Elastic Constants Of Liquid Crystals Research Articles

Dielectric and elastic properties of fluorine-containing tricyclic isothiocyanate liquid crystal

ABSTRACTThe dielectric and elastic properties of liquid crystals (LCs) generally depend on the molecule structure, such as polar group and carbon chain length. For further investigation of the influence of molecular structure on the dielectric and elastic properties of fluorine-containing tricyclic isothiocyanate LC, the experimental temperature was controlled at 25°C by precision hot stage, and a precision LCR meter was used to measure the capacitance of six LC cells under the voltage from 0.1 to 20 V at 1 kHz. An LC cell capacitance model and a dual-cell model were adopted to obtain the dielectric anisotropy, and the capacitance–voltage curves of six LC materials were plotted. The threshold voltage of Fréedericksz transition was analysed, and a finite difference iterative method was used to attain specific values of three elastic constants. The influence of molecular structure on the dielectric and elastic constants was finally analysed. Experimental results showed that the introduction of meta-difluoro group would increase the dielectric anisotropy and reduce the threshold voltage of LC. As the length of the alkyl carbon chain increased, the dielectric anisotropy would have an odd–even alternation effect, which would lead to changes in the elastic constants of LC.

Accurate measurement of the twist elastic constant of liquid crystal by using capacitance method

ABSTRACTIn this study, the twist elastic constant (k22) of liquid crystals (LCs) was accurately measured using capacitance method. The constant can be obtained on the basis of accurate measurement of other LC parameters, such as parallel and vertical dielectric constants (ε// and ε⊥), splay and bend elastic constants (k11 and k33), and rotational viscosity coefficient (γ1). First, by using dual-cell capacitance method and an LC cell capacitance model to measure ε// and ε⊥, k11 and k33 can be obtained from the threshold voltage determined from the voltage–capacitance curve of the parallel-aligned nematic LC layer and the comparison between the experimental and theoretical results based on the Frank elastic theory, respectively. In addition, γ1 can be obtained from the measurement of the dynamic response in the parallel-aligned nematic cell. Finally, k22 can be accurately determined using the threshold voltage of the twisted nematic LC cell. By adopting the above method, the measured k22 for LC E7 was 6.7 × 10−12 N. The proposed method is more rigorous and yields a more accurate measurement result than the other methods reported in the literature.

Effect of elastic constants of liquid crystals in their electro-optical properties

Recently following the success of the density functional theory (DFT) in obtaining the structure and thermodynamics of homogeneous and inhomogeneous classical systems such as simple fluids, dipolar fluid and binary hard spheres, this theory was also applied to obtain the density profile of a molecular fluid in between hard planar walls by Kalpaxis and Rickayzen. In the theory of molecular fluids, the direct correlation function (DCF) can be used to calculate the equation of state, free energy, phase transition, elastic constants, etc. It is well known that the hard core molecular models play an important role in understanding complex liquids such as liquid crystals. In this paper, a classical fluid of nonspherical molecules is studied. The required homogeneous (DCF) is obtained by solving Orenstein–Zernike (OZ) integral equation numerically. Some of the molecules in the liquid crystals have a sphere shape and this kind of molecular fluid is considered here. The DCF sphere of the molecular fluid is calculated and it will be shown that the results are in good agreement with the pervious works and the results of computer simulation. Finally the electro-optical properties of ellipsoid liquid crystal using DCF of these molecules are calculated.

Structure, elasticity and phase transitions in liquid crystals with deformations

ABSTRACTA 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.

Transient flickering behavior in fringe-field switching liquid crystal mode analyzed by positional asymmetric flexoelectric dynamics.

We analyzed a transient blinking phenomenon in a fringe-field switching liquid crystal (LC) mode that occurred at the moment of frame change even in the optimized DC offset condition for minimum image flicker. Based on the positional dynamic behaviors of LCs by using a high-speed camera, we found that the transient blink is highly related to the asymmetric responses of the splay-bend transitions caused by the flexoelectric (FE) effect. To remove the transient blink, the elastic property adjustment of LCs was an effective solution because the FE switching dynamics between the splay-enhanced and bend-enhanced deformations are highly dependent on the elastic constants of LCs, which is the cause of momentary brightness drop.

Effects of carbon nanotubes on electro-optic characteristics in vertically aligned liquid crystal display

Size- and aggregation-controlled dispersion of thin multiwalled carbon nanotube (t-MWCNT) in negative dielectric anisotropic liquid crystal (LC) material exhibits remarkable improvement in electro-optic response time in vertically aligned LC cells. The physical properties such as birefringence, dielectric anisotropy and clearing temperature of nanotube dispersed LC material appear to be almost invariant to that of pristine LC. Nevertheless, the response time shows noticeable improvement, especially in decaying time associated with transition from maximum to minimum transmission, hence important for faster switching LC devices. The effect is attributed to that vertically aligned t-MWCNTs along the field direction play role of vertical alignment layer between LCs, consequently resulting in increased bend elastic constant of LCs.

