Elastic constants of a nematic liquid crystal: Quadrupole-quadrupole interaction in the ellipsoidal approximation

The elastic constants of a nematic liquid crystal are calculated by means of a pseudo-molecular method that considers the quadrupolar intermolecular interaction with a screening length governing the range of the forces. The bulk as well as the surface-like elastic constants are determined as functions of the eccentricity of the interaction volume of ellipsoidal shape. It is shown that the elastic constants become negative for some values of the eccentricity, and, therefore, that the screened quadrupolar interaction could be the source of instabilities in the nematic phase and should be taken into account to interpret threshold phenomena in these systems.     

Elastic constants of some nematic liquid crystals with banana-shaped molecules

Results are given for the elastic constants in the nematic phase of some molecules with a curved (banana-like) molecular shape. In principle this could lead to a reduced bend elastic constant due to the possibility of adjusting to a bend deformation by a redistribution of the molecules. However, the elastic constants turn out to have quite normal values as compared with similar non-curved molecules.     

Collective effects in doped nematic liquid crystals

We studied the collective elastic interaction in a system of many macroparticles embedded in a nematic liquid crystal. A theoretical approach to the interaction of macroparticles via deformation of the director field [1] is developed. It is found that the director field distortion induced by many particles leads to the screening of the elastic pair interaction potential. This screening strongly depends on the shape of the embedded particles: it exists for anisotropic particles and is absent for spherical ones. Our results are valid for the homeotropic and the planar anchoring on the particle surface and for different Frank constants. We apply our results to cylindrical particles in a nematic liquid crystal. In a system of magnetic cylindrical grains suspended in a nematic liquid crystal, the external magnetic field perpendicular to the grain orientation results in inclining the grains to the director and induces an elastic Yukawa-law attraction between the grains. The appearance of this elastic attraction can explain the cellular texture in magnetically doped liquid crystals in the presence of the magnetic field [2].     

The Theory of the eleastic constants of nematics

Expressions are derived for the elastic constants of nematic liquid crystals by conceiving the molecular models as tensor fields. It is shown that the anisotropic part of the intermolecular pair potential can be dealt with completely.     

Dependence of viscoelastic parameters of nematic liquid crystals on pretilt angle and temperature

The viscoelastic parameters of nematic liquid crystal (LC) E7 in both splay and twist relaxation modes are investigated as functions of pretilt angle and temperature by the technique of dynamic laser light scattering. The results show that the elastic constants of the liquid crystal in the two modes not only depend on temperature, but also depend on pretilt angle. There is a critical pretilt angle (β_C) at which nematic LC begins exhibiting elastic property, and beyond which the elastic constants increase with pretilt angle, then keep constant after exceeding another angle (β_S, with β_S > β_C). This phenomenon is observed to be universal for different nematic LC’s, and significant not only in the understanding of the molecular mechanism of exhibiting viscoelastic properties in nematic LC, but also for their practical purpose.     

Measurement of elastic constants of nematic liquid crystals with use of hybrid in-plane-switched cell

A new method for quick and pretty accurate measurements of splay, twist and bend elastic constants of nematic liquid crystals is experimentally verified. The main concept relies on exploiting only the electric field and determining magnitudes of nematic elastic constants from threshold fields for Freedericksz transitions in only one hybrid in-plane-switched cell. In such cell the deformations of an investigated liquid crystal are controlled by three separated pairs of electrodes confining measurement domains. In two of them inter-digital electrodes are mounted on one cell cover. Splay, twist and bend elastic constants can be measured by a proper choice of electrodes?? configuration together with orienting cover coatings (without applying magnetic fields). In this paper, we describe layout of our cells and results of experimental tests by using different liquid crystals: 5CB and 6CHBT (with positive dielectric anisotropy), Demus?? esters (with negative dielectric anisotropy) and new liquid crystals mixtures produced in our university.     

One- and two-dimensional deformations in nematic liquid crystals: Influence of the flexoelectric polarization

Summary The elastic deformations in nematic liquid crystals are analysed in one and two dimensions. The influence of the flexoelectric polarization on the elastic properties of the medium is studied. It is shown that for one-dimensional deformations, the presence of the flexoelectric polarization introduces a renormalization of the elastic constants. On the contrary in the bidimensional case, the effect of the flexoelectricity is not a simple renormalization of the elastic constants. The profiles of the electric potential and of the tilt angle are evaluated for the cases in which the substrate is an insulating or conducting material. The validity of the calculations is discussed by considering the value of Debye's screening length of the nematic liquid crystal.     

