoring and K₂₂ is the twist elastic constant of liquid crystal) of 4 × 10^-2 to 2 μm^-1 satisfies the contradictory requirements for homogeneous as well as bistable alignments for the material studied, and the bookshelf structure is successfully formed with this condition.     

Surfactant-Water Systems with Small Layer Rigidity Phase Stability, Defects Models and Defects Mobility in Polyoxyethylene Surfactant with Water

Starting from recent experiments in non-ionic surfactants, we discuss various topics characteristic of low rigidity K₁ materials. (1) The stability of the lamellar and cubic phases is studied in a simple model involving K₂ the saddle-splay constant K₂, and entropy terms due to the chains. We expect the lamellar phase to have a large range of existence, and the cubic phase to be of small extent. (2) We compare to cubic phases stability in large K₁ materials. We discuss the mobility of edge dislocations on the basis of a new model of the core which involves stretching of the core layers in one dimension, and easy nucleation of pores in this region. The core extension is a characteristic length of low K₁ materials which is much larger than de Gennes' length for microemulsions with a similar low K₁.     

The magnetic field-induced deformations in nematic layers with non-zero splay-bend elastic constant

The magnetic field-induced deformations of weakly anchored nematic layers in the presence of the non-zero splay-bend elastic constant K₁₃ are analysed by use of the Pergamenshchik approach. Most of the anomalous phenomena reported by other authors, that do not occur if k₁₃ = 0, have been confirmed. New effects suitable for experimental verification are predicted: the discontinuous transition with hysteresis between the uniform undistorted state and the state uniformly aligned along the field, and the rotation of the director in the tilted layer during continuous increase and decrease of the perpendicular field.     

Investigation on the viscoelasticity of synchronous hepatocellular carcinoma cells

Having made use of the micropipette aspiration technique, we here investigated the viscoelastic properties of hepatocellular carcinoma (HTC) cells from the view of cell cycle. The synchronous G₁ and S phase cells were achieved through thymine-2-desoryriboside and colchicine sequential blockage method and double thymine-2-desoryriboside blockage method, respectively. The synchronization results detected with flow cytometer showed that it could meet the requirements of the experiments nicely. Experimental results were analyzed with a standard linear solid viscoelastic model, in which an elastic element, K₁, is in parallel with a Maxwell element composed of another elastic element, K₂, in series with a viscous element, μ. The results indicated that high K₁, K₂ values and low μ value was the general characteristics of the cells; G₁ phase cells had higher K₁ values and low μ value than S phase cells, which endowed G₁ phase cells with higher elasticity and faster passive deformability than S phase cells. The results maybe also reflected the difference of cytoskeleton between G₁ and S phase cells, and suggested that G₁ phase cells were more suitable for surviving and metastasis in blood circulation than S phase cells.     

Influence of cell and LC parameters on the dynamics of STN liquid crystal displays

The dynamics of super-twisted nematic (STN) liquid crystal displays have rarely been studied. In this article, the dynamic response of STN is analysed in detail. The evolution of director configuration with time was obtained by solving Ericksen-Leslie hydrodynamic equations. The time varying midlayer tilt angle is presented as a measure of dynamic response. The influence on STN dynamics of cell parameters including pretilt angle, twist angle, cell thickness, and of material parameters including d/p, K₂₂, K₃₃, were studied.     

Determination of stability constants for rare earth elements and fulvic acids extracted from different soils

Fulvic acids (FAs) were extracted by alkali extraction from different soil samples in China, then purified using resins and characterized by Fourier transform infrared spectroscopy. The complexing ability of FAs was investigated by measuring the stability constants of rare earth elements (REEs) (La³⁺, Ce³⁺, Sm³⁺, Gd³⁺, Y³⁺) with FAs by the ion exchange technique. The results indicated that maximum binding ability forY³⁺ (4.414.44) was higher than other REEs (La³⁺, Ce³⁺, Sm³⁺, Gd³⁺) (0.721.03). There were two types of binding sites in the functional groups of fulvic acids. The complexing reaction followed two steps. The stability constants (K₁ and K₂) of REEs with FAs were calculated from experimental data by division of Scatchard plots into two straight-line segments. Y³⁺ (log K₁=5.72±0.05, log K₂=4.83±0.01) also has higher stability constants than the other four REEs (log K₁=4.37±0.16, log K₂=3.62±0.28).     

Rapid measurement of fish freshness indices by an amperometric flow-injection system with a 16-way switching valve and immobilized enzyme reactors

A novel flow-injection system is proposed for the rapid measurement of the fish freshness indices K₁ and K₂: K₁=[([HxR+[Hx])×100/([IMP]+[HxR]+[Hx])] and K₂=[[Hx]×100/([HxR]+[Hx])], where [IMP], [HxR] and [Hx] are inosine-5′-monophosphate, inosine and hypoxanthine concentrations, respectively. For the estimation of index K₁, 5′-nucleotidase immobilized reactor and nucleoside phosphorylase (NP)/xanthine oxidase (XO) coimmobilized reactor were incorporated in series in the flow-injection line made up by a 16-way switching valve with two sample loops. For the estimation of index K₂, NP and XO immobilized reactors were also incorporated in the similar flow-line. Two sample portions passed through the flow-line with different residence times so that two peaks were obtained. The first and second peaks obtained in the K₁-determining system corresponded to the total of HxR and Hx and the total of Hx, HxR and IMP, respectively. Similarly, the first and second peaks obtained in the K₂-determining system corresponded to Hx and the total of Hx and HxR, respectively. Therefore, the indices K₁ and K₂ can be estimated by

