Twist Elastic Constant Research Articles

Twist elastic constant of chiral nematic cellulose nanocrystals determined by tactoid reconfiguration in electric field

Lyotropic chiral nematic cellulose nanocrystals (CNCs) have attracted significant attention and great progress has been made. Investigating their physical parameters, especially the twist elastic constant (K22), is pivotal for advancing our comprehension of fundamental viscoelastic property of chiral nematic phase. In this study, we demonstrate a straightforward method to simultaneously estimate K22 and helical twisting power (Kt) of chiral nematic CNCs. This method involves analyzing rheology properties and electro-response of CNCs, focusing on the rotational dynamics and structural reconfiguration of CNC tactoids under an electric field. By examining the rotation dynamics of CNC tactoids under an electric field, together with the viscosity characterization, the anisotropic dielectric susceptibility (∆χ) of chiral nematic CNC along the helix axis was determined. Subsequently, K22/∆χn was extracted by analyzing CNC tactoid pitch evolution under an electric field, employing the de Gennes model. The K22 for different concentrated CNCs is finally estimated by integrating experimental results and theory. It is shown that the chiral nematic CNCs present concentration-dependent K22, ranging from 0.05 to 0.14 pN, while Kt spans from 0.06 to 0.14 pN/μm. This study offers a comprehensive understanding of the CNC fundamental viscoelastic property and opens up new avenues for K22 measurement in other lyotropic liquid crystals.

Optical measurements of the twist constant and angle in nematic liquid crystal cells

We present a reliable optical method for measuring the twist elastic constant K2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {K}_2$$\\end{document} and for assessing the total twist angle in a standard nematic twist cell. The method relies on the use of a non-standard configuration of crossed polarisers and a twist cell, which allows us to measure accurately the twist-cell parameters by reducing the degeneracy between them. Grid patching and an efficient beam propagation method are utilised in the numerical models used for fitting the experimental data. The modelling shows that the polarisation dynamics in a twist cell is non-trivial and much more complex than in a planar cell. The twist elastic constant of three commonly used liquid crystals (5CB, 6CHBT and E7) was successfully extracted from cross-polarised intensity measurements.

Electro-optic characteristics of chiral nematic layers deformed by in-plane electric field

ABSTRACT Deformations of twisted and super-twisted layers composed of chiral and nonchiral nematic liquid crystals induced by in-plane electric field were studied numerically. The right-hand twisted structures with twist angles equal to 90°, 120°, 150°, 180°, 210°, 240° and 270° placed between crossed polarisers were considered. The optical transmission due to electro-optic effect which occurred in such systems was studied as a function of applied electric field strength. Steep and linear electro-optic characteristics were found in the case of nonchiral nematic confined in cells twisted by 90°. Such characteristics were favoured by large twist elastic constant, large dielectric anisotropy and weak azimuthal anchoring. In the case of super-twisted layers, useful characteristics were found for twist angles 210°, 240° and 270°, small twist elastic constant, strong azimuthal anchoring and large dielectric anisotropy.

Fast-relaxation, dye-doped cholesteric liquid-crystal smart window with a perfect planar state

A fast-relaxation dye-doped cholesteric liquid crystal (DDCLC) smart window without any defects is prepared by the doping of a low bend elastic constants liquid crystal dimer 1″,7″-bis-(4-cyanobiphenyl-4′-yl)heptane (CB7CB). The ratio of the bend elastic constant to the twist elastic constant of the liquid crystals (LCs) is adjusted so that it equates to unity. The transient planar (TP) state and the planar (P) state are combined, so the relaxation time from the homeotropic (H) state to the P state is greatly. Moreover, the oily streaks of the P state are removed and the light scattering is lessened. The polarisation-independent DDCLC smart window switches between three states: the haze-free dark state, the high-haze dark state and the transparent state. The smart window can be used in situations where absorbed sunlight reduces room temperature and protects privacy.

In situ measurements of twist and bend elastic constants in the oblique helicoidal cholesteric.

Unique electro-optical properties of the oblique helicoidal cholesteric (Ch_{OH}) stem from its heliconical director structure. An applied electric field preserves the single-harmonic modulation of the director while tuning the Ch_{OH} period and the corresponding Bragg-peak wavelength within a broad spectral range. We use the response of Ch_{OH} to the electric field to measure the elastic constants of twist K_{22} and bend K_{33} directly in the cholesteric phase. The temperature dependencies of K_{22} and K_{33} allow us to determine the range of the electric tunability of the Ch_{OH} pitch and the heliconical angle. The data are important for understanding how molecular composition and chirality influence macroscopic elastic properties of the chiral liquid crystals and for the development of Ch_{OH}-based optical devices.

