Theory of nine elastic constants of biaxial nematics

In this paper, a rotational invariant of interaction energy between two biaxial-shaped molecules is assumed and in the mean field approximation, nine elastic constants for simple distortion patterns in biaxial nematics are derived in terms of the thermal average （Dmn^（l）） （Dm＇n＇^（l＇））, where Dmn^（l） is the Wigner rotation matrix. In the lowest order terms, the elastic constants depend on coefficients Γ,Γ＇, λ, order parameters Q0 = Q0（D00^（2）） ＋Q2（D02^（2）＋D0-2^（2）） and Q2 = Q0（D20^（2）） ＋ Q2（D22^（2）＋D2-2^（2））. Here Γ and Γ＇ depend on the function form of molecular interaction energy vj′j″j （τ12） and probability function fk′k″k （τ12）, where r12 is the distance between two molecules, and λ is proportional to temperature. Q0 and Q2 are parameters related to multiple moments of molecules. Comparing these results with those obtained from Landau-de Gennes theory, we have obtained relationships between coefficients, order parameters used in both theories. In the special case of uniaxial nematics, both results are reduced to a degenerate case where K11=K33.

Dielectric anisotropy in liquid crystal mixtures with nematic and smectic phases

The modulation of dielectric anisotropy(△ε)is pivotal for elucidating molecular interactions and directing the alignment of liquid crystals.In this study,we combine liquid crystals with opposing dielectric anisotropies to explore the impact of varying concentrations on their properties.We report the sign-reversal of△εin both the nematic and smectic A phases of these mixed liquid crystals,alongside a dual-frequency behaviour across a broad temperature spectrum.Our research further quantifies the influence of mixture ratios under various temperatures and electric field frequencies.This exploration may pave the way for the discovery of new physical phenomena.

THE EXISTENCE AND UNIQUENESS OF TIME-PERIODIC SOLUTIONS TO THE NON-ISOTHERMAL MODEL FOR COMPRESSIBLE NEMATIC LIQUID CRYSTALS IN A PERIODIC DOMAIN

In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.

ENERGY CONSERVATION FOR THE WEAK SOLUTIONS TO THE 3D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOW

In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain.

Buckling morphology of glassy nematic films with staggered director field

The photo-induced buckling of axially periodic glassy nematic films with alternating stripped director domains is explored by the F¨oppl-von K′arm′an plate theory along with a modified kinetics approach.The effects of domain widths on the critical light intensity as well as the buckling morphology are examined numerically.It is found that in most cases the buckled film forms regularly aligned dimples and protrusions,but shows large scale bending perpendicular to the periodic axis if the widths of the stripes are nearly the same.In addition,change in light intensity is shown to alter the wavenumber of the buckling pattern.These results are expected helpful to the design of shape-shifting structures with glassy nematic films.

STUDY ON LIQUID CRYSTAL POLYMERS WITH TWO-DIMENSIONAL MESOGENIC UNITS

A series of liquid crystalline polymers with two-dimensional mesogenic units were synthesized by solution polycondensation at low temperature. All the polymers were liquid crystalline. The melting temperature T;（except that with substituent of methoxy） and the clearing temperature T;of the polymers change regularly with varying of the length of the alkyl substituent groups.

液晶材料

介绍了液晶材料的发展状况和种类,并对液晶材料在显示领域的应用做了具体的概述。其中含氟液晶、环己烷类液晶、乙烷类液晶因其极性低,分子粘度低,电阻率高,电压保持率高,从而在TFT-LCD中得到了广泛的应用。

SYNTHESIS AND CHARAOTERIZATION OF NOVEL THERMOTROPIO LIQUID ORYSTALLINE POLYESTERS BEARING NONLINEAR OPTICAL AZOBENZENE SIDE GROUP

A series of novel thermotropic liquid crystalline polyesters bearing nonlinear optical azobenzene side group were synthesized by high temperature solution polycondensation and their structures,thermal stability, phase transition behavior and crystallinity were characterized by IR,elemental analysis, TG-DTA, polarizing optical microscope (POM) equipped with a hot stage and X-ray diffraction techniques. The results demonstrate that all the synthesized polyesters exhibit nematic liquid crystalline phases and show relatively high glass transition temperatures and good thermal stability.

