Dielectric,viscous and elastic properties of nematogenic 1-(4- trans -propylcyclohexyl)-2-(4-cyanophenyl)ethane

This paper presents the results of measurements of the static and dynamic electric permittivity, the shear viscosity of a freely flowing sample, and the splay and bend elastic constants for 1-(4-trans -propylcyclohexyl)-2-(4-cyanophenyl)ethane (C3H7-CyHx-CH2CH2-Ph-C=N) (3CCPE). The static permittivity of the isotropic phase shows pre-nematic critical behaviour which is discussed in the frame of the fluid-like model of Mukherjee. From the temperature dependence of the dielectric relaxation time (corresponding to the molecular rotation around the short axis) and the shear viscosity, the strength of the nematic potential and the effective length of the 3CCPE molecule (in the isotropic phase), were estimated. The splay and bend elastic constants were determined from the voltage dependence of the capacitance of a planar nematic cell.     

Dielectric, viscous and elastic properties of nematogenic 1-(4- trans -propylcyclohexyl)-2-(4-cyanophenyl)ethane

This paper presents the results of measurements of the static and dynamic electric permittivity, the shear viscosity of a freely flowing sample, and the splay and bend elastic constants for 1-(4- trans -propylcyclohexyl)-2-(4-cyanophenyl)ethane (C 3 H 7 -CyHx-CH 2 CH 2 -Ph-C=N) (3CCPE). The static permittivity of the isotropic phase shows pre-nematic critical behaviour which is discussed in the frame of the fluid-like model of Mukherjee. From the temperature dependence of the dielectric relaxation time (corresponding to the molecular rotation around the short axis) and the shear viscosity, the strength of the nematic potential and the effective length of the 3CCPE molecule (in the isotropic phase), were estimated. The splay and bend elastic constants were determined from the voltage dependence of the capacitance of a planar nematic cell.     

Pattern formation and non-linear phenomena in stretched discotic liquid crystal fibres

This paper presents a non-linear numerical and bifurcation analysis of pattern formation phenomena in a discotic nematic liquid crystal confined to annular cylindrical cavities and subjected to extensional deformations. The results are of direct relevance to understanding the industrial melt spinning of mesophase carbon fibres, using discotic nematic liquid crystals precursor materials. Three types of orientation patterns are identified in this study: spatially constant (radial), monotonic (pinwheel), and oscillatory (zigzag). Numerical and closed form analytical results predicting continuous transformations between the radial, pinwheel, zigzag radial orientation modes are presented. The bifurcation analysis provides a direct characterization of the parametric dependence and the transitions between these three basic patterns, and provides a complete understanding of the multistability phenomena that is present in the oscillatory orientation patterns. In general it is found that small fibres of nearly elastically isotropic discotic nematic liquid crystals tend to adopt the classical ideal radial texture, while larger fibres with anisotropic elastic moduli tend to yield the zigzag texture. Fixed arbitrary surface orientation of intermediate size and anisotropy tend to adopt the pinwheel texture. The theoretical results are able to explain the main features and mechanisms that lead to the commonly observed cross-section textures of industrially spun mesophase carbon fibres.     

高分子液晶条带织构的计算机模拟

The relationship between the vector version and tensor version of Frank distortion energy for the liquid crystal was established, through which the relationship between the Frank elastic constants and the expansion coefficients of spatial derivatives for the orientational order parameter Sij of liquid crystalline polymer was obtained. Ginzberg-Landau equation for the orientational order parameter Sij was numerically solved by using the cell dynamical system, which involves a free energy functional containing Landau-de Gennes orientational free energy, Maier-Saupe anisotropic interaction free energy and Frank distortion free energy. Incase of the splay elastic constant being much lager than the bend elastic constant, the evolution process of band textures in liquid crystalline polymer during the shear relaxation and its small angle light scattering patterns were simulated. The influence of preshear rate on the band forming and band structure was investigated. It was found that the formation of longitudinal band textures is due to the much rapider longitudinal splay relaxation than the latitudinal bend relaxation, and the induced times of band forming and the characteristic length of band structure decrease with the increasing of preshear rate, which is consistent with the experimental results.     