Director configuration of liquid crystals in a cylindrical cavity with homeotropic anchoring conditions

We study numerically the equilibrium configurations of nematic liquid crystals confined in cylindrical cavities with strong and weak homeotropic anchoring conditions, respectively, on the basis of the elastic continuum theory and the difference iterative method. The lyotropic chromonic liquid crystal disodium cromoglycate exhibits a completely different spontaneous chiral configuration from 5CB due to the large ratio of the saddle-splay elastic constant to the twist elastic constant. We show that how the elastic constants affect the director alignment in chiral structure with strong homeotropic anchoring conditions. For the weak homeotropic anchoring conditions, the theoretically predicted transition from a twisted and escaped radial to an escaped twisted configuration of DSCG and the transition from an escaped radial to a UA configuration of 5CB, on reduction of the anchoring coefficient below a certain threshold, are confirmed to occur at A∼10−8J/m2. Remarkably, it provides a more accurate theoretical analysis for the prediction of director configurations in cylindrical cavities under different conditions in experiments.

Twist elastic constant in the SmC* phase of an antiferroelectric liquid crystal with and without photo-polymer networks.

Chiral liquid crystalline phases with pitches that are comparable to visible wavelengths, all Bragg-reflect visible light. We measured Bragg reflections from the chiral SmC* phase of the antiferroelectric liquid crystal (AFLC), AS612, and explored how applied electric fields and polymer networks modify these reflections. From the critical field that unwinds the helix and destroys Bragg reflections, the twist elastic constant of the SmC* phase is determined. We estimate from this result, the elastic constant of polymer network, which when introduced into the liquid crystal matrix, fixes the helical pitch (and hence, Bragg peaks). These parameters are crucial for designing both FLC and AFLC displays since networks enhance the mechanical properties of the liquid crystal host while not affecting their optical properties.

Lyotropic nematic liquid crystals: interplay between a small twist elastic constant and chirality effects under confined geometries

ABSTRACT There are two classes of liquid crystals (LCs): Thermotropic LCs where the organic molecule represents the anisotropically shaped mesogen and lyotropic LCs, where the mesogens are non-spherical supramolecular assemblies dispersed in a solvent. Various kinds of lyotropic nematic liquid crystals (LLCs) exist, differing in shape and composition of the aggregates: Chromonic, polymeric or micellar LLCs.However, micellar LLCs are the most ubiquitous kind of LLCs, occurring in soaps and biological systems. Although these nematic lyotropics are so different, they exhibit – contrary to thermotropic nematics – spontaneous reflection symmetry breaking under confinement. We discuss spontaneous mirror symmetry breaking under capillary confinement for a standard micellar ND phase and give a detailed director field structure of the twisted polar configuration. Furthermore, we measure for the first time a complete set of viscoelastic properties of a micellar nematic LLC, finding a small twist elastic constant K 22, which is at least one order of magnitude smaller than K 11 and K 33. As demonstrated by the following work, a small K 22 and therefore spontaneous mirror symmetry breaking under confinement is rather the rule than the exception in lyotropic nematics and constitutes a unique difference between lyotropic and typical thermotropic nematics, for which the well-known one-constant approximation holds. Abbreviations: LC: Liquid Crystal; LLC: Lyotropic liquid crystal; TER: twisted escaped radial director configuration; TP: twisted polar director configuration; : director; K 11: splay elastic constant of the nematic phase; K 22: twist elastic constant of the nematic phase; K 33: bend elastic constant of the nematic phase; s: strength of a defect/disclination; ER: escaped radial director configuration; CDEAB: N,N-ethylhexadecylammonium bromide; DOH: decan-1-ol; ND: nematic phase of disk-shaped building blocks; NC: nematic phase of rod-shaped building blocks; H-field: magnetic field; PR: planar radial director configuration; PP: planar polar director configuration; RR: right handed – right handed; LL: left handed – left handed; RL: right handed – left handed; LR: left handed – right handed.

