Effects of fields and anchoring on biaxial nematic ordering

Symmetry of a nematic liquid crystal phase is broken by an anchoring wall and also by an external field. Nematic system sandwiched between biaxial anchoring walls is introduced as a correspondent to a bulk nematic system exposed to a couple of fields, an electric field and a magnetic one in directions perpendicular to each other, and thermal behaviours of the system are studied. The crossover between a homeotropic structure and homogeneous one occurs, similarly to the bulk system in the fields, in which the anchoring condition of coexistence is shown to have the same expression as the one at the bulk. As to a characteristic phenomenon at the sandwiched system, it is proved that an appearance of a biaxial nematic order suppresses a uniaxial nematic order. A surface transition, i.e., a wetting phenomenon is shown to occur also in the biaxial nematics, even though the uniaxial order is suppressed therein.     

双轴性向列相液晶的相变理论

假设一双轴性向列相液晶分子简单相互作用模型，利用平均场理论，得到从各向同性相至单轴向列相、单轴向列相至双轴向列相的相变. 结果表明，在一定温度范围内，分子形状的非轴对称性可导致系统双轴向列相的产生. 在核磁共振实验中，导出双轴向列相序参数与谱线分裂频率间的一般关系，并讨论序参数测量性的可能性. 关键词： 向列相液晶 相变     

Biaxial surface order dynamics in calamitic nematics

Thermotropic nematic materials relax strong distortions by lowering the nematic order: the uniaxial symmetry is broken and is locally replaced by biaxial domains. We investigated the dynamics of the nematic order near a boundary surface of an asymmetric π-cell submitted to an external electric field, close to the electric order reconstruction threshold. An unexpected phenomenon is observed close, but below the threshold: the biaxial order spreads on the surface inducing a consequent bulk topological behaviour equivalent to the splay-bend fast transition allowed by order reconstruction at higher voltage.     

Investigation of the influence of molecule deformation on the dynamics and collective excitation spectra in nematic liquid crystals

The generalization of dynamic equations in uniaxial and biaxial nematic liquid crystals is obtained yielding an approach accounting for the deformation of structural elements of these media. Collective excitation spectra are calculated and their angular dependence is established. The possibility of propagation of one, two, and three acoustic waves in nematics is predicted, and extreme angular characteristics of these waves are elucidated. Results of investigation are compared with available experimental data and satisfactory agreement between them is demonstrated. Low-frequency asymptotics of two-time Green’s functions of uniaxial nematics are calculated. It is found that their structure depends essentially on the character of spatial anisotropy of the considered condensed medium and the shape of molecules. Polarization specific features of acoustic waves in uniaxial nematics are studied. It is shown that the first and second sounds are the superposition of the longitudinal and transverse components. The ratio of amplitudes of these components as a function of angle between the wave vector and the anisotropy axis is established.     

梳型高分子聚合物向列相液晶的相变

本文根据Freiser关于向列相液晶分子相互作用模型,利用平均场理论,建立了梳型高分子聚合物向列相液晶分子的哈密顿量,导出序参数自洽方程,得到各向同性相至单轴向列相以及单轴至双轴向列相的相变,结果表明,当分子主、侧链耦合项中排斥作用及主、侧链中较强向列相场的场强增大时,单轴至双轴向列相相变温度升高,并从一级相变逐渐变为二级相变。 关键词：     

Light transmission at the uniaxial-biaxial lyotropic nematics phase transitions

Results are reported on light transmission versus the temperature near the phase transitions between lyotropic nematics. Strong pretransitional effects are observed when the phase transitions occur between biaxial nematic and uniaxial phases. The light is strongly depolarized both at the calamitic-biaxial and at biaxial-discotic phase transitions. The results are qualitatively explained.     

