Mean-Field Limit and Phase Transitions for Nematic Liquid Crystals in the Continuum

We discuss thermotropic nematic liquid crystals in the mean-field regime. In the first part of this article, we rigorously carry out the mean-field limit of a system of N rod-like particles as \(N\rightarrow \infty \), which yields an effective ‘one-body’ free energy functional. In the second part, we focus on spatially homogeneous systems, for which we study the associated Euler–Lagrange equation, with a focus on phase transitions for general axisymmetric potentials. We prove that the system is isotropic at high temperature, while anisotropic distributions appear through a transcritical bifurcation as the temperature is lowered. Finally, as the temperature goes to zero we also prove, in the concrete case of the Maier–Saupe potential, that the system converges to perfect nematic order.     

EPR Investigations on Molecular Orientation of Paramagnetic Liquid Crystals in a Surface-Stabilized Liquid Crystal Cell: Studies on a Smectic C or Chiral Smectic C Phase

By electron paramagnetic resonance spectroscopy we investigated the molecular orientation in a surface-stabilized liquid crystal (LC) cell, which includes a racemic (±) or an enantiomerically enriched (S,S) paramagnetic LC, (2S,5S)-2,5-dimethyl-2-tridecyloxyphenyl-5-[4-(4-tridecyloxy-benzenecarbonyloxy)phenyl]pyrrolidine-1-oxy (2), whose spin source is fixed inside the rigid core. For both the smectic C (SmC) phase of (±)-2 and the chiral smectic C (SmC^*) phase of (S,S)-2 in a surface-stabilized LC cell (antiparallel configuration, thickness of 4 μm), the profile of the observed g-value as a function of the angle between the applied magnetic field and the cell plane could be explained by the orientation model, where, with some disordering, the molecules align uniformly with the direction which tilts from the normal line of the smectic layer being orthogonal to the rubbing direction on the cell surface. We divided the effect from the disordering into two parts, one of which is concerning the direction of the molecular long axis and the other is concerning the rotation around the molecular long axis. As a result of the analysis, the SmC^* phase gave quite lower ordering concerning the direction of the molecular long axis and a little lower ordering concerning the rotation around the molecular long axis than the SmC phase at the same temperature (80 °C). The obtained lower ordering in the SmC^* phase is probably due to the chirality that would result in the formation of a helical superstructure in a bulky state. Authors' address: Yohei Noda, Laboratory of Electron Spin Chemistry, Department of Chemistry, Graduate School of Science, Kyoto University, 606-8502 Kyoto, Japan     

Phase Conjugation by Degenerate Four-wave Mixing in Nematic Liquid Crystals

1.IntroductionOpticalphaseconjugationhasbeeninvestigatedextensivelybecauseofitswideapplicationsinimagingtechnology,phase--conjugationlasers,andopticalassociativememorysystems.Notedfortheirlargeopticalreorientationnonlinearities[IJ,nematicliquidcrystals(NLC)havebecomepromisingopticalmediaforapplicationsinthefieldofnonlinearopticsincludingnonlinearphaseconjugation.In1980,Feketectal.[2)firstrealizedphase--conjugationbydegeneratefour--wavemixing(DFWM)inNLCintheisotropicphase.Sincethen,thefie…     

Phase Controlled Laser Interference for Tunable Phase Gratings in Dye-Doped Nematic Liquid Crystals

A phase controlled multi-beam interference is applied to excite the doped liquid crystals. Control of the phase difference between the exciting beams allows the external control of the interference pattern inside the liquid crystal. The dynamic variation of the grating is made possible with a time-dependent phase change to derive the nonlinear refractive index as well as the responding speed of the material. The induced grating structure is numerically modelled with reorientational phase gratings in the liquid crystal, and the diffraction dynamics is found to be in good agreement between theoretical and experimental results.     

Carbon Nanoparticles in Nematic Liquid Crystals

Fullerene C60, C7o, single-walled and multi-walled carbon nanotubes and graphene sheets are doped to nematic liquid crystal （LC） host in the same percentage. Planar samples of these mixtures are prepared and our measurements constitute an optimization basis for possible applications. Fullerene balls are found to be the best compatible material for optical aims and reorientation of LC molecules, while the carbon nanotubes experience some reorientation possibility in LC media and graphene layers are good barriers to preserve reorientation.     

Two-Dimensional Spatial Solitons in Nematic Liquid Crystals

We study the propagation of spatial solitons in nematic liquid crystals, using the self-similar method. Analytical solutions in the form of self-similar solitons are obtained exactly. We confirm the stability of these solutions by direct numerical simulation, and find that the stable spatial solitons can exist in various forms, such as Oaussian solitons, radially symmetric solitons, multipole solitons, and soliton vortices.     

Stability of Disclinations in Nematic Liquid Crystals

In the light of φ-mapping method and topological current theory, the stability of disclinations around a spherical particle in nematic liquid crystals is studied. We consider two different defect structures around a spherical particle: disclination ring and point defect at the north or south pole of the particle. We calculate the free energy of these different defects in the elastic theory. It is pointed out that the total Frank free energy density can be divided into two parts. One is the distorted energy density of director field around the disclinations. The other is the free energy density of disclinations themselves, which is shown to be concentrated at the defect and to be topologically quantized in the unit of (k-k₂₄)π/2. It is shown that in the presence of saddle-splay elasticity a dipole (radial and hyperbolic hedgehog) configuration that accompanies a particle with strong homeotropic anchoring takes the structure of a small disclination ring, not a point defect.     