Extremely small twist elastic constants in lyotropic nematic liquid crystals

Recent measurements of the elastic constants in lyotropic chromonic liquid crystals (LCLCs) have revealed an anomalously small twist elastic constant compared to the splay and bend constants. Interestingly, measurements of the elastic constants in the micellar lyotropic liquid crystals (LLCs) that are formed by surfactants, by far the most ubiquitous and studied class of LLCs, are extremely rare and report only the ratios of elastic constants and do not include the twist elastic constant. By means of light scattering, this study presents absolute values of the elastic constants and their corresponding viscosities for the nematic phase of a standard LLC composed of disk-shaped micelles. Very different elastic moduli are found. While the splay elastic constant is in the typical range of 1.5 pN as is true in general for thermotropic nematics, the twist elastic constant is found to be one order of magnitude smaller (0.30 pN) and almost two orders of magnitude smaller than the bend elastic constant (21 pN). These results demonstrate that a small twist elastic constant is not restricted to the special case of LCLCs, but is true for LLCs in general. The reason for this extremely small twist elastic constant very likely originates with the flexibility of the assemblies that are the building blocks of both micellar and chromonic lyotropic liquid crystals.

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.

Study on concentric configuration of nematic liquid crystal droplet by Landau-de Gennes theory

ABSTRACT On the basis of Landau-de Gennes theory, the fine structures of escaped concentric and ideal concentric configurations confined in nematic liquid crystal droplets were investigated. The escaped concentric configuration rather than the ideal concentric configuration appeared under the same conditions and parameters reported in Liq. Cryst., 45(1): 102 − 111, 2017. After increasing k 22 (twist elastic constant in Frank theory), the escaped concentric configuration transformed into the ideal concentric configuration. Within the ideal concentric configuration, we found an unexpecting order reconstruction occurred around the +1 line disclination, which has yet to be reported. In addition, the structural transitions within droplets of different radii were simulated.

Anomalies in the twist elastic behaviour of mixtures of calamitic and bent-core liquid crystals

ABSTRACTThe splay, twist and bend elastic constants (K11, K22 and K33) have been measured as a function of temperature in bent-core/calamitic mixtures based on three different calamitic materials (5CB, 8CB and ZLI1132) and two bent-core dopants. The behaviour of the splay and bend constants are as expected; a reduction in K33 of ~20%, in line with predictions from mixing rules and other observations. Interestingly, no change is seen in the splay constant, K11 of the calamitic hosts. Surprisingly though, the twist elastic constant exhibits a reduction of 30 – 40% in all mixtures across the nematic range, an effect not previously reported and much larger than mixing rules can explain. The elastic behaviour is universal in our mixtures. We explain part of the reduction in the twist deformation by considering the influence of the chiral conformer fluctuations of the bent-core molecules on the twist elastic constants of the mixtures. However, the dramatic reduction can only be fully explained by also including contributions from chiral conformer fluctuations of the calamitic host, a form of chiral amplification.

Influence of the saddle-splay term on nematic liquid crystals confined between two coaxial cylinders

A theoretical study of saddle-splay term on nematic liquid crystal confined between two coaxial cylinders elucidates director configurations. By solving the numerical solution of Euler–Lagrange equation based on Frank elastic theory and finite-difference iterative method, the effect of saddle-splay term on cylindrical system have been discussed explicitly. We investigate the spontaneous deformation by saddle-splay term K24 in the weak axial anchoring conditions. And we compare the effect of the twist elastic constant K22 on director distortion to the influence of saddle-splay term K24 in the twist anchoring conditions. Finally, we calculate the critical radius ratio and the critical twist elastic constant in the planar anchoring conditions, in which the spontaneous deformation occurs.

Non-monotonic, lily-like twist distribution in toroidal nematics.

Toroidal nematics are droplets of nematic liquid crystals in the form of a circular torus. When the nematic director is subject to planar degenerate boundary conditions, the bend-only director field with vector lines along the parallels of all nested torodial shells is an equilibrium solution for all values of the elastic constants. Local stability analyses have shown that an instability is expected to occur for sufficiently small values of the twist elastic constant. It is natural to wonder whether in this regime the global equilibrium would be characterized by a monotonic twist, or not. In the former case, the twist distribution over the torus' circular cross-section would be represented pictorially by a fennel-like surface emanating from the centre. We prove that instead the stable twist distribution is represented by a lily-like surface. Thus, generically the twist distribution is not monotonic and its maximum may fall well within the torus, far away from the boundary. To cope with the peculiar complexity of the elastic free-energy functional in the fully non-linear setting, we developed an ad hoc deep-learning optimization method, which here is also further validated and documented for it promises to be applicable to other similar problems, equally intractable analytically.

