Saddle-splay Elastic Constant Research Articles

Influence of planar anchoring on escaped-twisted configurations of liquid crystals in a cylindrical cavity

ABSTRACT Lyotropic chromonic liquid crystals (LCLCs) confined in cylindrical cavity can form an escaped-twisted (ET) configuration, resulting from the saddle-splay elastic constant is great much than twist elastic constant. The thermotropic liquid crystal 5CB does not meet the conditions for the formation of ET configuration, but it can be achieved under the appropriate planar anchoring and the action of chiral dopant. The equilibrium configuration of nematic liquid crystals confined in cylindrical cavities with azimuthal and axial surface anchoring conditions respectively is studied by the elastic continuum theory and the difference iterative method. We obtain the analytical solution of the distribution of the director without chiral dopant and the numerical solution of the chiral dopant. We find that the planar anchoring, the saddle-splay elastic constant and the chirality determine whether an ET configuration is formed. Furthermore, the cavity radius and the bend elastic constant can affect the value of twist angle. It provides a good theoretical basis for the determination of anchoring energy and saddle-splay elastic constant.

Flexoelectric effects on escaped twisted configurations of nematic liquid crystal 5CB with chiral dopants in a cylindrical cavity

ABSTRACT In a cylindrical cavity with a degenerate planar anchoring, the lyotropic chromonic nematic liquid crystals without intrinsic chirality tend to exhibit an escaped twisted configuration for the large saddle-splay-to-twist elastic modulus ratio, which is not found in most thermotropic liquid crystals. In this work, we consider thermotropic nematic liquid crystal 5CB with a chiral dopant confined in a cylindrical cavity with a degenerate planar anchoring. Based on the elastic theory of liquid crystal and the variation method, Euler equation and boundary conditions are obtained. The numerical results show that the director of 5CB forms an escaped twisted configuration, and the twist angle is influenced by the chiral parameter and the saddle-splay elastic constant. Under an axial electric field, the dielectric effect and the flexoelectric effect affect the LC director distribution. The single flexoelectric coefficient e 1 has a large radial orientation effect on the director. The results provide a clearer understanding of the director configuration in the cylindrical cavity under the electric field and a theoretical basis for the measurement of the flexoelectric coefficients.

Multiple Twisted Chiral Nematic Structures in Cylindrical Confinement

In this article, we theoretically and numerically study the chirality and saddle-splay elastic constant ( K 24 ) -enabled stability of multiple twist-like nematic liquid crystal (LC) structures in cylindrical confinement. We focus on the so-called radially z-twisted (RZT) and radially twisted (RT) configurations, which simultaneously exhibit twists in different spatial directions. We express the free energies of the structures in terms of dimensionless wave vectors, which characterise the structures and play the roles of order parameters. The impact of different confinement anchoring conditions is explored. A simple Landau-type analysis provides an insight into how different model parameters influence the stability of structures. We determine conditions for which the structures are stable in chiral and also nonchiral LCs. In particular, we find that the RZT structure could exhibit macroscopic chirality inversion upon varying the relevant parameters. This phenomenon could be exploited for the measurement of K 24 .

Orientation instability of the layer of a nematic liquid crystal

The origin of periodic structures in a layer of a lyotropic nematic liquid crystal observed in the director (vector, describing the anisotropic properties of the medium) reorientation experiment is studied. Such perturbations with the wavevector perpendicular to the initial orientation can develop in a liquid crystal layer in the unstable equilibrium state when the director is parallel to the walls under the condition that its orthogonality to the boundary corresponds to the minimum anchoring energy. It is shown that the linear dependence of the domain period on the layer thickness observed experimentally can be theoretically described when the Frank orientation elasticity energy is considered in the most general form taking the divergence terms into account and the anchoring energy of orientation is small as compared with the bulk energy. A relation between the coefficient of the divergence terms (saddlesplay elastic constant) and two other coefficients in the Frank energy is obtained.

Saddle-splay-term-induced orientational instability in nematic-liquid-crystal cells and director fluctuations at substrates.

We analyze stability of the planar orientational structure in a nematic-liquid-crystal cell with planar anchoring conditions at both substrates. Specifically, we study the instabilities of the ground state caused by surface elasticity with the saddle-splay elastic constant K24 violating the Ericksen inequalities. We express the surface part of static correlation functions as a functional integral over the fluctuation field induced by director fluctuations at confining walls and derive the stability conditions for the planar structure with respect to the fluctuation modes characterized by the in-plane wave numbers and by the parity. These conditions are analyzed in the cell thickness-fluctuation wavelength plane through the parametrization for the boundary curve of the instability region. For relatively small K24, the fluctuation mode of the critical wavelength is found to render the structure unstable when the thickness of the cell is below its critical value. The parity of the critical mode changes as the twist-splay ratio K(2)/K(1) is passing through unity. Further increase of K24 beyond the second threshold value, 4K(1)K(2)/(K1+K2), leads to the instability with respect to short wavelength fluctuations regardless of the cell thickness. We compute the critical thickness and the critical wavelength as a function of K24, the twist-splay ratio, and the azimuthal anchoring strength.

Spontaneous periodic distortions in nematic liquid crystals: dependence on the tilt angle.

The possibility of spontaneous periodic distortions, depending on the tilt angle in a nematic liquid crystal sample, is investigated by means of a general formulation of the stability problem. It is shown that due to the presence of a surfacelike term in the free-energy density, the uniform pattern can be destabilized, giving rise to a periodic distortion of the director. Our analysis establishes, in general terms, the conditions for the formation of stable periodic structures in nematic samples. In particular, we determine the wavelengths for which the periodic distortion exists by investigating its dependence on the tilt angle, characterizing the uniform pattern, and on the saddle-splay elastic constant. The effect considered in our paper is a finite size effect, related to the slab geometry of the nematic sample under consideration.

