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.     

A biaxial nematic liquid crystal composed of matchbox-symmetric molecules

By means of Monte Carlo simulations in the isothermal-isobaric ensemble, we investigate the structure and phase behaviour of a thermotropic liquid crystal composed of matchbox-symmetric (or board-like) molecules. Besides the isotropic phase the liquid crystal exhibits also uniaxial and biaxial nematic phases. The interaction potential is derived through an expansion in terms of Stone's rotational invariants [A. J. Stone, Mol. Phys. 78, 241–256 (1978).] that can be reexpressed in terms of Cartesian tensors. This latter formulation is particularly well suited for computer simulations. We analyse the orientation distribution function which allows us to distinguish between intrinsic and extrinsic biaxiality. In addition, we study the orientation-dependent correlation functions. In the limit of large intermolecular separations, the value of the orientation correlation function corresponds to the uniaxial and biaxial order parameters which are coupled in a complex fashion.     

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     

Birefringence study on lyotropic micellar nematic phase in a binary mixture

We report the results of our studies on optical and thermal properties of two non-mesogenic compounds, namely, didodecyl dimethyl ammonium bromide (DDAB) and glacial acetic acid. The mixture exhibits schlieren texture of lyotropic micellar nematic (N_D), SmA, SmB, and SmG phases, respectively, at different concentrations of DDAB sequentially when the specimen is cooled from isotropic phase. The order parameter (S) of lyotropic micellar nematic (N_D) phase is estimated with the help of temperature dependence of optical anisotropy from the measured values of refractive index and density data. The temperature variation of order parameter of the experimental curve is in agreement with the Mayer–Saupe theoretical curve. The formation of the above phases has been confirmed by optical studies.     

External magnetic field-dependent tricritical points of uniaxial-to-biaxial nematic transition

External magnetic field-dependent behavior of tricritical points of uniaxial–biaxial nematic phase transition in a mixture of prolate and oblate molecules has been studied using the Landau phenomenological theory. Topological classification of phase diagrams in the field-temperature coordinates is performed using a sixth-order term in order parameter tensor. For both prolate and oblate molecules, the tricritical order parameters corresponding to the uniaxial–biaxial increase with the intensity of the external magnetic field. Field-induced paranematic phase has only been reported for prolate molecules, but for oblate molecules, field-induced splitting of the order parameter has been reported.     

双轴晶体光轴角的计算

通过坐标变换把折射率椭球方程x~2/n_1~2 y~2/n_2~2 z~2/n_3~2=1从主介电坐标系Oxyz转换到另一个新的坐标系Ox′y′z′中,这个新的坐标系Ox′y′z′可以通过将坐标系Oxyz绕原点旋转得到.只要使新的折射率椭球方程与x′y′平面的交线是一个圆,就可以确定z′轴就是晶体的光轴.由此得出了双轴晶体光轴角的计算公式.     

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.     

Temperature dependence of ratio between dielectric anisotropy and order parameter in fluorinated nematic liquid crystals

Temperature dependence of ratio between dielectric anisotropy and order parameter of fluorinated nematic liquid crystal is investigated by using a semi-empirical molecular orbital package that can accurately calculate an angle between molecular dipole moment and long axis. We optimize the molecular conformations with three semi-empirical Hamiltonians AM1, PM3 and PM5, and then make a comparison between computational results and experimental measurements. It is shown that the results obtained from AM1 method are in good agreement with the measurements. The present study offers an applicable method to predict the dielectric properties of liquid crystal material.     

Temperature dependence of ratio between dielectric anisotropy and order parameter in fluorinated nematic liquid crystals

Temperature dependence of ratio between dielectric anisotropy and order parameter of fluorinated nematic liquid crystal is investigated by using a semi-empirical molecular orbital package that can accurately calculate an angle between molecular dipole moment and long axis. We optimize the molecular conformations with three semi-empirical Hamiltonians AM1, PM3 and PM5, and then make a comparison between computational results and experimental measurements. It is shown that the results obtained from AM1 method are in good agreement with the measurements. The present study offers an applicable method to predict the dielectric properties of liquid crystal material.     

