Splay-bend Elastic Constant Research Articles

Experimental Study of Anchoring Characteristics and Splay-Bend Surface-Like Elasticity of Nematics with Using Non-Twisted Nematic Cells

Question of second-order terms in bulk elastic free energy functional for nematics is discussed and investigated experimentally. Under assumption that these surface-like terms contribute only to surface free energy functional, they were firstly substituted by boundary conditions. Several flat-parallel cells (of thickness from 1.9 µm to 31.2 µm) filled with 5CB nematics of planar initial orientation (induced by substrates covered with rubbed SE130 polyimide) were investigated in static electric fields by measurement of their optical transmittance influenced by planar deformation states. The splay and bend elastic constants and anchoring characteristics were determined from these experimental data. The polar anchoring for this nematics-substrate system can not be qualified uniquely as strong or weak. Simulated optical transmittance characteristics computed with using these parameters imitate results of experiment with good accuracy within measurement errors. It is demonstrated that precise determining of nematics-substrate coupling and nematics material parameters is sufficient for quantitative description of nematics deformations. Afterwards the values of components of the free energy of nematics layer corresponding to the bulk elastic deformation, bulk interaction with electric field, nematics interaction with boundary and splay-bend surface contribution are computed from experimental data in two cases which can be interpreted as weak and strong anchoring. The following comparison of them leads to conclusions on the negligible magnitude order of the splay-bend elastic constant.

Study of anchoring characteristics and splay-bend elastic constant based on experiments with non-twisted nematic liquid crystal cells

AbstractPossible influence of a nematics splay-bend elastic constant and corresponding free energy functional term on adequacy of description of nematics states is studied by comparing results of theoretical considerations and computer simulations with experimental data. Planar deformation states enforced in flat nematics cells by symmetric aligning cover coatings and external electric or magnetic fields are studied in one-dimensional approximation. Nematics material parameters and nematics-substrate coupling characteristics are determined from experimental data by immediate measurement or by solving inverse problems. Two series of cells with thicknesses between twenty and forty-four micrometers (in fact two wedge cells) with two different orienting substrates are investigated by measuring a cell optical response in a birefringence experimental system. Good agreement between optical retardation measured and simulated is observed. Posterior comparison of free energy contributions from substrate interactions and a hypothetical surface-like term leads to a conclusion that the last one together with a splay-bend elastic constant should be very small and can be neglected.

Pseudomolecular models for nematic liquid crystals

The limits of the pseudomolecular approach to evaluate the elastic properties of nematic liquid crystals are critically analyzed. We discuss the importance of the uniformly convergent series entering into this description. If these series are not uniformly convergent, the elastic constants evaluated in this manner are meaningless. A special kind of mixing of Maier-Saupe and Nehring-Saupe interaction laws is analyzed. We show that the splay-bend elastic constant has a nonmonotonic behavior with respect to the mixing factor. This result indicates that the subsurface deformations, if any, are not only due to the splay-bend term.

Measurement of the splay-bend elastic constant in lyotropic ferronematic liquid crystals: The influence of the bounding surfaces

We report the first experimental investigation devoted to analyze the influence of a ferrofluid on the surface properties of lyotropic liquid crystals doped with magnetic particles. By means of optical methods, the bulk orientation of the director vs the temperature is determined. The theoretical analysis shows that near the nematic–isotropic transition, the thermodynamical model for the temperature surface transition works reasonably well. On the contrary, in the low temperature region near the lamellar–nematic transition, important deviations from the theoretical behavior are observed. In order to interpret our experimental data, we propose a simple phenomenological extension of the thermodynamical model that takes into account the different contributions to the surface energy and of the residual lamellar order in the nematic phase. We show, furthermore, that the effective splay-bend elastic constant depends on the ferrofluid doping concentration, in agreement with a recently proposed theory.

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

Abstract The magnetic field-induced deformations of weakly anchored nematic layers in the presence of the non-zero splay-bend elastic constant K 13 are analysed by use of the Pergamenshchik approach. Most of the anomalous phenomena reported by other authors, that do not occur if k 13 = 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.

Surface fields and the splay-bend elastic constant.

