Light-field-induced spatially periodic freedericksz transition in a planar nematic cell

It is shown that a threshold spatially periodic reorientation of the director by a light field is possible in a planar nematic liquid crystal cell if the ratio of the Frank elastic constants, K ₂/K ₁, exceeds a critical value. The periodic director structure arising in the cell leads to a self-diffraction of the incident light wave. The dependences obtained for this phenomenon make it possible to determine the values of the elastic constants K ₁ and K ₂, the director reorientation threshold, and the period of the director structure from the experimental values of the self-diffraction angle.     

Inhomogeneous threshold director reorientation in a planar nematic flexoelectric cell with finite anchoring energy

The dependence of the threshold parameters and the period of the electric-field-induced spatially periodic reorientation of the director in a flexoelectric nematic liquid crystal (NLC) on the anchoring conditions at the surface of a planar NLC cell has been studied. The threshold electric field and the corresponding wave-number of the periodic structure of the director field have been numerically calculated for arbitrary values of the anchoring energy. In the case of strong anchoring, the corresponding analytical expressions are obtained in a single-constant approximation. A decrease in the azimuthal anchoring energy leads to an increase in the intervals of possible values of the flexoelectric parameter ν and the ratio K₂/K₁ of the Frank elastic constants. A decrease in the polar anchoring energy leads to narrowing of these intervals as compared to the case of infinitely strong anchoring at the NLC cell surface.     

Critical Elastic Coefficient of Liquid Crystals and Hysteresis

P. G. de Gennes predicted the analogies between the effect of the elastic coefficients to liquid crystals and the effect of applied magnetic fields to superconductors, and predicted that all elastic coefficients diverge to infinity at smectic-C to nematic transition. One would expect quantitative comparison in the analogies. In the case of equal elastic coefficients (K ₁ = K ₂ = K ₃ = K), we define the critical value K ^c of the elastic coefficients and make comparison of it with the upper critical magnetic field H _{C 3} for type II superconductors. We classify the smectic liquid crystals into subcritical, critical and supercritical cases according to the Ginzburg-Landau parameter κ, the wave number q and the boundary value of the director at the surface. We show that in the subcritical case the liquid crystal does not undergo phase transition; and in the supercritical case both phase transition and hysteresis occur. The prediction of de Gennes is true in the critical case where μ _π (u ₀, q) = κ ² and K ^c = + ∞.     

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.     

Laser light scattering technique for non-invasive<Emphasis Type="Italic">in situ</Emphasis> simultaneous measurements on elastic constants and viscosity coefficients of nematic liquid crystals

The laser light scattering technique for non-invasivein situ simultaneous measurements on elastic constants and viscosity coefficients of nematic liquid crystals is introduced. By measuring the autocorrelation function of the scattered light from nematic liquid crystals at different scattering angles, the splay and twist elastic constantsK ₁₁ andK ₂₂ are obtained from the amplitudes of the autocorrelation function, and the viscosity coefficients ofη _Splay andη _Twist are determined using the viscoelastic ratiosK ₁₁/η _Splay andK ₂₂ η _Twist from the telaxation parameters of the two modes.     

Statistical theory of the elastic constants of nematic liquid crystals

A statistical mechanical theory of the Frank elastic constants is formulated. The free energy functional is constructed for the deformed sample and the free energy density is defined for the case of small spatial gradients. The Frank constants are expressed in terms of the direct correlation function c(1, 2) and the orientational single particle distribution function. For the example of Onsager spherocylinders three constants K ₁, K ₂ and K ₃ are calculated. The results of these calculations are similar to those given by Priest and by Straley.     

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.     

The structure of the distortion free-energy density in nematics: Second-order elasticity and surface terms

Summary By means of a phenomenological approach, we demonstrate that the mixed splay-bend elastic constantK ₁₃ in the free energy density of nematic liquid crystals must be considered zero, unless the bulk contributions of the squares of the distortion second-order derivatives are taken into account, together with the squares of the first-order derivatives times the second-order derivatives, and with the fourth powers of the first-order derivatives. Such contributions just reduce to one in the presence of—and close to—a threshold. Furthermore, the saddle-splayK ₂₄-term instead is shown always to play an essential role, as the bulk first-order elasticity, in determining the distortion free energy of nematics with weak anchoring subjected to spatial deformations. Finally, the new surfacelike elastic constants are shown to have a nilpotent character: thus they behave as well asK ₂₄ from the point of view of the variational calculus. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

The influence of anchoring energy on the prolate shape of tactoids in lyotropic inorganic liquid crystals

A model was constructed to describe the prolate shape of anisotropic regions, tactoids, coexisting with the isotropic phase in lyotropic inorganic liquid crystals. The elastic energy of the tactoid, the surface energy, and the interaction energy between the director field and the boundary of the tactoid were taken into account. Large-sized tactoids were shown to be prolate because of the competition between the elastic energy of the nematic phase of the tactoid and the surface energy. Small-sized tactoids were prolate because of the competition of the surface energy with the anchoring energy between the director and the boundary of the tactoid. The suggested model was applied to experimental data to determine the ratio of the elastic constants K₃/K₁ and the ratio between the anchoring energy W and the surface tension σ depending on the “time of aging” of vanadium pentoxide sols in water.     