Monte Carlo simulations of biaxial structure in thin hybrid nematic film based upon spatially anisotropic pair potential

Hybrid nematic films have been studied by Monte Carlo simulations using a lattice spin model, in which the pair potential is spatially anisotropic and dependent on elastic constants of liquid crystals. We confirm in the thin hybrid nematic film the existence of a biaxially nonbent structure and the structure transition from the biaxial to the bent-director structure, which is similar to the result obtained using the Lebwohl–Lasher model. However, the step-like director's profile, characteristic for the biaxial structure, is spatially asymmetric in the film because the pair potential leads to K1 ≠ K3. We estimate the upper cell thickness to be 69 spin layers, in which the biaxial structure can be found.

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.

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 K 13 . 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.

Monte Carlo simulations of intrinsic anchoring in nematic liquid crystals based on spatially anisotropic pair potential

The free surfaces of nematic liquid crystals are studied based upon the molecular pair potential model, which is spatially anisotropic and dependent on elastic constants of liquid crystals. The study is based on the simple cubic lattice model with the aid of Monte Carlo simulation. An elastic deformation is imposed, forming a hybrid cell-like nematic sample so that the anchoring at free nematic interfaces (intrinsic anchoring) is well studied. It is found that the preferred orientation at the free interface and the corresponding extrapolation length change with the modification of potential parameters, but are not dependent on temperature.

Molecular theory of elastic constants of liquid crystals. III. Application to smectic phases with tilted orientational order.

Using the density-functional formalism we derive an expression for the distortion free energy of systems with continuous broken symmetry and use it to derive an expression for the elastic constants of smectic phases in which the director is tilted with respect to the smectic layer normal. As in the previous papers of this series [Y. Singh, S. Singh, and K. Rajesh, Phys. Rev. A 45, 974 (1992); Y. Singh, K. Rajesh, V. J. Menon, and S. Singh, Phys. Rev. E 49, 501 (1994)], the expressions for the elastic constants are written in terms of order and structural parameters. The structural parameters involve the generalized spherical harmonic coefficients of the direct pair correlation function of an effective isotropic liquid. The density of this effective isotropic liquid depends on the nature and amount of ordering present in the system and is evaluated self-consistently. We estimate the value of elastic constants using reasonable guesses for the order and structural parameters.

A Method for Determining Elastic Constants of Nematic Liquid Crystals at High Electric Fields

The elastic constants of liquid crystals are very important parameters for physical studies of liquid crystals and for liquid crystal displays. In this paper, a new method of determine the elastic constant ratio K11/K33 and the elastic constant K11 of nematic liquid crystals by measurement of their optical retardation and capacitance at high electric fields is proposed. We derive theoretical formulas for the elastic constants, and then set up an optical retardation and capacitance measurement system. Finally, the experimental results for two commonly used liquid crystal compounds are discussed.

Statistical theory of elastic constants of biaxial nematic liquid crystals

Microscopic expressions for the elastic constants of liquid crystals composed of biaxial or uniaxial molecules are derived in the case of a weak anchoring, small distortions, and a small density. Both biaxial and uniaxial phases are considered. The expressions involve the one-particle distribution function and the potential energy of two-body short-range interactions. The theory was used to calculate the temperature dependence of the elastic constants for a system of rigid molecules similar to elipsoids with three different axes.

Molecular theory of elastic constants of liquid crystals. II. Application to the biaxial nematic phase.

The expression of distortion free energy derived in our earlier paper [Phys. Rev. A 45, 974 (1992)] is used to derive expressions for the 12 elastic constants of a biaxial nematic phase. These expressions 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, the density of which is determined using a criterion of the weighted density-functional formalism. Using a reasonable guess for the values of the order and structural parameters we estimate the relative magnitudes of these constants. The values of three constants, which are associated with the deformations confined to a plane perpendicular to the principal director N Λ , are (three or four) orders of magnitude smaller than the other constants. Two of the three mixed modes which arise because of biaxial ordering and vanish in the uniaxial phase are also about one order of magnitude smaller than other constants. In going from the uniaxial to the biaxial phase each constant associated with splay, twist, and bend splits into two and a mixed mode which in the uniaxial phase is just equal to the difference of splay and twist becomes a new constant. It is shown that the contributions to elastic constants arising from biaxial ordering and the departure from the axial molecular symmetry are small.