We show that a surface field localized near the bounding surface over a mesoscopic length gives rise to a subsurface discontinuity. Our result is compared with a recent elastic theory in which the subsurface distortion is due to the splay-bend elastic constant. By means of our model, the interpretation of continuous surface variations of the average nematic orientation is given and compared with the elastic model.

Determination of the effective splay-bend elastic constant of a lyotropic nematic liquid crystal.

The effective splay-bend elastic constant ${\mathit{k}}_{13}$ is studied by means of an optical technique for a lyotropic nematic liquid crystal. The ratio between ${\mathit{k}}_{13}$ and the usual Frank elastic constant found in this experiment is positive and of the order of 1. This result agrees with the one obtained recently for thermotropic liquid crystals. \textcopyright{} 1996 The American Physical Society.

Subsurface deformations in nematic liquid crystals.

The existence of subsurface deformations in a nematic liquid crystal sample of finite thickness is considered from a molecular point of view. A lattice approximation is used to take into account the intermolecular interactions responsible for the nematic phase. The analysis shows that for the Maier-Saupe interaction law the director profile is a smooth function in the whole sample. In contrast, in the framework of our simple model, for the induced-dipole--induced-dipole interaction law the director profile presents a large subsurface deformation. The results of our calculation are compared with the elastic theories for nematic liquid crystals recently proposed. In particular it is shown that the intermolecular interactions responsible for the effective splay-bend elastic constant are the origin for the subsurface discontinuity in pretilted nematic liquid crystal samples. Our predictions are obviously limited by the applicability of the na\"{\i}ve model considered in the present analysis. \textcopyright{} 1996 The American Physical Society.

Surface Effects in Dynamics of Thermal Director Fluctuations

Abstract The two-time correlation function of the director fluctuations is calculated for a homeotropically aligned nematic cell in an external magnetic field. The anchoring strength, the splay-bend elastic constant are taken into account. An influence of the surface parameters on light-scattering data is discusses. It is shown, the ratio K 13/K 33 affect the frequency spectrum of the scattered light when the in-plane component of the scattering vector is equal to zero. A geometry of an experiment, that gives the frequency spectrum different from single Lorentzian, is offered.

On the validity of the elastic model for temperature induced surface transitions

Temperature induced surface alignment transitions in nematic liquid crystals are analysed by means of an elastic model in which the effective splay-bend surface-like elastic constant is taken into account. Experimental data in hybrid cells are analysed and the value of the effective splay-bend elastic constant is found to be in good agreement with that obtained in homogeneous samples for the same liquid crystal. The validity of the model is successfully checked on data from the literature, for such different temperature dependences as those of MBBA at the free surface and on two types of SiO x deposited surfaces, and for E7 on a fluoropolymeric surface, exhibiting a temperature induced surface alignment transition from planar to homeotropic.

Experimental determination of the effective splay-bend elastic constant.

Experimental determination of the effective splay-bend elastic constant.

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.

Distortions induced by the K13 surfacelike elastic term in a thin nematic liquid-crystal film.

We have investigated some of the consequences of the inclusion of a nonzero (and fairly large) ${\mathit{K}}_{13}$ term in the elastic free energy of a thin nematic liquid-crystal layer, where ${\mathit{K}}_{13}$ is the splay-bend elastic constant. A sufficiently thin film is predicted to deform spontaneously in zero applied field, for large enough values of ${\mathit{K}}_{13}$. This deformation breaks the mirror symmetry of the film around its midplane and disappears at a critical value of the applied field which is a function of sample thickness. In the particular case where the boundaries favor parallel anchoring, the midplane of the spontaneously deformed layer will contain a nonsingular \ensuremath{\pi} wall. The existence of this anomalous distortion mode leads to dramatic changes in the topology of the Fr\'eedericksz phase diagram: the onset of the Fr\'eedericksz transition is predicted to occur at the critical field for infinitely strong anchoring, and the distorted state eventually becomes unstable with respect to the undistorted configuration as the strength of the applied field is further increased. For small ${\mathit{K}}_{13}$ no spontaneously deformed state occurs and the critical field of the Fr\'eedericksz transition is merely found to be shifted from its value for ${\mathit{K}}_{13}$=0. The possibility of experimentally observing some of these effects is also briefly discussed.