Structure and elastic properties of a nematic liquid crystal: A theoretical treatment and molecular dynamics simulation

The Frank elasticity constants which describe splay (K ₁), twist (K ₂), and bend (K ₃) distortion modes are investigated for 4-n-pentyl-4'-cyanobiphenyl (5CB) in the nematic liquid crystal. The calculations rest on statistical-mechanical approaches where the absolute values of K _i (i=1,2,3) are dependent on the direct correlation function (DCF) of the corresponding nematic state. The DCF was determined using the pair correlation function by solving the Ornstein-Zernike equation. The pair correlation function, in turn, was obtained from molecular dynamics (MD) trajectory. Three different approaches for calculations of the elasticity constants were employed based on different level of approximation about the orientational order and molecular correlations. The best agreement with experimental values of elasticity constants was obtained in a model where the full orientational distribution function was used. In addition we have investigated the approximation about spherical distribution of the intermolecular vectors in the nematic phase, often used in derivation of various mean-field theories and employed here for the construction of the DCF. We found that this assumption is not strictly valid, in particular a strong deviation from the isotropic distribution is observed for short intermolecular distances. Received 22 March 2000 and Received in final form 9 June 2000     

The effect of spontaneous polarization on two-dimensional elasticity of smectic liquid crystals

The influence of polarity on orientational elasticity and on structures formed in the director field is studied in free-standing smectic films. Periodic stripe patterns and 2π-walls in a magnetic field are investigated. Measurements are performed on a nonpolar racemic mixture, on an optically pure ferroelectric compound, and in mixtures with different concentrations of the chiral isomers of opposite signs. The structure of periodic stripes changes drastically with the polarity of the film. The ratio of the bend K _B and splay K _S elastic constants for smectic films is determined as a function of polarization from the structure of periodic stripe patterns and 2π-walls. We find that the elastic anisotropy K _B /K _S increases essentially with increasing the polarity of the film. Changes of the elasticity and the structure of periodic stripes are explained by polarization charge effects.     

Theoretical description of fluctuations in free-standing smectic-A films including spatial non-uniformity of their elastic characteristics

A theoretical study is reported of fluctuations in smectic layer displacements and of the correlations between them in free-standing smectic-A films formed of liquid-crystal compounds with smectic-A-isotropic liquid (Sm-A-I) and Sm-A-nematic (Sm-A-N) bulk phase transitions. The study took into account the dependence of the elastic constants for bending, K, and tension (compression), B, of smectic layers on distance to the free film surfaces. The calculations are compared with the results obtained within Hołyst’s model for spatially uniform, free-standing smectic-A films. It has been established that, below the temperature at which smectic order in the bulk of a liquid crystal disappears, taking into account the profiles of the elastic moduli K and B does not produce noticeable differences from this model. However, at temperatures considerably above the Sm-A-I and Sm-A-N phase transitions, their inclusion results in considerable discrepancies from the predictions of Hołyst’s model. Fiz. Tverd. Tela (St. Petersburg) 41, 1882–1889 (October 1999)     

Nematic liquid crystals at rough and fluctuating interfaces

Nematic liquid crystals at rough and fluctuating interfaces are analyzed within the Frank elastic theory and the Landau–de Gennes theory. We study specifically interfaces that locally favor planar anchoring. In the first part we reconsider the phenomenon of Berreman anchoring on fixed rough surfaces, and derive new simple expressions for the corresponding azimuthal anchoring energy. Surprisingly, we find that for strongly aligning surfaces, it depends only on the geometrical surface anisotropy and the bulk elastic constants, and not on the precise values of the chemical surface parameters. In the second part, we calculate the capillary waves at nematic-isotropic interfaces. If one neglects elastic interactions, the capillary wave spectrum is characterized by an anisotropic interfacial tension. With elastic interactions, the interfacial tension, i.e., the coefficient of the leading q² term of the capillary wave spectrum, becomes isotropic. However, the elastic interactions introduce a strongly anisotropic cubic q³ term. The amplitudes of capillary waves are largest in the direction perpendicular to the director. These results are in agreement with previous molecular dynamics simulations.     