GLOBAL EXISTENCE OF WEAK SOLUTIONS TO THE NON-ISOTHERMAL NEMATIC LIQUID CRYSTALS IN 2D

In this article, we prove the global existence of weak solutions to the non- isothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance. It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many ＂singular＂ times, at which the energy concentration occurs and the director field losses its second order derivatives.

Determining the sum of flexoelectric coefficients in nematic liquid crystals by the capacitance method

A detailed theoretical analysis of determining the sum of flexoelectric coefficients in nematic liquid crystals using the capacitance method is given. In the strong anchoring parallel aligned nematic （PAN） and hybrid aligned nematic （HAN） cells, the dependences of the capacitance on the sum of flexoelectric coefficients and the applied voltage are obtained by numerical simulations, and the distributions of the director and the electric potential for different applied voltages and flexoelectric coefficients are also given. Based on this theoretical analysis, we propose an experimental design for measuring the capacitance of a liquid crystal cell using the improved precision LCR meter E4980A （Agilent）. Through comparing the experimental data with the simulated results, the sum of flexoeletric coefficients can be determined.

STUDIES ON THE NATURE OF THE MACROMOLECULAR CONDENSED STATE OF "NASCENT" ULTRA HIGH MOLAR MASS POLYETHYLENE

Ultra high molar mass polyethylene(UHPE)powder as polymerized in a slurry process has been studied,in its nascent state,after recrystallization on rapid cooling from the melt and after hot compression molding to a film,by DSC,effect of annealing the recrystallized specimen at 120 similar to 130 degreesC,morphology by polarizing optical microscopy and small angle X-ray scattering.Based on the experimental results obtained the macromolecular condensed state of the nascent UHPE powder is a rare case of a multi-chain condensed state of non-interpenetrating chains,involving interlaced extended chain crystalline layers and relaxed parallel chain amorphous layers.On melting,a nematic rubbery state of nanometer size domain resulted.The nematic-isotropic transition temperature was judged from literature data to be at least 220 degreesC,possibly higher than 300 ℃,the exact temperature is however not sue because of chain degradation at such high temperatures.The recrystallization process from the melt is a crystallization from a nematic rubbery state.The drop of remelting peak temperature by 10 K of the specimen recrystallized from its melt as compared to the nascent state has its origin in the decrease both of the crystalline chain stem length and of the degree of crystallinity.The remelting peak temperature could be returned close to that of the nascent state by annealing at 120~130 ℃.

Magnetic-Field-Induced Weak Order in Nematic Liquid Crystals Formed by Biaxial Molecules

Nematic liquid crystal system of interacting biaxial particles via dispersion forces is studied.The molecular orienting potential form in a magnetic field is given for the first time.Weakly ordered isotropic phase is treated in the two-particle cluster approximation.Taking account of the molecular biaxiality,it is found that the ratio of the lowest supercooling temperature T^(*)to the nematic-isotropic phase transition temperature TC approaches the observed value,and the validity of the mean field theory is clarified.

Nonlinear analysis of photo-induced wrinkling of glassy twist nematic films on compliant substrates

A kinetics approach is developed for the geometrically nonlinear analysis of photo-induced wrinkling of glassy twist nematic films on soft elastic substrates.In this way,the problem is reduced to finding the steady state of an overdamped evolution system according to a kinetic law,rather than directly solving the coupled nonlinear equations.This enables one to account for the complicated director distribution and obtain the precise wrinkling morphology of the film.Though the approach proposed here is for a twist nematic film,it can be extended to study glassy nematic films with other director distributions.

