The formation of biaxial nematic phases in binary mixtures of thermotropic liquid-crystals composed of uniaxial molecules

ABSTRACT

Monte Carlo simulations in the isothermal-isobaric ensemble are used to investigate the formation of an ordered, biaxial nematic phase in a binary mixture of thermotropic liquid crystals. The orientational dependence of the interaction between molecules of each pure component is the same as in the well-known Maier-Saupe model; each pure component of the mixture is therefore capable of forming a uniaxial nematic phase. For the interaction between molecules of different components, we use the same Maier-Saupe model but change the sign of the coupling constant. As a consequence a T-shaped arrangement of these molecules is energetically favoured. The formation of the biaxial phase occurs in two steps. At higher temperatures T, one of the components forms a uniaxial nematic phase whereas the other is in a quasi two-dimensional restricted isotropic liquid state. We develop a simple theoretical model to understand the high degree of (ostensible) nematic order in the latter. At lower T, the second component becomes nematic and then the entire mixture of the two compounds has biaxial symmetry. The biaxial nematic phase does not demix into domains rich in molecules of one or the other species.     

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     

Probing the orientation of porphyrin oligomers in a liquid crystal solvent – a triplet state electron paramagnetic resonance study

ABSTRACT

Linear porphyrin oligomers have found various applications as synthetic molecular wires in the context of light harvesting, solar energy conversion and molecular electronics. In many of these applications a partial ordering of the molecules helps to improve the reaction efficiency or device performance. In this work we study the orientational properties of the building blocks of such porphyrin-based molecular wires, namely a porphyrin monomer and the corresponding butadiyne-bridged dimer. The porphyrins have been embedded in the nematic liquid crystal solvent 4-cyano-4'-pentylbiphenyl (5CB) and the anisotropic properties of their photogenerated triplet states were characterised by transient electron paramagnetic resonance (EPR) spectroscopy. When aligned in strong magnetic fields, the liquid crystal molecules impose their orientational anisotropy onto the solute guest molecules whose orientation-dependent magnetic properties can then be explored. The line shape analysis of the porphyrin triplet state EPR spectra – highly sensitive to small conformational changes – confirms the orientation of the zero-field-splitting (ZFS) tensors previously determined for these molecules by magnetophotoselection experiments. A biaxial distribution function is shown to be necessary to simulate the experimental EPR data. The biaxial behaviour, in conjunction with symmetry considerations, allows an unambiguous assignment of the three ZFS tensor axes to the molecular axes. From the determined orientational distributions of the porphyrins in 5CB, the biaxial order parameters for both molecules were calculated.     

Interface in nematics

Summary The structures of the interface between an isotropic liquid and a nematic liquid crystal and also between different uniaxial nematic phases are studied. It is shown that, at a planar orientation in the case of the nematic-isotropic liquid interface and also at a mutually orthogonal orientation of the director in the case of two nematic phases, the interface has the structure of a biaxial nematic liquid crystal. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Fluctuations of orientational order in a uniaxial nematic liquid crystal with biaxial molecules and its response to an external field

Homogeneous thermal fluctuations of the orientational order parameters S and G of biaxial molecules in a uniaxial nematic liquid crystal are investigated in the framework of the molecular-statistical theory. It is demonstrated that the molecular biaxiality significantly affects the order parameters S and G, their temperature dependences in the nematic phase, the amplitude and the temperature dependence of the order parameter fluctuations in the nematic and isotropic phases, and the character of the transition from the nematic phase to the isotropic liquid phase. It is established that the fluctuations of the parameters S and G in the nematic phase are related to the temperature dependences of S and G and the susceptibilities χ_S and χ_G of the nematic liquid crystal to external fields, which leads to a change in the parameters S and G at a fixed director orientation. Explanations are offered for the known experimental data on the orientational ordering of biaxial molecules under the action of external fields in the isotropic phase of nematic liquid crystals.     

