Constants Of Nematic Liquid Crystals Research Articles

On the elusive saddle-splay and splay-bend elastic constants of nematic liquid crystals.

The elastic behavior of nematics is commonly described in terms of the three so-called bulk deformation modes, i.e., splay, twist, and bend. However, the elastic free energy contains also other terms, often denoted as saddle-splay and splay-bend, which contribute, for instance, in confined systems. The role of such terms is controversial, partly because of the difficulty of their experimental determination. The saddle-splay (K24) and splay-bend (K13) elastic constants remain elusive also for theories; indeed, even the possibility of obtaining unambiguous microscopic expressions for these quantities has been questioned. Here, within the framework of Onsager theory with Parsons-Lee correction, we obtain microscopic estimates of the deformation free energy density of hard rod nematics in the presence of different director deformations. In the limit of a slowly changing director, these are directly compared with the macroscopic elastic free energy density. Within the same framework, we derive also closed microscopic expressions for all elastic coefficients of rodlike nematics. We find that the saddle-splay constant K24 is larger than both K11 and K22 over a wide range of particle lengths and densities. Moreover, the K13 contribution comes out to be crucial for the consistency of the results obtained from the analysis of the microscopic deformation free energy density calculated for variants of the splay deformation.

Contribution of Multiwalled carbon nanotubes to dielectric and elastic properties in E7 nematic liquid crystal

In this article, electrical parameters, and elastic constants of nematic liquid crystal (NLC) contributed multiwalled carbon nanotubes (MCN) are presented by dielectric spectroscopy method. The effects of reorientation on the nematic liquid crystal by doping of multi-walled carbon nanotubes were investigated to reveal. Analyzes of dielectric strength Δε′(ω), absorption coefficient α, relaxation time τ, dielectric anisotropy Δε′V, dielectric anisotropy ratio γ, splay elastic constant K11, and cross-over angular frequency ωco of MCN contribution to E7 nematic liquid crystal with DC supply voltage are presented. Reorientation of elastic dipolar liquid crystal molecules was demonstrated by reducing the positive type (p type) dielectric anisotropy value in the broadband angular frequency range with the MCN contribution to the E7 coded nematic liquid crystal. The supply voltage applied to the NLC samples was observed to have nearly Debye-type relaxation mechanism in the host E7 LC structure, tending to switch to a Debye-type relaxation mechanism by MCN doping. Dipole effects were enhanced by doping of multi-walled carbon nanotubes in the orientation of elastic NLC molecules, and the relaxation time of host E7 NLC and doped MCN/E7 NLC decreased with increasing bias voltages. Cole-Cole analysis with different supply voltages, it has been seen that it turns into a new equivalent circuit depending on the MCN contribution.

Impact of ferroelectric nanoparticles on the dielectric constant of nematic liquid crystals

ABSTRACT The influence of ferroelectric BaTiO3 nanoparticles on the dielectric constant in the isotropic phase of the isotropic-nematic phase transition is studied within Landau phenomenological theory. The ferroelectric BaTiO3 nanoparticles dependence of transition temperature and dielectric constant in the isotropic phase is calculated. We compare our theoretical results with experimental data available in the literature.

Highly improved dielectric behaviour of ferronematic nanocomposite for display application

ABSTRACTWe report the investigation of influence of nickel zinc ferrite magnetic nanoparticles (NZFO (Ni0.5Zn0.5Fe2O4)) on phase transition, optical and dielectric properties in a nematic liquid crystal (NLC). The interaction of NZFO nanoparticles with NLC was confirmed by the formation of ferronematic droplets due to the transfer of magnetic orientational effect onto the underlying NLC matrix. The doping results in shift of nematic to isotropic transition to low-temperature region. An enhancement in the value of refractive index is observed in the nematic region after the addition of NZFO nanoparticles. The dielectric constant of NLC was remarkably enhanced by 10 times after doping, which is found to be maximum at 0.1 wt% concentration of NZFO nanoparticles. The decrease in the value of dissipation factor in low-frequency region shows that the magnetic nanoparticles are able to trap ionic impurities effectively. The obtained results suggest that the optimum amount of doping concentration is 0.1 wt% of NZFO nanoparticles in NLC due to high dielectric constant with low dissipation factor and high refractive index with high dispersive power at room temperature.