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.     

Effect of high electric fields on the nematic to isotropic transition in a material exhibiting large negative dielectric anisotropy

We report the experimental high electric field phase diagram of a nematic liquid crystal which exhibits a large negative dielectric anisotropy. We measure simultaneously the birefringence (Δn) and the dielectric constant (epsilon_⊥) at various applied fields as functions of the local temperature of an aligned sample. We also measure the higher harmonics of the electrical response of the medium. The following experimental results are noted: (i) enhancement of orientational order parameter S in the nematic phase due to both the Kerr effect and quenching of director fluctuations; (ii) enhancement in the paranematic to nematic transition temperature (T_PN) with field; (iii) divergence of the order parameter susceptibility beyond the tricritical point as measured by third harmonic electrical signal; (iv) a small second harmonic electrical signal which also diverges near T_PN, indicating the presence of polarised domains. Our measurements show that ΔT_PN(= T_PN(E)-T_NI(0)) varies linearly with |E| whereas the Landau de Gennes theory predicts a dependence on E². It is argued that the quenching of director fluctuations by the field makes the dominant contribution to all the observations, including the thermodynamics of the transition.     

Interaction between disinclinations in nematic liquid crystals

The forces of interaction between disinclinations in nematic liquid crystals as well as between a disinclination and a wall are calculated on the basis of the elastic theory of Oseen and Frank under the assumption K₁₁ = K₃₃.     

Studies on binary mixtures of 4-pentyloxy-4′-cyanobiphenyl with three 4, 4′-di(alkoxy)azoxybenzenes

Eighteen binary mixtures of 4-pentyloxy-4′-cyanobiphenyl (5OCB) and 4, 4′-di(alkoxy)azoxybenzenes (nOAB) with n = 5, 6, and 7 at different concentrations have been studied in detail. Over a wide concentration range, induced SmA phase was observed in all the mixtures except in one. In most of the mixtures, the refractive indices no, ne, and Δn lie between the values of pure components. The optical birefringence of the mixtures is found to decrease non-additively with concentration. The molecular polarizability anisotropy and the orientational order parameter <P₂> of the mixtures were calculated. Nature of variation of polarizability anisotropy with concentration is similar to that of Δn. In allmixtures <P₂> is more in smectic phase than in nematic phase and it also shows non-additive behaviour. Observed <P₂> values of the mixtures were compared with McMillan’s and Maier-Saupe theoretical values and good agreement is found in some mixtures. The transition temperatures obtained by fitting <P₂> data to McMillan’s theory agree with the observed values within a few degrees. Ratio of elastic constants K₃₃ and K₁₁ is determined for mixtures having nematic phase and found to diverge at T_NA transition point.     

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.     

Fluctuation shift of the nematic–isotropic phase transition temperature

A macroscopic counterpart to the microscopic mechanism of the straightening dimer mesogens conformations, proposed recently by S.M. Saliti, M.G. Tamba, S.N. Sprunt, C. Welch, G.H. Mehl, A. Jakli, and J.T. Gleeson [Phys. Rev. Lett. 116, 217801 (2016)] to explain their experimental observation of the unprecedentedly large shift of the nematic–isotropic transition temperature is discussed. The proposed interpretation is based on singular longitudinal fluctuations of the nematic order parameter. Since these fluctuations are governed by the Goldstone director fluctuations, they exist only in the nematic state. External magnetic field suppresses the singular longitudinal fluctuations of the order parameter (similarly as is the case for the transverse director fluctuations, although with a different scaling over the magnetic field). The reduction of the fluctuations changes the equilibrium value of the magnitude of the order parameter in the nematic state. Therefore, it leads to additional (with respect to the mean field contribution) fluctuation shift of the nematic–isotropic transition temperature. Our mechanism works for any nematic liquid crystals, however the magnitude of the fluctuation shift increases with decrease in the Frank elastic moduli. Since some of these moduli supposed to be anomalously small for so-called bent-core or dimer nematic liquid crystals, just these liquid crystals are promising candidates for the observation of the predicted fluctuation shift of the phase transition temperature.     

Fluctuational spatial dispersion in achiral liquid crystals

An investigation is made of the spatial dispersion of the permittivity of achiral liquid crystals with large-scale fluctuations. It is observed that for large correlation lengths the terms with spatial dispersion are anomalously large. The specific form of these terms is obtained for orientational fluctuations in a nematic and fluctuations of the deformations of the smectic layers in a smectic-A in an orienting magnetic field. It is shown that these effects may be observed optically by means of accurate measurements of the angular dependence of the refractive indices of electromagnetic waves. Zh. éksp. Teor. Fiz. 114, 182–190 (July 1998)