丝状相液晶由表面相互作用产生的相变

导出双轴丝状相液晶在指向矢与易取向轴重合时的表面相互作用能.应用Ritz方法,对半无 界液晶体得出沿表面法向的双轴相(B_c)至沿表面某一轴的双轴相(B_a)的相变.随着表面锚泊强度双轴性部分的增大,B_a的产生机制逐渐由降低温度 转为表面锚泊,因此B_a相可出现在较高温度和较大温度范围内.在表面锚泊强度 单轴性部分α值的一定范围内,增大α值可使B_a在较高温度产生,但α值的进 一步增大则使液晶又从B_α返回B_c相. 关键词： 液晶 相变 表面能     

Detection of phase biaxiality in liquid crystals by use of the quadrupole shift in 131Xe NMR spectra

An experimental method to unambiguously distinguish between uniaxial and biaxial liquid crystal phases is introduced. The method is based on the second order quadrupole shift (SOQS) observable in 131Xe NMR spectra of xenon dissolved in liquid crystals. It is shown that besides revealing the biaxiality, the 131Xe SOQS offers a novel method to determine the tilt angle in smectic C phases. As an example, the 131Xe SOQS in a ferroelectric liquid crystal is reported. It yields up a biaxial phase in between isotropic and smectic C phases.     

A Hierarchy of Defects in Biaxial Nematics

We study the topological properties of the manifolds which describe uniaxial and biaxial nematics in order to compare and classify all types of bulk and surface defects that can arise in a nematic liquid crystal. We explain how topological charges can be assigned both to isotropic defects in uniaxial nematics and to uniaxial defects in biaxial nematics; we further see how it is possible to distinguish between isolated surface defects and surface defects which extend in the bulk, and between surface defects which can relax in the bulk and defects forced to stay on the surface. Received: 28 November 1994 / Accepted: 30 September 1996     

Optical and structural anisotropy of a uniaxial nematic consisting of biaxial molecules with internal rotation

A relation is established between the refractive indices of a uniaxial nematic liquid crystal (LC) consisting of biaxial molecules with internal rotation and the properties of molecules and their structural ordering. It is shown that the correlation between the conformation degree of freedom associated with internal rotation of π-conjugate molecular fragments and the orientation degrees of freedom of the molecules as a whole leads to the existence of two mixed parameters of orientation-conformation order, which contribute to the optical anisotropy of the LC along with the parameters of the conformation and orientation order of the molecules. The effect of the correlation of the molecular degrees of freedom on the values of these order parameters and the properties of molecular polarizability is analyzed. The dependence of the polarizability of molecules on their orientation ordering in the LC is explained.     

Sequence of four orthogonal smectic phases in an achiral bent-core liquid crystal: evidence for the SmAP(α) phase

The mesomorphic properties of an achiral bent-core liquid crystal derived from 4-cyanoresorcinol are studied by polarizing optical microscopy, x-ray diffraction, and second harmonic electro-optic response. It shows a novel sequence of four nontilted or orthogonal smectic phases on cooling: SmA-SmAP(R)-SmAP(X)-SmAP(A). Here SmAP(X) is the new orthogonal polar uniaxial smectic phase. The electric-field-induced transformations in the SmAP(X) phase give rise to two biaxial states separated by a uniaxial one. The second harmonic electro-optic response in this phase is interpreted in terms of the polar interaction with the electric field. A comparison of the experimental results with the next-nearest-neighbor model for the structure of the SmAP(X) phase shows it to be an SmAP(α) phase.     

Equivalent permittivity tensor in anisotropic random media

An explicit result for the equivalent (or effective) permittivity tensor is derived for dispersions of anisotropic (biaxial) particles embedded in an isotropic matrix. The overall medium has a positional disorder but an orientational order and it exhibits a uniaxial behaviour. Each crystal is partially oriented along a given director (preferential direction) and the degree of orientation is taken into account by a suitable order parameter. The equivalent permittivity tensor of the whole heterogeneous material is described in terms of the order parameter, the volume fraction of the dispersed phase, the principal values of the permittivity tensor of the crystals and the components of the director along which the crystals are preferentially aligned.     