where i₁ and i₂ present the peak current of the first and second peaks, respectively, and f the ratio of the peak currents of the first and second peaks for a Hx standard solution. A sea bream was selected as a model fish and it was stored at 4 °C after death. A good correlation was found between the index K₁ and the storage time over a period of 400 h, with a correlation coefficient of 0.992, but no correlation between the index K₂ and the storage time. The measurements could be performed at a rate of 22 samples per hour with satisfactory precision (0.6–1.2% R.S.D.), without calibration for each species, accurate weighing of fish meat and any interferences in fish meat.     

The formula of anchoring energy for a nematic liquid crystal

The interface energy for a nematic liquid crystal (NLC) is considered as the sum of potential energy between LC molecules and molecules of the substrate surface, and a formula for anchoring energy is derived by elementary principles. The anchoring energy for a NLC should have two terms, the first term is the same as the Rapini-Papoular expression, the second is related to the normal of interface and resultes from the biaxial property of a NLC induced by interface. Hence there are two anchoring coefficients, W₁ and W₂. We demonstrate that W₁ is equal to the tilt angle strength A_θ, and W₂ corresponds to the difference between A_θ and the azimuthal strength A_ϕ. Thus A_θ-A_ϕ is due to the biaxial property of the NLC near the interface. Applying this formula to the twisted NLC cell, we discuss the threshold and saturation field, as well as the maximal tilt angel θ_m with respect to A_θ/A_ϕ. Previously proposed formulae are discussed from our point view.     

On the K13 surface-like elastic constant An experimental method to test different theoretical models

Oldano and Barbero showed that, due to the presence of the surface-like elastic constant K₁₃ in the expression of the elastic free energy density, F₂, in a nematic liquid crystal, the functional F₂ is unbounded from below and thus it is impossible to find an equilibrium director distortion. In particular, they showed that the surface-like elastic constant favours a discontinuity of the director-field at the interfaces. In recent years two quite different theoretical approaches have been proposed to eliminate the mathematical difficulties related to the K₁₃ problem. Barbero et al., expanded the free energy functional F up to the fourth order in the director derivatives and showed that the minimization problem becomes mathematically well posed. A strong subsurface director distortion on a length scale of the order of the molecular length is predicted by using this approach. This point has been critized by V. Pergamenshchik who considers the subsurface strong distortion as an artefact of theory and proposes an alternative method to account for the effect of K_{1 3}. This method is virtually coincident with that already proposed by Hinov on the basis of an a priori assumption. In this paper we discuss some direct consequences of these two different approaches and we propose two simple experimental measurements which should lead to different results depending on which model is the correct one, allowing in this way a test of the different theoretical models.     

Viscoelastic coefficients of glass-forming nematics

In this paper, we report measurements of the viscoelastic properties of nematic liquid crystals which exhibit a glass transition in the nematic phase. We have studied the Freedericksz transition in planar cells with a magneto-optical method. K₁ was determined from the critical field, and the rotational viscosity, γ₁, from the response time for the director orientation by the external field. We found a temperature dependence of γ₁ of the Vogel type, with absolute values ranging over several orders of magnitude, and K₁ values similar to those of conventional thermotropic low molar mass nematics.     

2H-N.M.R. studies of flexibility and orientational order in nematic liquid crystals

Deuteron magnetic resonance spectroscopy (²H-N.M.R.) has been used to investigate the effect of the nematic environment on the flexibility and orientational order of two perdeuteriated cyanobiphenyl homologues: 4-methyl-4'-cyanobiphenyl (1CB-d₁₁) and 4-n-pentyl-4'-cyanobiphenyl (5CB-d₁₉). The systems studied were low concentrations of 1CB-d₁₁ and 5CB-d₁₉ dissolved in the nematic phases of 5CB, N-(-4-ethoxybenzylidene)-4'-n-butylaniline (EBBA), Merck ZLI-1132 (1132) and a 55wt% mixture of 1132: EBBA. The spectra are dramatically different in these environments. Previous studies on small solutes have suggested that in the 55wt% 1132: EBBA mixture (at 301.4 K) the dominant orienting mechanism depends on the size and shape of the molecule which suggests that it is a short range repulsive interaction. This interaction has been modelled by treating the liquid crystal as an elastic continuum and the solute as a collection of van der Waals spheres which stretch the liquid crystal in the two dimensions perpendicular to the director. The distortion of the liquid crystal depends on the dimensions of the solute, and the elastic energy is described in terms of a Hooke's law force constant, k. The model is extended to include flexible liquid crystal molecules and quadrupolar couplings are calculated for each conformation of the 5CB chain. Statistical averaging over all conformations gives an excellent fit to the experimental spectrum. The results for 1CB and 5CB show that in the other nematic phases contributions from additional mechanisms must be included. Previous studies of ²H₂ and other solutes indicate that the additional mechanism is the interaction between the solute molecular quadrupole moment and the mean electric field gradient of the liquid crystal.