Large Electro‐Optic Kerr Effect in Ionic Liquid Crystals: Connecting Features of Liquid Crystals and Polyelectrolytes

The electro-optic Kerr effect in simple dipolar fluids such as nitrobenzene has been widely applied in electro-optical phase modulators and light shutters. In 2005, the discovery of the large Kerr effect in liquid-crystalline blue phases (Y. Hisakado et al., Adv. Mater. 2005, 17, 96-98.) gave new directions to the search for advanced Kerr effect materials. Even though the Kerr effect is present in all transparent and optically isotropic media, it is well known that the effect can be anomalously large in complex fluids, namely in the isotropic phase of liquid crystals or in polyelectrolyte solutions. Herein, it is shown that the Kerr effect in the isotropic phase of ionic liquid crystals combines the effective counterion polarization mechanism found in polyelectrolytes and the unique pretransitional growth of the Kerr constant found in the isotropic phase of nematic liquid crystals. Maximum Kerr constants in the order of several 10-11 m V-2 (ten times higher than the Kerr constant of the toxic nitrobenzene and less temperature sensitive than Kerr constants of nematic liquid crystals) make ionic liquid crystals attractive as new class of functional materials in low-speed Kerr effect applications.

All-optical measurement of elastic constants in nematic liquid crystals.

In this article we present a new all-optical method to measure elastic constants connected with twist and bend deformations. The method is based on the optical Freedericksz threshold effect induced by the linearly polarized electro-magnetic wave. In the experiment elastic constants are measured of commonly used liquid crystals 6CHBT and E7 and two new nematic mixtures with low birefringence. The proposed method is neither very sensitive on the variation of cell thickness, beam waist or the power of a light beam nor does it need any special design of a liquid crystal cell. The experimental results are in good agreement with the values obtain by other methods based on an electro-optical effect.

Measuring liquid crystal elastic constants with free energy perturbations.

A first principles method is proposed to calculate the Frank elastic constants of nematic liquid crystals. These include the constants corresponding to standard splay, twist and bend deformations, and an often-ignored surface-like contribution known as saddle-splay. The proposed approach is implemented on the widely studied Gay-Berne (3, 5, 2, 1) model [J. G. Gay and B. J. Berne, J. Chem. Phys., 1981, 74, 3316], and the effects of temperature and system size on the elastic constants are examined in the nematic phase. The results of simulations for splay, twist, and bend elastic constants are consistent with those from previous literature reports. The method is subsequently applied to the saddle-splay elastic constant k24 which is found to exist at the limits of the Ericksen inequalities governing positive definite free energy. Finally, extensions of the method are discussed that present a new paradigm for in silico measurements of elastic constants.

Pseudo-molecular approach for the elastic constants of nematic liquid crystals interacting via anisotropic dispersion forces

Abstract The bulk and the surface-like elastic constants of a nematic liquid crystal are calculated for an ensemble of particles interacting via anisotropic dispersion forces using the pseudo-molecular method. The geometrical anisotropy of the molecules is also taken into account in the calculations by choosing a molecular volume of ellipsoidal shape. Analytical expressions for the elastic constants are obtained as a function of the eccentricity in the molecular volume shape. The method allows one to explore the dependence on the molecular orientation with respect to the intermolecular vector by analyzing the magnitude and the behaviour of macroscopic elastic parameters defining the nematic phase.

All-optical measurements of elastic constants in nematic liquid crystals

Reorientation of liquid crystals induced by light is used as a method to measure elastic constants. Especially this all-optical method can determine constant connected with twist deformation, which is not easy in conventionally known methods. Experimental results show very good accuracy in comparison with other methods. Full Text: PDF

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

AbstractA 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.