Transition of deformation mechanisms in nanotwinned single crystalline SiC

ABSTRACT

The ability to experimentally synthesise ceramic materials to incorporate nanotwinned microstructures can drastically affect the underlying deformation mechanisms and mechanics through the complex interaction between stress state, crystallographic orientation, and twin orientation. In this study, molecular dynamics simulations are used to examine the transition in deformation mechanisms and mechanical responses of nanotwinned zinc-blende SiC ceramics subjected to different stress states (uniaxial compressive, uniaxial tensile, and shear deformation) by employing various twin spacings and loading/crystallographic orientations in nanotwinned structures, as compared to their single crystal counterparts. The simulation results show that different combinations of stress states and crystal/twin orientation, and twin spacing trigger different deformation mechanisms: (i) shear localised deformation and shear-induced fracture, preceded by point defect formation and dislocation slip, in the vicinity of the twin lamellae, shear band formation, and dislocation (emission) avalanche; (ii) cleavage and fracture without dislocation plasticity, weakening the nanotwinned ceramics compared to their twin-free counterpart; (iii) severe localised deformation, generating a unique zigzag microstructure between twins without any structural phase transformations or amorphisation, and (iv) atomic disordering localised in the vicinity of coherent twin boundaries, triggering dislocation nucleation and low shearability compared to twin-free systems.     

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：     

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.     

Polydispersity stabilizes biaxial nematic liquid crystals

Inspired by the observations of a remarkably stable biaxial nematic phase [van?den?Pol et?al., Phys. Rev. Lett. 103, 258301 (2009)], we investigate the effect of size polydispersity on the phase behavior of a suspension of boardlike particles. By means of Onsager theory within the restricted orientation (Zwanzig) model we show that polydispersity induces a novel topology in the phase diagram, with two Landau tetracritical points in between which oblate uniaxial nematic order is favored over the expected prolate order. Additionally, this phenomenon causes the opening of a huge stable biaxiality regime in between uniaxial nematic and smectic states.     

Linear birefringence studies of structural phase transitions of KCdF3

Two weakly discontinuous structural phase transitions have been observed on single domains of KCdF₃ at T_c1 = 487.5 K and at T_c2 = 472.7 K in the temperature dependence of the linear birefringence (LB). Beginning with the cubic high temperature phase the crystal becomes successively uniaxial and biaxial birefringent. Within the classical Landau approximation the LB has proved to be proportional to the square of the respective order parameter of the transformations. A relation which describes the coupling between both order parameters is discussed. In disagreement with Hidaka et al. [7] we do not observe a third phase transition near 240 K by the LB technique.     

Mixed spin-1/2 and spin-1 Ising model with uniaxial and biaxial single-ion anisotropy on the Bethe lattice

The mixed spin-1/2 and spin-1 Ising model on the Bethe lattice with both uniaxial as well as biaxial single-ion anisotropy terms is solved exactly by combining star-triangle and triangle-star mapping transformations with exact recursion relations. Magnetic properties (magnetization, phase diagrams, and compensation phenomenon) are investigated in detail. Particular attention is focused on the effect of uniaxial and biaxial single-ion anisotropies that basically influence the magnetic behavior of the spin-1 atoms.      

Study of crystals in medium-and long-wavelength IR ranges by surface-electromagnetic-wave spectroscopy

First observation of excitation of surface electromagnetic waves (SEW) is reported in the reststrahlen region in for biaxial crystal KTiOPO₄ (KTP) using a tunable CO₂ laser around 10 μm, and for CaF₂, BaF₂, MgO (cubic crystals), and LiNbO₃ (uniaxial crystal) in the far IR using ith a free-electron laser. The parameters of SEW propagation in these crystals have been obtained by the interference method of SEW phase spectroscopy, and the possibility of determining the complex dielectric permittivity of crystals from the SEW propagation parameters demonstrated in the range of SEW existence. Fiz. Tverd. Tela (St. Petersburg) 40, 237–241 (February 1998)     

Electric-field-induced polar biaxial order in a nontilted smectic phase of an asymmetric bent-core liquid crystal

A polarization reorientation process has been studied by means of optical second-harmonic generation in an optically uniaxial smectic phase of an asymmetric bent-core liquid crystal. A nontilted polar smectic order with a biaxial order is induced by applying an electric field to the uniaxial nonpolar smectic phase. This phenomenon was well simulated by the two-dimensional Langevin process, i.e., electric-field-induced continuous molecular reorientation against thermal agitation. The simulation suggests that about 200s of molecules form a polar domain and cooperatively respond to the applied field. The existence of the polar domains and their reorientation are consistent to the dielectric measurement; a high dielectric constant of about 60 at the kHz range is markedly suppressed by applying a bias field.