向列相液晶中光学相位共轭技术的研究进展

对向列相液晶中光学相位共轭技术的研究进展进行了介绍,分析总结了向列相液晶中光学相位共轭过程的机理与实验方法,并对向列相液晶中的光学相位共轭技术的应用前景进行了展望。     

Emergent biaxiality in nematic microflows illuminated by a laser beam

Anisotropic fluids (e.g. liquid crystals) offer a remarkable promise as optofluidic materials owing to the directional, tunable, and coupled interactions between the material, flow, and the optical fields. Here we present a comprehensive in silico treatment of this anisotropic interaction by performing nonequilibrium molecular dynamics simulations. We quantify the response of a nematic liquid crystal (NLC) undergoing a Poiseuille flow in the Stokes regime, while being illuminated by a laser beam incident perpendicular to the flow direction. We adopt a minimalistic model to capture the interactions, accounting for two features: first, the laser heats up the NLC locally; and second, the laser polarises the NLC and exerts an optical torque that tends to reorient molecules of the nematic phase. Because of this reorientation the liquid crystal exhibits small regions of biaxiality, where the nematic director is one symmetry axis and the axis of rotation for the reorientation of the molecules is the other one. We find that the relative strength of the viscous and the optical torques mediates the flow-induced response of the biaxial regions, thereby tuning the emergence, shape and location of the regions of enhanced biaxiality. The mechanistic framework presented here promises experimentally tractable routes toward novel optofluidic applications based on material-flow-light interactions.     

Comparison of optical compensations based on discotic liquid crystals with linear and non-linear orientation for wide viewing angle twisted nematic liquid crystal displays

Optical compensation film using discotic liquid crystals has been commercialized to suppress light leakage of twisted nematic (TN) liquid crystal (LC) cells in the dark state when the viewing directions are off-axes. In the conventional film, the tilt angle variation of the discotic LC layers is linear, whereas that of the rod-like LC layers in the TN cell is non-linear with twist alignment. We investigated the optical compensation effects in terms of iso-contrast ratio, gray scale inversion and color shift with linear and non-linear orientation in a tilt angle or twist and non-twist orientation on TN-LC cells. The results showed that the optical compensation with non-linear orientation exhibited an improved performance in suppressing light leakage in the dark state.     

Monte Carlo simulations of biaxial structure in thin hybrid nematic film based upon spatially anisotropic pair potential

Hybrid nematic films have been studied by Monte Carlo simulations using a lattice spin model, in which the pair potential is spatially anisotropic and dependent on elastic constants of liquid crystals. We confirm in the thin hybrid nematic film the existence of a biaxially nonbent structure and the structure transition from the biaxial to the bent-director structure, which is similar to the result obtained using the Lebwohl--Lasher model. However, the step-like director's profile, characteristic for the biaxial structure, is spatially asymmetric in the film because the pair potential leads to K₁ ≠ K₃. We estimate the upper cell thickness to be 69 spin layers, in which the biaxial structure can be found.     

光在双轴晶体表面的反射与折射

介绍了光在双轴晶体表面反射、折射问题的求解方法.用该方法可以方便精确地计算晶体任意取向下光从任意方向入射时折射光的折射率、偏振态、波矢方向、能流方向. 推导了反射光、折射光的振幅和能量的计算公式. 并以KTP晶体为例，给出了数值计算的结果. 关键词： 双轴晶体 双折射 菲涅耳公式 布儒斯特角     

Chromonic liquid crystalline phase transition involving a biphasic region of nematic and hexagonal phases

We report the results of our studies on the optical and thermal properties of binary mixture of two compounds viz. abietic acid and poly ethylene glycol (PEG). The mixture shows a very interesting co-existent biphasic region of lyotropic nematic (N + I) and intermediate hexagonal (M + I) phases, sequentially when the specimen is cooled from its isotropic phase at different concentrations of abietic acid in PEG. The aggregated molecular size has been confirmed by X-ray studies. The temperature variation of optical anisotropy, electrical conductivity, ultrasonic velocity, and molar and adiabatic compressibility has also been discussed.     