Polar interactions between bent–core molecules as a stabilising factor for inhomogeneous nematic phases with spontaneous bend deformations

ABSTRACT

It is generally accepted that the transition into the twist–bend nematic phase (N_TB) is driven by an elastic instability related to the reduction of the bend elastic constant. Here we use a molecular–statistical theory to show that sufficiently strong polar interactions between bent-shaped molecules may lead to experimentally observed reduction of the bend elastic constant in the nematic phase even if electrostatic dipole–dipole interactions are not taken into account. We propose a simple model of bent–core particles and derive explicit analytical expressions which enable one to understand how polar molecular shape affects the elastic constants, and, in particular, the important role of the bend angle. Numerical graphs showing temperature variations of all elastic constants are also presented including the variation of the bend and splay elastic constants before and after the renormalisation determined by local polar order of molecular steric dipoles and the corresponding polar correction to the one-particle distribution function.     

Fourth-order nematic elasticity and modulated nematic phases: a poor man’s approach

We propose an extension of Frank-Oseen’s elastic energy for bulk nematic liquid crystals which is based on the hypothesis that the fundamental deformations allowed in nematic liquid crystals are splay, twist and bend. The extended elastic energy is a fourth-order form in the fundamental deformations. The existence of bulk spontaneous modulated or deformed nematic liquid crystal ground states is investigated. The analysis is limited to bulk nematic liquid crystals in the absence of limiting surfaces and/or external fields. The non deformed ground state is stable only when Frank-Oseen’s elastic constants are positive. In case where at least one of them is negative, the ground state becomes deformed. The analysis of the stability of the deformed states in the space of the elastic parameters allows to characterise different types of deformed nematic phases. Some of them are new nematic phases, for instance a twist – splay nematic phase is predicted. Inequalities between second-order elastic constants which govern the stability of the twist–bend, splay–bend, and splay–twist states are obtained. Their stability in respect to triple splay–bend–twist deformations is investigated.     

A numerical technique for predicting microstructure in liquid crystalline polymers

A numerical technique has been developed to model texture in nematic liquid crystals. The technique differentiates between splay, twist and bend distortions and includes splay-splay compensation. The technique is tested by the simulation of the Freedericksz transition and by the determination of minimum energy director fields for specific boundary conditions. To model the bulk, periodic boundary conditions are imposed. The effect of elastic anisotropy on disclination character has been investigated by terminating simulations before all the defects have been annihilated. With a low twist constant, twist disclinations are observed; with a high twist constant, wedge disclinations are observed. With a low twist constant and high splay constant, realistic for polymeric liquid crystals, features observed experimentally are simulated.     

主链型高分子液晶向列相向错观察的进展

综述了主链型高分子液晶向列相向错在实验观察方面的进展。从纹影织构的观察和展曲、弯曲弹性常数相等条件下的二维曲率弹性理论出发探讨了向错结构的几何特征。简要涉及了弹性常数不相等对向错的影响、向错核心的本质和反转墙的观察;给出了拓扑强度s高达4的高阶向错的实验观察结果;归纳出描绘向错周围指向矢场的主要实验方法:1)片晶装饰;2)条带织构装饰;3)表面微裂纹装饰。本文对上述方法进行了讨论和比较,列举了一些电子显微镜和光学显微镜照像的图例。     

Nematic to smectic-A phase transition in mixture of liquid crystal and nonmesogenic impurities: existence of tricritical point

Experiments on the mixture of liquid crystals and nonmesogenic impurities showed the significant role of nonmesogenic impurities on the nematic–smectic-A phase transition. Using both Flory–Huggins theory of isotropic mixing and Landau–de Gennes theory, we present a phenomenological theory that discusses the role of such impurities on the nematic–smectic-A phase transition in a mixture of smectic liquid crystal and nonmesogenic impurities. We discuss the impact of nonmesogenic impurities on the order parameters, Frank elastic constants (splay and bend) and transition temperature of the nematic–smectic-A phase transition. Our theoretical results show that there exists a tricritical point for which the second-order nematic–smectic-A phase transition becomes first order at a tricritical point by increasing the concentration of nonmesogenic solute. We find a remarkable agreement between theoretical and experimental results.     