Study of intrinsic anchoring in nematic liquid crystals based on modified Gruhn-Hess pair potential

A nematic liquid crystal slab composed of N molecular layers is investigated using a simple cubic lattice model, based upon the molecular pair potential which is spatially anisotropic and dependent on elastic constants of liquid crystals. A perfect nematic order is assumed in the theoretical treatment, which means the orientation of the molecular long axis coincides with the director of liquid crystal and the total free energy equals to the total interaction energy. We present a modified Gruhn-Hess model, which is relative to the splay-bend elastic constant K₁₃. Furthermore, we have studied the free nematic interfacial behavior (intrinsic anchoring) by this model in the assumption of the perfect nematic order. We find that the preferred orientation at the free interface and the intrinsic anchoring strength change with the value of modification, and that the director profile can be determined by the competition of the intrinsic anchoring with external forces present in the system. Also we simulate the intrinsic anchoring at different temperatures using Monte Carlo method and the simulation results show that the intrinsic anchoring favors planar alignment and the free interface is more disordered than the bulk.     

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.     

Laser light scattering technique for non-invasive in situ simultaneous measurements on elastic constants and viscosity coefficients of nematic liquid crystals

Theelasticconstantsandtheviscositycoefficientsarethekeyparametersforthephysicalpropertiesofnematicliquidcrystals(LCs)[1,2],fortheyarecorrespondingtothethresholdvoltageandtherespondingtimeofliquidcrystaldisplaydevices[3,4].Sofarnotechniquethatcansimultaneouslymeasurethetwoparametersinsituhasbeenreported.TheelasticconstantsandviscositycoefficientsofnematicLCsatthepresentaremeasuredusingdifferentmethodsindependently.TheviscositycoefficientsisgenerallymeasuredwithOstwaldviscosimeter,andtheelasti…     

Monte Carlo模拟空间各向异性势向列相液晶微滴

基于分子两体势,用Monte Carlo方法计算向列相液晶微滴.两体势基于格点模型,是空间各向异性的且依赖于液晶的弹性常数.假定向列相液晶微滴具有自由表面,引入切向内禀强度定量描写表面引发的分子内禀易取向的强弱.通过各向异性势的两种方案,在低温下计算切向内禀强度和二阶序参数在微滴内不同区域的变化,与Lebwohl-Lasher模型作对比分析.结果表明:只有一种方案在微滴表面产生内禀易取向,且内禀强度值的大小与K₃₃/K₁₁值有关;空间不完整的向列相液晶使得微滴由内层到外层有序度越来越低.     

The molecular-statistical calculation of the elastic constants of uniaxial nematics

Using the molecular-statistical theory of the thermodynamic properties of nematics and perturbation theory, the expressions for the elastic constants of uniaxial nematics are derived in terms of the mutual interactions between their constituent molecules. Next the elastic constants of the Maier-Saupe model are calculated and compared with the original result. The appearing difference is discussed briefly. Finally, in view of existing discrepancies, the elastic constants of the Onsager model are recalculated. For that purpose the hard rod interaction is conceived as the limit of a non-singular interaction. The elastic constants of hard core models are shown to increase with increasing temperature at constant density. In view of this behaviour the usefulness of hard core models for an understanding of the nematic state seems rather limited.     

Structure,elasticity and phase transitions in liquid crystals with deformations

ABSTRACT

A molecular-statistical theory describing the nematic liquid crystals (LCs) with spherical inclusions (or point defects) is proposed. At given size of inclusions and nematic order parameters at the surfaces of inclusions (zero in the case of point defects) and far from inclusions (where the nematic LC is almost uniform), the distribution of nematic order parameters in the bulk of LC with inclusions was found to be fully determined by the elastic constants of LC. We have found and explained the two-step heat-driven transformation from the nematic phase into the isotropic phase, with the intermediate phase in between. The nematic order parameters and the elastic constants are evaluated in the framework of a unified approach based on the features of pair interaction potentials of the individual LC molecules. It is shown that, in the case of K₃₃ < K₁₁, the point defects should destroy the conventional nematic phase.     

Elastic Constants of Superconducting MgB2 from Molecular Dynamics Simulations with Shell Model

The elastic constants of superconducting MgB₂ are calculated using a molecular dynamics method (MD) with shell model. The lattice parameters, five independent elastic constants, equations of state (EOS), Debye temperature, and bulk modulus of MgB₂ are obtained. Meanwhile, the dependence of the bulk modulus B, the lattice parameters a and c, and the unit cell volume V on the applied pressure are presented. It is demonstrated that the method introduced here can well reproduce the experimental results with a reasonable accuracy.     