Molecular orientation of lyotropic nematic phase in a mixture of two non-mesogenic compounds

We report the results of our studies on the optical and thermal properties of the mixture of two non-mesogenic compounds, namely, sodium dodecyl sulfate (SDS) and glacial acetic acid (GAA). The mixture exhibits very interesting schlieren texture of lyotropic micellar nematic (N_D) phase, SmA and SmB phases, respectively, at different concentrations of SDS in GAA sequentially when the specimen is cooled from its isotropic phase. The order parameter (S) of the lyotropic micellar nematic (N_D) phase is estimated with the help of temperature dependence of optical anisotropy from the measured values of refractive index and density data. The experimental curve showing the temperature variation of order parameter is very well fitted with the Mayer–Saupe theoretical curve. X-ray studies have also been discussed. The formation of the above phases has been confirmed by optical and differential scanning calorimetry studies.     

Orientational order parameters of a binary mixture showing both induced smectic and re-entrant nematic phases

The phase diagram of a new binary system of two polar nematic compounds, 4-cyanophenyl [4′ (4″-n-heptylphenyl)] benzoate(7CPB) and 4-cyanophenyl 4-nonylbenzoate (9.CN), shows the presence of both the induced smectic and re-entrant nematic phases in a certain concentration range 0.4 < x _9.CN < 0.87. The results of X-ray diffraction and density measurements are reported here. Orientational order parameters have been determined in the induced smectic, normal nematic and re-entrant nematic phases from X-ray diffraction measurements. The order parameters have been fitted to those calculated from modified McMillan's theory as proposed by Luckhurst and Timimi. The agreement is found to be closer to the modified model. The experimental variation of the layer thickness with mole fraction of 9.CN has also been explained fairly well by assuming the presence of two types of homo dimers (7CPB + 7CPB, 9.CN + 9.CN) and one type of hetero dimer (7CPB + 9.CN).     

Exposure and temperature dependences of contact angle of liquid crystals on photoaligning surface

We report on first studies of wetting of liquid crystal on photoaligning surface. We observed strong light-induced variations of a contact angle of a liquid LC 5CB on a photoaligning surface of fluoro-polyvinyl-cinnamate (PVCN-F) and we connected these variations with changes of PVCN-F polarity. We also present drastic changes of the contact angle of a nematic liquid crystal (MLC-6080) on the PVCN-F surface in a vicinity of temperature anchoring transition of liquid crystal from homeotropic orientation to planar one. We did not find any peculiarities in temperature dependence of the contact angle of isotropic liquid (glycerol) on PVCN-F and of nematic liquid crystal on pure glass in the same temperature range. It allows us to suggest that rearrangement of LC molecules and flexible fragments in the LC-polymer interface are responsible for the change of surface tensions both of LC and polymer and the observed jump of the contact angle.     

Temperature dependence of biaxial strain and its influence on phonon and band gap of GaN thin film

Hexagonal GaN epilayer grown on sapphire substrate by metal organic chemical vapour deposition (MOCVD) is studied using Raman scattering and photoluminescence in a temperature range from 100\,K to 873\,K. The model of strain (stress) induced by the different lattice parameters and thermal coefficients of epilayer and substrate as a function of temperature is set up. The frequency and the linewidth of $E_2^{\rm high}$ mode in a GaN layer are modelled by a theory with considering the thermal expansion of the lattice, a symmetric decay of the optical phonons, and the strain (stress) in the layer. The temperature-dependent energy shift of free exciton A is determined by using Varshni empirical relation, and the effect of strain (stress) is also investigated. We find that the strain in the film leads to a decreasing shift of the phonon frequency and an about 10meV-increasing shift of the energy in a temperature range from 100\,K to 823\,K.