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.

Anomalously low twist and bend elastic constants in an oxadiazole-based bent-core nematic liquid crystal and its mixtures; contributions of spontaneous chirality and polarity

The splay, twist and bend elastic constants of an oxadiazole based bent core liquid crystal and it's mixtures have been measured across the entire nematic range.

Non-linear optical measurement of the twist elastic constant in thermotropic and DNA lyotropic chiral nematics

Throughout the whole history of liquid crystals science, the balancing of intrinsic elasticity with coupling to external forces has been the key strategy for most application and investigation. While the coupling of the optical field to the nematic director is at the base of a wealth of thoroughly described optical effects, a significant variety of geometries and materials have not been considered yet. Here we show that by adopting a simple cell geometry and measuring the optically induced birefringence, we can readily extract the twist elastic coefficient K22 of thermotropic and lyotropic chiral nematics (N*). The value of K22 we obtain for chiral doped 5CB thermotropic N* well matches those reported in the literature. With this same strategy, we could determine for the first time K22 of the N* phase of concentrated aqueous solutions of DNA oligomers, bypassing the limitations that so far prevented measuring the elastic constants of this class of liquid crystalline materials. The present study also enlightens the significant nonlinear optical response of DNA liquid crystals.

Chiral nematic liquid crystal microlenses

Nematic liquid crystals (NLCs) of achiral molecules and racemic mixtures of chiral ones form flat films and show uniform textures between circular polarizers when suspended in sub-millimeter size grids and immersed in water. On addition of chiral dopants to the liquid crystal, the films exhibit optical textures with concentric ring patterns and radial variation of the birefringence color. Both are related to a biconvex shape of the chiral liquid crystal film; the rings are due to interference. The curvature radii of the biconvex lens array are in the range of a few millimeters. This curvature leads to a radial variation of the optical axis along the plane of the film. Such a Pancharatnam-type phase lens dominates the imaging and explains the measured focal length of about one millimeter. To our knowledge, these are the first spontaneously formed Pancharatnam devices. The unwinding of the helical structure at the grid walls drives the lens shape. The relation between the lens curvature and material properties such as helical pitch, the twist elastic constant, and the interfacial tensions, is derived. This simple, novel method for spontaneously forming microlens arrays can also be used for various sensors.

Field-induced oblique helicoidal cholesteric phases in mixtures of chiral and achiral liquid crystalline molecules

ABSTRACTWe present a mean field theory to describe phase transitions in mixtures of chiral and achiral liquid crystalline molecules in the presence of an external field. When a longitudinal external field is applied parallel to the pitch axis of a chiral nematic phase (N*), the director of the N* phase can lead to an oblique heliconical cholesteric () state with a twist–bend distortion, in which a bend elastic constant is smaller than a twist elastic constant . We predict that the exists between N* and nematic (N) phases and can be controlled by temperature and concentration. We find various phase transitions: the first-order (isotropic) and the second-order , transitions, on the temperature–concentration plane. We also predict the pitch and the phase diagrams, depending on temperature and concentration under the external field.

Bipolar to toroidal configuration transition in liquid crystal droplets

ABSTRACTLiquid crystal (LC) droplets dispersed in isotropic media are of significant interest for scientific community and great importance for industries. The confinement can generate many fascinating LC director configurations and enable important practical applications. With tangential anchoring condition at the droplet surface, theoretically there are several possible configurations: bipolar, twisted bipolar, escaped toroidal, toroidal and so on. Bipolar configuration is usually observed in droplets made from common LCs while the toroidal configuration is rarely observed and it is hard to create especially in thermotropic LCs. Their realisations depend on the splay, bend and twist elastic constants ratio, and anchoring condition of the LC and polymer interface. We constructed thermotropic LCs with abnormally small bend elastic constants, with which stable toroidal configuration were successfully created. We provide a brand new method to create toroidal droplet by simply varying the bend elastic constant. We observed the transition from bipolar configuration to toroidal configuration. We performed a detailed study of the texture of toroidal droplets.