Determination of Temperature Dependence of Kerr Constant for Nematic Liquid Crystal

Nematic liquid crystals are the preferred materials for linear and nonlinear optics, where frequently required photosensitivity is provided by appropriate doping. This investigationis concerned with the determination of the Kerr constant of nematic liquid crystal (9CHBT). The temperature dependence of the Kerr constant B for azo dye doped nematic liquid crystalshas been studied. The sample has a positive Kerr constant which increases with decreasing of temperature. The linear dependence of the Kerr constant on (T – T*)−1is found to be ingood agreement with the predications of the Landau-de Gennes model.

Composite Method for Measurement of Splay, Twist and Bend Nematic Elastic Constants by Use of Single Special In-Plane-Switched Cell

A method for quick and pretty accurate measurements of splay, twist and bend elastic constants of nematic liquid crystals is proposed. The main concept relies on exploiting only electric field in a plane-parallel liquid crystal cell of special configuration with thin transparent comb-like electrodes on one cover and usual transparent plane electrode on the other. Rubbing in direction parallel to comb electrode stripes enforces homogeneous planar or homeotropic orientation of nematic molecules. Fréedericksz’ transition of pure splay, twist or bend form is initialised by applying voltage between the electrodes appropriately. The method was tested with three different comb-like electrode configurations and three nematics: 4-pentyl-4′-cyanobiphenyl, 4-trans-4′-n-hexyl-cyclohexyl-isothiocyanatobenzene and Demus’ esters.

Effect of direct correlation functions on elastic constants of molecular liquids

We study the effect of molecule sizes and intermolecular interactions on Frank elastic constants in nematic liquid crystals with ellipsoid of revolution molecules. We use the Poniewierski-Stecki equations which depend on direct correlation functions of ellipsoid molecules and apply the new direct correlation function using the Marko method and contact distance of ellipsoids. The elastic constants for different molecular elongations, using repulsive interaction of hard ellipsoids of revolution and attractive dispersion interaction are calculated. These elastic constants are deduced from a new direct correlation function. It is shown that they are in good agreement with Singh and singh results and qualitatively corresponds to the experiments. The ratios of calculated elastic constants are in agreement with the available experimental results.

Models for ionic contribution to the complex dielectric constant of nematic liquid crystals

We analyze the models that account the ionic contribution to the complex dielectric constant of a nematic liquid crystal. We compare the predictions of the model of [Sawada, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 318, 225 (1998)] based on the assumption that the electric field in the liquid coincides with the applied one, with the model of Macdonald where the electric field in the sample is determined in self-consistent manner by solving the equation of Poisson. We show that the model of Sawada , widely used to determine the bulk density of ions and their diffusion coefficient in liquid crystal cells, predicts a thickness dependence of the real and imaginary parts of the dielectric constant different from that predicted by the model of Macdonald. On the contrary, the predictions of the two models coincide for what concerns the frequency dependencies of the two components of the dielectric constant. By considering a typical case, we show that the numerical values of the ionic properties derived by means of the model of Sawada may differ even more than 1 order of magnitude by those predicted by the model of Macdonald. A rescaling procedure allowing to evaluate the bulk density of ions and the ionic diffusion coefficient determined by means of the model of Sawada in agreement with the one of Macdonald is proposed.

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

AbstractDeformations 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.

Local affine-connection approach to the elastic constants of nematic liquid crystals

In this paper, the affine connection approach [D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986)] will be defined in terms of a local transformation. Accordingly, the macroscopic anisotropy of the nematic medium will be conceived as resulting from a local transformation where, at each point of the sample, the spherical molecules of an idealized hypothetic isotropic liquid have their shape changed to the ellipsoidal form of the nematic liquid crystals molecules. When such local character is imposed to this transformation, the patterns determined by the director configuration of the nematic medium acquire an intrinsic curvature whose correct treatment requires the replacement of the techniques and methods of the usual calculus by those of the differential geometry of nonflat surfaces. Such an approach will be used in the calculus of the nematic elastic constants. As a result, the dependence of the elastic constants on the scalar order parameter, on the eccentricity of the nematic molecules, and on the interaction between them will be determined and compared with the experimental data of the 4-methoxybenzylidene-4-n-butylaniline.