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE COMPRESSIBLE NEMATIC LIQUID CRYSTAL SYSTEM IN R3

In this paper,we study a nematic liquid crystals system in three-dimensional whole space R3 and obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis and energy estimates if the initial data belongs to L1（R3） additionally.

LPS'S CRITERION FOR INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

In this paper we derive LPS＇s criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in R^3. We show that if 0 〈 T 〈 ＋∞ is the maximal time interval for the unique smooth solution u ∈ C^∞（[0, T）,R^3）,then ｜u｜＋｜△d｜∈L^q（[0,T],L^p（R^3））,where p and q satisfy the Ladyzhenskaya-Prodi-Serrin＇s condition：3/p＋2/q=1 and p∈（3,＋∞].

Phenomenological description of semi-soft nematic elastomers

Nematic elastomers are new materials that have many remarkable properties.In this article,we study how nonlinear elasticity of semi-soft nematic elastomers can be described phenomenologically.We start with a theory based on strain tensor only,and then continue to develop a phenomenological description with the liquid crystal order tensor included explicitly.Such a description has the virtue of being able to treat the strain tensor and the liquid crystal order tensor equally and thus making the complicated symmetries of nematic elastomers easier to understand.

Synthesis and mesomorphic behavior of benzothiazole-based liquid crystals having terminal methoxyl group

A homologous series of benzothiazole derivatives, 6-methoxy-2-（4-alkanoyloxybenzylidenamino）benzothiazoles, were synthesized and characterized using FT-IR, ^1H and ^13C NMR, mass spectrometry and elemental analysis. Enantiotropic nematic phase was observed throughout the entire series. Smectic C phase only emerged from the decanoyloxy derivative onwards. The terminal methoxyl group and the ester linkage influenced the mesomorphic behavior of the present series.

Flexoelectric-Induced Voltage Shift in Hybrid Aligned Nematic Liquid Crystal Cell

Flexoelectric-induced voltage shift in a weak anchoring hybrid aligned nematic fiquid crystai cell is investigated theoretically. Based on the elastic theory of liquid crystal and the variation method, the equations for the bulk and the boundary of the cell are derived. By computer simulation, the dependence of the shift voltage on the sum of the ttexoelectric coefficients and the anchoring energy strength is obtained. As a result, a novel method to determine the sum of the flexoelectric coefficients by measuring the shift voltage is put forward.

STABILITY OF EQUILIBRIA OF NEMATIC LIQUID CRYSTALLINE POLYMERS

We provide an analytical study on the stability of equilibria of rigid rodlike nematic liquid crystalline polymers （LCPs） governed by the Smoluchowski equation with the Maier-Saupe intermolecular potential. We simplify the expression of the free energy of an orientational distribution function of rodlike LCP molecules by properly selecting a coordinate system and then investigate its stability with respect to perturbations of orientational probability density. By computing the Hessian matrix explicitly, we are able to prove the hysteresis phenomenon of nematic LCPs： when the normalized polymer concentration b is below a critical value b＊ （6.T314863965）, the only equilibrium state is isotropic and it is stable; when b＊ 〈 b 〈 15/2, two anisotropic （prolate） equilibrium states occur together with a stable isotropic equilibrium state. Here the more aligned prolate state is stable whereas the less aligned prolate state is unstable. When b 〉 15/2, there are three equilibrium states： a stable prolate state, an unstable isotropie state and an unstable oblate state.

BLOW-UP CRITERION OF CLASSICAL SOLUTIONS FOR THE INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

In this paper, we consider the short time classical solution to a simplified hydro-dynamic flow modeling incompressible, nematic liquid crystal materials in R3. We establisha criterion for possible breakdown of such solutions at a finite time. More precisely, if （u, d）is smooth up to time T provided that ∫T 0‖△×u（t, ·）‖BMO（R3） ＋‖△d（t, ·）‖8L4（R3）dt 〈∞.