Magnetic field controlled optical phase retardation in a hybrid nematic cell

We have studied the phase retardation of linearly polarized light in a hybrid nematic liquid crystal cell. For a certain range of directions of the applied magnetic field the phase retardation is found to change non-monotonically with the magnetic induction. The observed behaviour is described rather well by the standard Frank elastic theory. The corrections resulting from subsurface deformations, which are characteristic both for second order elasticity approach and for surface field theory, are also considered. The analysis of the experimental data suggests that the presence of distortions in the zero-field director configuration is the necessary condition for the non-monotonic phase retardation, which implies that such an experiment could be used for the detection of misalignment of the effective pretilts in a nematic cell.     

Optical response of a nematic liquid crystal cell at the splay – bend transition: a model and dynamic simulation

We study the dynamical optical response of a nematic liquid crystal cell that undergoes the splay–bend transition after applying a voltage across the cell. We formulate a simplified model that takes into account both the flexoelectric coupling and the surface rotational viscosity. The dynamic equations of the model are solved numerically to calculate the temporal evolution of the director profile and of the transmittance. We evaluate the response time as a function of a number of parameters, such as dielectric and elastic anisotropies, asymmetry of the surface pretilt angles, anchoring energy, surface rotational viscosity and flexoelectricity.     

Recent advances in the observation of disclinations of main-chain nematic polymers

Experimental observation of disclinations of main-chain nematic polymers is reviewed. The geometry of disclination structure is discussed both from observations of schlieren texture and the theory of curvature elasticity for a two-dimensional case with equal splay and bend moduli. The effects of non-equal elastic moduli, the nature of the disclination core and the observation of inversion wails are briefly mentioned. Examples of experimental observation of disclinations of high topological strengths up to S=4 are given. The main experimental methods to map the director field around disclinations are 1) lamellar decoration, 2) band-texture decoration and 3) surface microcrack decoration. The methods are discussed and compared, and examples illustrated by electron micrographs or photomicrographs are presented.     

Computational study of the texture formation in mesophase pitch-based carbon fibres

This paper studies the thermal relaxation phenomena after melt-extrusion of a rigid discotic uniaxial nematic mesophase pitch using mathematical modelling and computer simulation. The Ericksen and Landau-de Gennes continuum theories are used to investigate the structure development and texture formation across mesophase pitch-based carbon fibres. The two-dimensional model captures five types of transverse patterns, which match the commonly observed textures for mesophase pitch-based carbon fibres. They are: random, zig-zagged radial, radial, quasi-onion and onion. These textures represent the various combinations possible from the interplay between structure (i.e. texture) development and cooling during the fibre spinning process. During the thermal relaxation after the cessation of extensional flow the discotic nematic molecules store elastic free energy decays. The distorted nematic molecular profiles reorient to release the stored elastic free energy. The difference in time scales for molecular reorientation and thermal relaxation result in different transverse textures. The rate at which the fibres are cooled is the main factor in controlling the structure development. A slow cooling rate would permit the nematic discotic molecules to reorient to a well-developed (radial or onion) texture. The random texture is a result of rapid quenching. The numerical results are consistent with published experimental observations.     

Lyotropic self-assembly of high-aspect-ratio semiconductor nanowires of single-crystal ZnO

Lyotropic nanowire dispersions are attractive precursors for semiconductor device fabrication because they permit the alignment control of active nanomaterials. The reliable production of nanowire-based mesophases, however, is very challenging in practice. We show that appropriately functionalized high-aspect-ratio nanowires of single-crystal ZnO spontaneously form nematic phases in organic and aqueous media. These systems show isotropic, biphasic, and nematic phases on increasing concentration, in reasonable agreement with Onsager's theory for rigid rods interacting via excluded volume. Suspensions were readily processed to produce films with large-area monodomains of aligned nanowires. Imprints of the director field in quiescently dried films display a propensity for bend deformation in the organic mesophase versus splay deformation in the aqueous case, suggesting that system elasticity may be tuned via surface functionalization. These results provide critical insight for the utilization of semiconductor nanowires as novel mesogens and further enable the use of solution-based routes for fabricating optoelectronic devices.     