Structural defects in smectic c* liquid crystals

In this paper the structure of a smectic c* liquid crystalline material which can be switched in an electric field is investigated by electron microscopic techniques. Using this method the director field is revealed and typical disclinations observed. Analysis of these features enables the elastic anisotropy of the material to be calculated. Sample description. For our structure investigations a liquid crystalline material (4-(3-(s)-methyl-2-(s)-chloropentanoyloxy)-4'-octyloxy-biphenyl) with two chiral centres was synthesised using known procedures [I]. This material has been investigated by broadband dielectric spectroscopy, the softand Goldstone modes were analysed [2a] as well as the high frequency rotation of the molecules around their long axis [2b]. The structural formula is : * * C~HS-~H-CH-C-)-~(CH~)7-~H3 I CH~ Cl O c322KSi 328KSt338Ki The transition temperatures as determined by D.S.C. measurement and dielectric spectros3U K ~ 3~8 K 338 K copy are crystalline S~ phase, Sf -SA phase and St isotropic. Sample preparation. The sample was pressed between two glass plates coated with polyimide and separated by 10 ~m (ITO cells supplied by E.H.C.CO., LTD. of Japan). It was heated into tile isotropic region in order to erase the structures due to the previous tllennal and mechanical history and then cooled into the Sf phase. Subsequently a d.c. electric field was applied perpendicular to the glass plates. It was established by polarising light microscopy that switching the d.c. field caused bright-dark reversal (Figs. lc, 16). 346 JOURNAL DE PHYSIQUE II N° 3 a) b) c) Fig. I. Light micrographs showing effect of electric field on sample (a) E = 0, (b) E up, (c) E down. The sample was not unifornlly oriented and contained many defects. On cooling to room temperature, dark stripes with a pitch of about 10 ~m appeared within the domains which were of focal conic nature (Fig. lc). The domain size was in the millimetre region. Electron microscopy was chosen as the method of investigation because it offers the unique advantage of revealing details about the microstructure. In order to obtain information about the smectic phase, the cell was quenched very rapidly from 325 K to room temperature and opened, leaving material on both glass plates. The liquid crystalline sample had solidified, and the intemal structure was revealed by a special ion etching technique. The freshly exposed surface was tllen shadowed and a direct replica produced. Experimental results. ELECTRON MICROSCOPY. In order to obtain samples suitable for electron microscopy two different routes are possible ; (a) high resolution phase contrast techniques and (b) surface replication methods. In method (a) tile smectic planes or individual molecules are imaged directly. We have described this method in several publications [3-6]. Method (b) has tile disadvantage of lower resolution and therefore not revealing individual molecules. However, the light microscopic results indicated that the defects are rather large scale, therefore method (b) seemed more appropriate. The sample was cooled from the isotropic into the smectic c* phase and rapidly quenched. In order to reveal tile structure beneath the surface of the bulk sample, the surface was etched by a special ion etching technique using oxygen ions and subsequently coated in a perpendicular direction with carbon and at an appropriate oblique angle with pt/C. The replica was then prepared for electron microscopy using standard methods [7]. Using this technique a number of specific disdination structures were revealed, as indicated in figures 2-6. It is well established that the disclination structure can be used to calculate the elastic constants of liquid crystals [8, 9]. In order to understand the principles which make it possible to understand these electron micrographs, it is necessary to analyse these defects and to recall some basic concepts about ferroelectric liquid crystals. This is done in the following discussion. N° 3 STRUCTURAL DEFECTS IN SMECTIC c* LIQUID CRYSTALS 347

Molecular theory of elastic constants of liquid crystals: Application to uniaxial phases.

We use density-functional theory to derive an expression for the distortion free energy of molecular ordered phases and expand it in terms of the order parameters characterizing the structure of the phase and the molecular correlation function of an effective isotropic liquid. We derive expressions for the elastic constants of the uniaxial nematic and smectic-A phases of the liquid crystals and express the results in terms of the spherical-harmonic coefficients of the direct pair-correlation function of the effective isotropic liquid. These harmonic coefficients are obtained by solving the Ornstein-Zernike equation using the Percus-Yevick closure relation for a hard-core system and using a perturbation method for a model system interacting via a pair potential that has angle-dependent attractive parts in addition to hard-core repulsion. It is shown that the repulsive part of the pair interaction makes a dominant contribution to the elastic constants of the liquid crystals.

On the Curvature Elasticity Theory of Fluid Membranes

Based on the Oseen-Frank-Nehring-Saupe theory of uniaxial liquid crystals, we give in this report a revised approach that the bending rigidity k, the elastic modulus of Gaussian curvature k and the spontaneous curvature c 0 may be expressed in terms of the various elastic constants of liquid crystals by k=(k 11 -2k 13 )d, k=(2k 13 -k 22 -k 24 )d and c 0 =k 11 S 0 /(k 11 -2k 13 )d respectively

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

Abstract 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/K 22 (A is the surface anchoring and K 22 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.

A new torsion pendulum technique to measure the twist elastic constant of liquid crystals

A new experimental method to measure the twist elastic constant of nematic liquid crystals is proposed. The method is based on a direct measurement of the torque which the nematic liquid crystal exerts on the surfaces when a magnetic field is applied. The reliability of this technique is tested by measuring the twist elastic constant of the nematic liquid crystal 4-n-pentyl-4'-cyanobiphenyl (5CB). The experimental results are compared with previous measurements performed by other authors Technique basee sur une mesure directe du couple exerce par le directeur sur les surfaces quand le nematique est soumis a un champ magnetique. Application a la mesure de K 22 du pentyl-4 cyano-4' biphenyle

Determination of the elastic constants of liquid crystals from the intensities of infrared absorption bands

Determination of the elastic constants of liquid crystals from the intensities of infrared absorption bands