Numerical investigation of influence of ionic space charge and flexoelectric polarization on measurements of elastic constants in nematic liquid crystals

Deformations of nematic layers caused by magnetic field allow determination of the elastic constants of liquid crystal. In this paper, we simulated numerically the deformations of planar and homeotropic nematic layers. The flexoelectric properties of the nematic and presence of ions were taken into account. Our aim was to show the influence of flexoelectricity on the results of the real measurement of the elastic constants k₃₃ and k₁₁. In these simulations, we calculated the optical phase difference ΔΦ between the ordinary and extraordinary rays of light passing through the layer placed between crossed polarizers as a function of the magnetic field induction B. One of the elastic constants can be calculated from the magnetic field threshold for deformation. The ratio k₃₃/k₁₁ can be found by means of fitting theoretical ΔΦ(B) dependence to the experimental results. The calculations reveal that the flexoelectric properties influence the deformations induced by the external magnetic field. In the case of highly pure samples, this may lead to false results of measurement of the elastic constants ratio k₃₃/k₁₁. This influence can be reduced if the nematic material contains ions of sufficiently high concentration. These results show that the flexoelectric properties may play an important role, especially in well purified samples.     

Representation of pair correlations in nematics

A complete expansion of equilibrium pair correlation functions for a uniaxial nematic phase composed of axially symmetric, non-polar and chiral molecules is proposed. Full advantage is taken of the symmetry of the nematic state and of the molecules. The explicit analysis and classification of the terms involving spherical harmonics with indices not exceeding 4 is given and illustrated using computer simulations for the nematic phase of a Gay-Berne mesogen. The theory is contrasted with the commonly used approach employing invariants that describe orientational correlations in molecular fluids. The role of the new representation in obtaining a correct understanding of a variety of observables, like the elastic constants, is demonstrated. In particular, the long-standing puzzle concerning the splay-bend degeneracy is resolved. Received 11 April 2000 and Received in final form 19 July 2000     

Elestic constants in the interfacial layer at the nematic-liquid-crystal-vapour interface

Summary Close to the interface between a nematic liquid crystal (NLC) and another medium, the elastic constants become functions of distancez from the interface and of angle θ between the directorn and the unit vectork orthogonal to the interface. Furthermore, due to the breaking of the translation symmetry at the interface, a lot of new subsurface elastic contributions can appear. In a previous paper we investigated these subsurface anomalies by using a simple molecular model based on induced-dipole-induced-dipole interactions and by making numerical calculations in the special case of a planar director distortion. In this way, only the numerical values of some effective subsurface elastic constants that characterise planar director distortions could be obtained. In this paper we make a more complete analytical calculation of all the subsurface elastic constants by using a microscopic model and a more general theoretical procedure. The microscopic interaction energy is written in a general form that allows us to investigate different kinds of intermolecular interactions (induced diple-induced dipole, quadrupole-quadrupole and so on). Both thez-dependence and the θ-dependence of the subsurface elastic constants are obtained in a closed analytical form. In the special case of induced-dipole-induced-dipole interactions and for planar director distortions, our analytical results are shown to agree with the previous numerical results. The important macroscopic effect of these elastic subsurface anomalies is discussed.     

Flexoelectric polarization and second order elasticity for nematic liquid crystals

The flexoelectric properties of nematic liquid crystals are analysed. It is shown that in the frame of the usual elasticity two coefficients characterize completely the flexoelectric properties of the liquid crystal. These coefficients, in the limit of small scalar order parameter, i.e. near the clearing point, are approximately equal. More precisely they have the same linear term in the scalar order parameter, and differ for terms quadratic in this parameter. Their difference behaves, hence, as the usual nematic liquid crystal elastic constants, whereas their sum depends on the temperature, like the mixed splay-bend elastic constant. It is shown furthermore that in the frame of a second order elastic theory in the flexoelectric polarization there are no terms from the second order spatial derivatives of the nematic director, or the nematic tensor order parameter. Consequently also in the frame of the second order elasticity the flexoelectric polarization is given by the usual expression. This conclusion is important in connection with the surface polarization recently discovered in pretilted nematic liquid crystal samples.     

弹性形变对丝状相液晶相变的影响

应用Saupe形式的弹性自由能,研究了简单的扭曲,展曲和弯曲形变对相变的影响.结果表明,弹性形变可以产生从各向同性相至双轴丝状相的一级相变,对螺状相液晶,当系统手征性增加并超过某一临界值时,一级相变可过渡到二级相变. 关键词：     

The nature of prolate shape of tactoids in lyotropic inorganic liquid crystals

A tactoid phase is obtained, which is an anisotropic mesophase dispersed in an anisotropic solution. A model is constructed that describes the shape of anisotropic regions, i.e., tactoids. It is demonstrated that the prolate shape of tactoids is caused by the competition between the elastic energy of the nematic phase and the surface energy. This model is used to find the ratio of elastic constants K3/K₁ from the experimental data. It is experimentally found that a magnetic field orients and stretches tactoids. An explanation of this phenomenon is suggested.