The elastic anisotropy of nematic elastomers

We examine the robustness of order in nematic elastomers under mechanical strains imposed along and perpendicularly to the director when director rotation is prohibited. In contrast to electric and magnetic fields applied to conventional nematics, mechanical fields are shown theoretically and experimentally to greatly affect the degree of nematic order and related quantities. Unlike in liquid nematics, one can impose fields perpendicular to the director, thereby inducing biaxial order which should be susceptible to experimental detection. Nematic elastomers with unchanging director and degree of order should theoretically have the same elastic moduli for longitudinal and transverse extensions. This is violated when nematic order is permitted to relax in response to strains. Near the transition we predict the longitudinal modulus to be smaller than the transverse modulus; at lower temperatures the converse is true, with a crossover a few degrees below the transition. The differences are ascribed to the different temperature dependence of the stiffness of uniaxial and biaxial order. We synthesised side chain single-crystal nematic polymer networks, performed DSC, X-ray, birefringence, and thermo-mechanical characterisations, and then obtained linear moduli from stress-strain measurements. Received 29 September 2000     

Enhancement by polydispersity of the biaxial nematic phase in a mixture of hard rods and plates

The phase diagram of a polydisperse mixture of uniaxial rodlike and platelike hard parallelepipeds is determined for aspect ratios kappa=5 and 15. All particles have equal volume, and polydispersity is introduced in a highly symmetric way. The corresponding binary mixture is known to have a biaxial phase for kappa=15, but to be unstable against demixing into two uniaxial nematics for kappa=5. The phase diagram for kappa=15 is qualitatively similar to that of the binary mixture, regardless of the amount of polydispersity, while for kappa=5 a sufficient amount of polydispersity stabilizes the biaxial phase. This provides clues for designing an experiment to observe this long searched biaxial phase.     

Bound states of linear defects in biaxial nematics and superfluid liquids

It is shown that linear defects in biaxial nematics may form dynamically stable bound states if these defects are linked, almost parallel, and repel one another. Such a situation is possible for pairs of linear defects with a certain topology. This effect can also be observed for nearly parallel vortices in superfluid liquids and superconductors.     

Cracks and topological defects in lyotropic nematic gels

We report on the effects of the coupling of nematic order and elasticity in anisotropic lyotropic gels consisting of large nematic domains of surfactant coated single wall carbon nanotubes embedded in a cross-linked N-isopropyl acrylamide polymer matrix. We observe the following striking features: (i) undulations and then cusping of the gel sidewalls, (ii) a nematic director field that evolves as the gel sidewalls deform, (iii) networks of surface cracks that are orthogonal to the nematic director field, and (iv) fissures at the sidewall cusps and associated topological defects that would not form in liquid nematics.     

Two-dimensional,blue phase tactoids

ABSTRACT

We use full nematohydrodynamic simulations to study the statics and dynamics of monolayers of cholesteric liquid crystals. Using chirality and temperature as control parameters, we show that we can recover the two-dimensional blue phases recently observed in chiral nematics, where hexagonal lattices of half-skyrmion topological excitations are interleaved by lattices of trefoil topological defects. Furthermore, we characterise the transient dynamics during the quench from isotropic to blue phase. We then proceed by confining cholesteric stripes and blue phases within finite-sized tactoids and show that it is possible to access a wealth of reconfigurable droplet shapes including disk-like, elongated and star-shaped morphologies. Our results demonstrate a potential for constructing controllable, stable structures of liquid crystals by constraining 2D blue phases and varying the chirality, surface tension and elastic constants.     

Reduction theory for symmetry breaking with applications to nematic systems

We formulate Euler–Poincaré and Lagrange–Poincaré equations for systems with broken symmetry. We specialize the general theory to present explicit equations of motion for nematic systems, ranging from single nematic molecules to biaxial liquid crystals. The geometric construction applies to order parameter spaces consisting of either unsigned unit vectors (directors) or symmetric matrices (alignment tensors). On the Hamiltonian side, we provide the corresponding Poisson brackets in both Lie–Poisson and Hamilton–Poincaré formulations. The explicit form of the helicity invariant for uniaxial nematics is also presented, together with a whole class of invariant quantities (Casimirs) for two-dimensional incompressible flows.     