Determination of the elastic constants of nematic liquid crystals by means of the affine transformation model

In this paper the affine connection approach will be used to calculate the elastic constants of nematic liquid crystals. Following this approach, which was originally conceived to compute the nematic viscosity coefficients, an expression for the elastic constants, without adjustable free parameters, will be formulated in terms of a temperature dependent metric, whose non‐isotropic part is proportional to the tensorial order parameter of the nematic phase. The dependence of the elastic constants on the scalar order parameter, in the geometry of the nematic molecules, and in the anisotropic part of the molecular interaction, will be determined.

Measurement of the twist elastic constant of nematic liquid crystals using pi-cell devices

We present a fast and accurate method for measurement of the twist elastic constant of nematic liquid crystals using pi-cell devices. We observe that there are two bifurcations during the transition from the bend state to the planar 180° twisted state, each of which leads to a voltage threshold. The Fréedericksz threshold voltage due to a tilt bifurcation occurs at a lower voltage and is “softened” by the required surface pretilt in the device. The higher of the two thresholds is due to a bifurcation between left- and right-handed 180° twisted states and we term this the T to V state threshold. This voltage threshold is independent of device thickness, and is not softened by the pretilt. We show that the T to V state threshold is highly sensitive to changes in the twist elastic constant, K22, and use this threshold to evaluate the magnitude of K22 for a variety of materials. These results show very good agreement with those obtained using the standard magnetic Fréedericksz twist threshold experiment. This method does not require a complex experimental setup and has an accuracy of better than ±8%.

Elastic constants of nematic liquid crystals of uniaxial symmetry

We study, in detail, the influence of molecular interactions on the Frank elastic constants ofuniaxial nematic liquid crystals composed of molecules of cylindrical symmetry. This workis based on a weighted density functional formalism developed by us in a previous paper(Singh et al 1992 Phys. Rev. A 30 583). A brief summary of the status of theoreticaldevelopment for the elastic constants of nematics is presented. Considering a pair potentialhaving both repulsive and attractive parts, numerical calculations are reported for threenematics: MBBA, PAA and 8OCB. For these systems the length-to-width ratiox0 is estimated from the experimentally determined structure of the molecules. The repulsiveinteraction is represented by a repulsion between hard ellipsoids of revolution (HER) andthe attractive potential is represented by the quadrupole and dispersion interactions. Fromthe numerical results we observe that in the density range of nematics the contributions ofthe quadrupole and dispersion interactions are small as compared to the repulsiveHER interaction. The inclusion of attractive interactions reduces the values ofelastic constant ratios. The absolute values of elastic constants are sensitive tothe values of potential parameters. The elastic constants and their ratios are inagreement with the experimental and computer simulation values. The temperaturevariation of elastic constants and their ratios are reported and compared withthe experimental values. It is found that the calculated values are in agreementwith the experimental data. The twist elastic constant has a weak temperaturedependence but a pronounced influence is found on the bend elastic constants.

Method for Determining Material Constants of Nematic Liquid Crystals by Use of Wedge Cells

A wedge cell of the wedge angle of order of few milliradians was used to measure the phase shift between ordinary and extraordinary rays of transmitted light, for the Fréedericksz transition induced by a magnetic or an electric field. A nematic liquid crystal, PCB, filling the cell, was of the planar alignment enforced by the treatment of the flat boundary plates. A polyimide, MK8–poly (amic acid), was used as aligning substance. A system of interference fringes appeared in the cell placed in normally incident light between the analyser and the polariser crossed. In the neighbourhood of each fringe the cell can be considered as a flat-parallel one and hence it is equivalent to a system of flat cells of different precisely determined thickness. The dependence of the phase shift on applied external fields was measured for several interference fringes. The nematic liquid crystal material parameters (the splay and bend elastic constants, the anisotropy of diamagnetic susceptibility and the boundary tilt angle as a function of the torque) were determined by fitting the calculated characteristics to the measured ones.