Axially twisted chiral nematic structures in cylindrical cavities

Here we report a theoretical study of chiral nematic liquid crystals, confined to cylindrical cavities with planar anchoring conditions. Three different model structures are considered: radially twisted, eccentric radially twisted, and axially twisted structure. The Frank-Oseen free energy with additional surface energy terms is used to find nematic director fields and free energies of the structures in different ranges of material parameters. We are particularly interested in the influence of chirality, anchoring strength, and the saddle-splay elastic constant on the stability regions of the described structures. For low chiralities the radially twisted structure is stable, while for high chiralities the axially twisted structure is stable. The stability region of the eccentric radially twisted structure is confined to a limited intervals of anchoring strengths and chiralities. Most of our attention is devoted to details of the axially twisted structure. In the high chirality limit the axially twisted structure resembles a simpler model structure which in our previous work we called an asymmetric conical structure. The tilt of the nematic director of the axially twisted structure out of the plane perpendicular to the cylinder axis is small except in the layer at the cylinder boundary. Polarization microscopy simulations of the three structures are also shown.

Chiral nematic liquid crystals in cylindrical cavities.

We report a theoretical study of various structures of chiral nematic liquid crystals, confined to submicrometer cylindrical cavities with tangential anchoring conditions. The Frank-Oseen free energy with additional surface energy terms is used to find nematic director fields, free energies, and stability diagrams of relevant structures. The dependence of various chiral nematic structures on the chirality parameter, pore size, elastic constants, and polar and azimuthal surface anchoring strengths is studied. We are particularly interested in the influence of the saddle-splay elastic constant on the structures. For ordinary values of material parameters, only radially twisted and asymmetric conical structure are stable. The former is stable at low chiralities, while the latter is stable for high chiralities. The radially twisted structure is commonly known as double twisted structure, while the asymmetric conical structure has not been considered, to the authors' knowledge. The phase diagram including both structures is determined by comparing their free energies. Theoretical predictions are in agreement with available experimental data. \textcopyright{} 1996 The American Physical Society.

Saddle-splay elasticity of nematic structures confined to a cylindrical capillary.

The stability of nematic structures within a cylindrical capillary whose wall exhibits a homeotropic boundary condition is studied. The structures are obtained numerically from Euler-Lagrange equations resulting from the minimization of the Frank free energy functional. Stability diagrams are presented showing dependence on elastic properties, surface anchoring, and external transversal field strength. Emphasis is given to the effects of the saddle-splay elastic constant (${\mathit{K}}_{24}$), which plays an important role in the weak anchoring regime. A new structure---the planar polar structure with two line defects---is predicted. It is shown that it is stable in a finite interval of the external field strength in the strong anchoring regime.

Bend-stripes in hybrid aligned nematic layers

Abstract The occurrence of bend-stripes also involving twist distortion is investigated in hybrid aligned nematic layers, with stronger tilt-anchoring at the homeotropic substrate than at the planar one. The modulated structure is found to exist above the thickness threshold d a for the aperiodic bend-splay deformation. The periodicities of the director azimuth and polar angle are incommensurate along the normal to the cell plates. In principle, two independent periodic modes are possible, the first one stable, with threshold d p = d a, the second one metastable, with threshold d p > d a, according to the values of the torsional extrapolation lengths. Both transitions are continuous with respect to the in-plane wavenumber. The second mode can appear only if the difference between the torsional and the tilt extrapolation lengths is positive at the planar substrate. Moreover, both thresholds are independent of the saddle-splay elastic constant.

Influence of K 24 on the structure of nematic liquid crystal droplets

Abstract A phenomenological free energy is used to describe the stable ordering of nematic liquid crystals confined to supramicron spherical cavities. In particular the effects of the saddle splay elastic constant, K 24, on the equilibrium structures and phase diagram of droplets with homeotropic surface anchoring are discussed. Some structures are illustrated by the corresponding simulated polarization microscope textures. Possibilities for an experimental determination of the saddle-splay elastic constant and surface anchoring strength by studying the radial-axial structural transition in such droplets are analysed. It is shown that the K 24 term in the elastic free energy stabilizes a deformed droplet structure even in the limit of the zero anchoring strength.

Focal conic domains with positive Gaussian curvature and saddle-splay rigidity of smectic L alpha phases.

We report on the experimental observation of a different type of focal conic domain with positive Gaussian curvature. A particular type of these domains is usually given the name ``spherulites.'' Their appearance is due to a low (probably negative) value of the saddle-splay elastic constant. These domains are observed in the lamellar ${\mathit{L}}_{\mathrm{\ensuremath{\alpha}}}$ phase with a low cosurfactant to surfactant (c/s) ratio. The increase of this ratio results in usual focal domains with negative Gaussian curvature. It allows us to conclude that the saddle-splay constant is governed by the c/s ratio, and changes sign from positive to negative when c/s decreases.

Hybrid Aligned Nematic Films with Horizontally Degenerated Boundary Conditions and Saddle-Splay Elastic Term

The elastic energy of topological points defects and strings connecting pairs of defects is discussed for the geometry of hybrid aligned nematic film with horizontally degenerated boundary conditions. Experimental determination of their structure enables to reach an estimation of the saddle-splay elastic constant.