Computational study of the texture formation in mesophase pitch‐based carbon fibres

This paper studies the thermal relaxation phenomena after melt‐extrusion of a rigid discotic uniaxial nematic mesophase pitch using mathematical modelling and computer simulation. The Ericksen and Landau–de Gennes continuum theories are used to investigate the structure development and texture formation across mesophase pitch‐based carbon fibres. The two‐dimensional model captures five types of transverse patterns, which match the commonly observed textures for mesophase pitch‐based carbon fibres. They are: random, zig‐zagged radial, radial, quasi‐onion and onion. These textures represent the various combinations possible from the interplay between structure (i.e. texture) development and cooling during the fibre spinning process. During the thermal relaxation after the cessation of extensional flow the discotic nematic molecules store elastic free energy decays. The distorted nematic molecular profiles reorient to release the stored elastic free energy. The difference in time scales for molecular reorientation and thermal relaxation result in different transverse textures. The rate at which the fibres are cooled is the main factor in controlling the structure development. A slow cooling rate would permit the nematic discotic molecules to reorient to a well‐developed (radial or onion) texture. The random texture is a result of rapid quenching. The numerical results are consistent with published experimental observations.     

Saddle-splay and mechanical instability in nematics confined to a cylindrical annular geometry

Abstract

The occurrence of a mechanical instability is predicted for a nematic liquid crystal confined to a cylindrical annular geometry. The surfaces impose either a bend distortion (azimuthal configuration) or a splay distortion (radial configuration) in the plane of the cylinders′ cross-section. Remarkably, the instability appears also with strong anchoring, and, when the torsional anchoring is weak, then the saddle-splay elastic constant K24 deeply influences the critical radii.     

Alignment of liquid crystals using Langmuir‒Blodgett films of unsymmetrical bent-core liquid crystals

ABSTRACT

The properties of the thin films of liquid crystal (LC) molecules can be governed easily by external fields. The anisotropic structure of the LC molecules has a large impact on the electrical and optical properties of the film. The Langmuir monolayer (LM) of LC molecules at the air–water interface is known to exhibit a variety of surface phases which can be transferred onto a solid substrate using the Langmuir?Blodgett (LB) technique. Here, we have studied the LM and LB films of asymmetrically substituted bent-core LC molecules. The morphology of LB film of the molecules is found to be a controlling parameter for aligning bulk LC in the nematic phase. It was found that the LB films of the bent-core molecules possessing defects favour the planar orientation of nematic LC, whereas the LB films with fewer defects show homeotropic alignment. The defect in LB films may introduce splay or bend distortions in the nematic near the alignment layer which can govern the planar alignment of the bulk LC. The uniform layer of LB film facilitates the molecules of nematic to anchor vertically due to a strong van der Waals interaction between the aliphatic chains leading to a homeotropic alignment.     

A surface-induced transition in polymeric nematics

New polymeric liquid crystals can be treated as standard nematic liquid crystals when only their bulk properties are at issue, but they exhibit peculiar surface properties. The most striking one is that biaxial distributions may be induced on a confining surface. On continuously varying the surface anchoring conditions, we find a first-order phase transition from planar to homeotropic alignment in the bulk. Moreover, the decay towards these uniaxial states is radically different in the two cases: it is asymptotically exponential in the former, whereas it happens abruptly at a finite depth in the latter. There is precisely one surface biaxial distribution that induces bistability between these decay modes: it depends on the elastic constants in the Landau-de Gennes free energy functional. The analysis of the model we propose can prove useful in detecting the sign of the difference between splay and bend constants.     

Determination of elastic constants of a binary system (7CPB+9.CN) showing nematic,induced smectic Ad and re-entrant nematic phases

The temperature variation of the splay and bend elastic constants of a binary system exhibiting nematic-induced smectic A_d and re-entrant nematic phases measured by electric field-induced Freedericksz transition method has been reported. As bend deformation is not permitted in the smectic A phase, bend elastic constant (K₃₃) could only be determined in the nematic and re-entrant nematic phases. In both the nematic phases, the splay elastic constant has the same order of magnitude and does not show any pretransitional effect. However, in the induced smectic A_d phase, the value of K₁₁ is about one to two orders higher than that in the nematic phases. The bend elastic constant shows a strong pretransitional effect near the nematic–smectic and smectic–re-entrant nematic phase transitions. The influence of the presence of the induced smectic phase is observed even in those mixtures which have no induced smectic phases. As the smectic phase is approached, the ratio K₃₃/K₁₁ increases rapidly and diverges to infinity.