双轴向列相液晶的Monte Carlo模拟

利用Monte Carlo方法模拟棒状液晶分子随温度变化的相变行为,采用热力学统计方法得到能量与温度的关系,得出比热随温度的变化规律,通过图像的峰值确定相变点;重点模拟计算序参数矩阵元与温度的关系,得到不同分子结构参数下液晶系统的温度相图,模拟结果显示,当两个短棒长度相等时,不存在双轴相.     

QCD手征相变中的π介子增强(英文)

讨论了在LHC的Pb-Pb碰撞过程中,如果QGP SU(2)手征相变出现二级相变,那么系统将会有π弦产生,并且π弦最终将衰变为π介子。于是以上效应将导致在低动量区域（p~150—400 MeV）内的π介子增强。对应于不同的冷却温度T_f=130,120,110 MeV,产生于π弦衰变的π介子的数量分别是Nt≈270,150, 60. It is pointed out that if the QGP SU(2) chiral phase transition in the LHC Pb Pb collision process is taken place and the phase transition is in the second order, then pion strings will be formed, and decay. These phenomena lead to the pion enhancement in the low momentum region(p150—400 MeV) and the number of pions produced from pion string decay can be estimated about Nt≈270, 150, 60 for different freeze temperature Tf=130, 120, 110 MeV respectively.     

Nucleation of Topological Dipoles¶in Nematic Liquid Crystals

A topological dipole is a pair of point defects with opposite topological charges. In this paper we show by example how the nucleation of such a dipole within a smooth field can drive a metastable state into a stable one. Building on our previous work, we construct a mathematical model for the dynamics of both monopoles and dipoles in a capillary filled with a nematic liquid crystal. Though our analysis is fit for liquid crystals, a similar mechanism is also likely to apply to the field theory for other ordered media. Received: 10 July 1997 / Accepted: 25 June 1998     

Phase Transitions in Ionic Crystals under Ultrahigh Pressures

Structural phase transitions induced in alkali-halide crystals by an ultrahigh pressure are investigated. The pressure of the B1–B2 transition in an infinite crystal is calculated with the use of ion pair interaction potentials obtained by the self-consistent method in the context of nonuniform electron gas theory. In the approximation of seven coordination spheres, relative changes in volumes of B1 and B2 modifications of a number of alkali-halide crystals are calculated.     

Structural Transformations in Nematic Liquid Crystals with a Hybrid Orientation

Journal of Experimental and Theoretical Physics - The structural transformations in a nematic liquid crystal (NLC) layer with a hybrid orientation (planar director orientation is created on one...     

The Structural Transitions in Liquid Crystals Doped with Fine Magnetic Particles

The stable ferronematics and ferrosmectics (combination of liquid crystals with fine magnetic particles) were prepared for 8CB liquid crystal and magnetc particles 11 nm in diameter. The structural transitions i.e. magnetic Fredericksz transition were indicated by means of dielectric and conductivity measurements.The experimental results i.e. the proof of initial condition ( is director of LC molecules and is magnetic moment of particles) and the increase of the threshold field of Fredericksz transition vs volume conduction of magnetic particles are in qualitative agreement with the Burylov and Raikher theory of thermotropic ferronematics.     

Forced Synchronization of Electroconvective Roll Oscillations in Nematic Liquid Crystals

The forced phase locking in a system of the oscillating electroconvective rolls that form in a nematic liquid crystal layer in a dc electric field is studied. As a result of the action of an additive ac electric field with a small amplitude, the system of oscillators is found to be divided into clusters, where oscillations are fully phase locked. The electroconvective rolls in neighboring clusters oscillate in antiphase and the clusters are separated by Ising walls. The phase locking is shown to be maximal at the forcing frequency that is close to the double frequency of the natural oscillations of rolls. A model is proposed to describe spatially distributed phase oscillators, and it takes into account the symmetries of a system of electroconvective rolls and external forcing. The results of numerical simulations agree well with the experimental data.     

Ultrasound and Orientational Relaxation of Nematic Liquid Crystals at High Pressures

Acoustic properties of the anisotropic phase of N-96 nematic crystals and its solutions with benzene in a rotational magnetic field are investigated. Time dependences of the ultrasound absorption anisotropy on the concentration, temperature, pressure, and magnetic field rotation frequency are investigated. Values of the critical frequency and its dependence on the state parameters (P, T) are experimentally determined. The rotational viscosity ratios of the diamagnetic susceptibility anisotropy are calculated and the character of their temperature and pressure dependences is established. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 82–84, May, 2005.     

Remarks on Dynamics of the Freedericksz Transition in Nematic Liquid Crystals

An improved discussion on the dynamics of the Freedericksz transition in nematics is proposed. It is pointed out that the relaxation time γ^-1 of the directors follows, an a²(a - 1) law in the twist deformation case. The possible chaotic motion of the directors in an external field ia briefly discussed.     

侧链型液晶聚合物对手性向列相液晶螺旋结构的影响研究

通过改变表面的锚定条件,可以在不借助外部条件的情况下获得热力学稳定态的长程有序的螺旋结构.通过调节沉积在硅晶片上的液晶聚合物[6-(4-甲氧基-偶氮苯-4'-氧基)甲基丙烯酸乙酯](PMMAZO)的接枝密度来调节表面锚定,从而实现对螺旋结构的螺距和螺旋方向的准确控制.随着接枝密度的增加,螺旋结构的倾斜变形增加,螺距的大...