Elasticity and polarization of Ga<Subscript>x</Subscript>Al<Subscript>1-x</Subscript>N alloys subjected to uniaxial and biaxial compression

Elasticity and polarization of Ga_xAl_1-xN alloys subjected to uniaxial and homogeneous biaxial compression are calculated using first-principles methods. The uniaxial compression along the c-axis reduces Young’s modulus along the c-axis, and enhances bulk modulus and total polarization, whereas the biaxial compression in the plane perpendicular to the c-axis enhances bulk and Young’s moduli. It is also found that when the in-plane biaxial compression is applied by constraining the a-axis lattice constant to that of AlN, the bulk and Young’s moduli dramatically increase with increasing Ga concentration, and the total polarization could be suppressed, even annihilated, and finally enhanced by controlling Ga concentration.     

Dynamics of nematics with conformational degrees of freedom

On the basis of Hamilton approach the dynamics of the biaxial nematics is considered. All hydrodynamic parameters, connected with broken symmetry, are introduced in terms of the distortion tensor. The equations of ideal hydrodynamics are obtained and the three spectra of collective excitations of biaxial nematics are considered, taking into account the rod-shape of molecules.     

Molecular theoretic study of Freedericksz transition. Symmetry breaking of oblique axial order

Freedericksz transition, which is usually analyzed by an elastic theory, is studied on the basis of statistical mechanical ground, where nematics with positive dielectric anisotropy in homogeneous anchoring cell is exposed to an electric field in the direction of wall normal. In low temperature region, an oblique axial symmetry breaking occurs, which is nothing but the Freedericksz transition. In high temperature and high field region, biaxial nematic phase with principal axis parallel to the field direction at interior area of the system is proved to appear. A phase diagram on the field versus temperature plane is obtained and compared with the one at a bulk with common biaxial symmetry, where both of electric and magnetic fields are applied in directions perpendicular to each other. In the latter, no symmetry breaking occurs, in contrast with the former case above-mentioned, and the reason why this difference occurs is elucidated.     

Distribution of Topological Defects on Axisymmetric Surface

We propose a general method of determining the distribution of topological defects on axisymmetric surface,and study the distribution of topological defects on biconcave-discoid surface, which is the geometric configuration of red blood cell. There are three most possible cases of the distribution of the topological defects on the biconcave surface:four defects charged with 1/2, two defects charged with 1, or one defect charged with 2. For the four defect charged with 1/2, they sit at the vertices of a square imbedded in the equator of biconcave surface.     

52Cr spinor condensate: a biaxial or uniaxial spin nematic

We show that the newly discovered 52Cr Bose condensate in zero magnetic field can be a spin nematic of the following kind: a "maximum" polar state, a "colinear" polar state, or a biaxial nematic ferromagnetic state. We also present the phase diagram with a magnetic field in the interaction subspace containing the chromium condensate. It contains many uniaxial and biaxial spin nematic phases, which often but not always break time reversal symmetry, and can exist with or without spontaneous magnetization.     

Mechanical properties of novel forms of graphyne under strain: A density functional theory study

The mechanical properties of two forms of graphyne sheets named α-graphyne and α2-graphyne under uniaxial and biaxial strains were studied. In-plane stiffness, bulk modulus, and shear modulus were calculated based on density functional theory. The in-plane stiffness, bulk modulus, and shear modulus of α2-graphyne were found to be larger than that of α-graphyne. The maximum values of supported uniaxial and biaxial strains before failure were determined. The α-graphyne was entered into the plastic region with the higher magnitude of tension in comparison to α2-graphyne. The mechanical properties of α-graphyne family revealed that these forms of graphyne are proper materials for use in nanomechanical applications.     

Dispersion of bulk and surface electromagnetic waves in bigyrotropic finely stratified ferrite-semiconductor medium

Expressions for effective parameters are derived for a medium composed of alternating layers of a uniaxial ferromagnet and a semiconductor. The medium under investigation is a biaxial bigyrotropic crystal. In the case of a transverse magnetooptical configuration, bulk and surface waves at the vacuum-periodic structure interface are considered. Numerical analysis of dispersion relations for intrinsic TE and TM modes controlled in different frequency ranges is carried out.