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.

WEAK-STRONG UNIQUENESS FOR THREE DIMENSIONAL INCOMPRESSIBLE ACTIVE LIQUID CRYSTALS

The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data.

SYNTHESIS AND CHARACTERIZATION OF LIQUID CRYSTAL POLYMERS WITH T-SHAPED TWO-DIMENSIONAL MESOGENIC UNITS (Ⅱ)

A series of liquid crystalline polymers with T-shaped two-dimensional mesogenic unitswere synthesized via low temperature solution polycondensation of 2-(4'-alkoxy-phenyl)hydroquinone with various diacyl dichlorides. The polymers were found to be nematic andshown thermotropic liquid crystalline behaviors through observations using DSC, polarizedmicroscopy and X-ray diffraction. The melting temperature T_m and the isotropizationtemperature T_i of the polymers change regularly with varying of the monomer structures.

SYNTHESIS AND CHARACTERIZATION OF LIQUID CRYSTAL POLYESTERS WITH T-SHAPED TWO-DIMENSIONAL MESOGENIC UNITS(Ⅲ)

A new series of liquid crystal polyesters with T-shaped two-dimensional mesogenic units weresynthesized by melt polycondensation of the diacetates of 2-(4'-alkoxy -phenyl)-hydroquinones with 4,4'-alkylenedioxydibenzoic acid. The polymers were characterized by using polarized microscopy, DSC and X-ray diffraction. It was realized that all the polymers have nematic thermotropic liquid crystallinecharacteristics. The melting temperature (T_m) and isotropization temperature (T_i) of the polymers changeregularly with varying lengths of the alkoxy side group and the length of the alkylene group in the main chainin company with an even-odd effect. The mesophase temperature range also varies regularly with the polymerstructure. It is shown that the mesophase range has been widened.

SYNTHESIS AND CHARACTERIZATION OF LIQUID CRYSTAL POLYMERS WITH T-SHAPED TWO-DIMENSIONAL MESOGENIC UNITS

Two series of new liquid crystalline polymers with T-shaped two-dimensional mesogenic units were synthesized by low temperature solution polycondensations of 4-substituted N-2, 5-dihydroxybenzylidene aniline monomers with different diacyl dichlorides. The polymers were found to be nematic and shown liquid crystalline behavior. The melting temperature T-m and the clearing temperature T-i of the polymers change regularly with varying of the monomer structures.

SYNTHESIS OF LIQUID CRYSTALLINE COPOLYESTERS WITH T-SHAPED TWO-DIMENSIONAL MESOGENIC UNIT AND CROWN ETHER CYCLE

A novel series of liquid crystalline copolyesters with T-shaped two-dimensional mesogenic unit and crown ether cycle of cis-4,4′-bis(4-hydroxyphenylazo)dibenzo-18-crown-6 was prepared via solution condensation polymerization from 4,4′-(α,ω-hexanedioyloxy)dibenzoyl dichloride(M_1),2-(4′-ethoxyphenyl)hydroquinone(M_2)and cis-4,4′-bis(4- hydroxyphenylazo)dibenzo-18-crown-6(M_3).The molecular weights of copolyesters are not high,and the intrinsic viscosity [η]of copolyesters ranges from 0.29-0.43.The monomers ...

Multi-dimensional multiplexing optical secret sharing framework with cascaded liquid crystal holograms

Secret sharing is a promising technology for information encryption by splitting the secret information into different shares.However,the traditional scheme suffers from information leakage in decryption process since the amount of available information channels is limited.Herein,we propose and demonstrate an optical secret sharing framework based on the multi-dimensional multiplexing liquid crystal(LC)holograms.The LC holograms are used as spatially separated shares to carry secret images.The polarization of the incident light and the distance between different shares are served as secret keys,which can significantly improve the information security and capacity.Besides,the decryption condition is also restricted by the applied external voltage due to the variant diffraction efficiency,which further increases the information security.In implementation,an artificial neural network(ANN)model is developed to carefully design the phase distribution of each LC hologram.With the advantage of high security,high capacity and simple configuration,our optical secret sharing framework has great potentials in optical encryption and dynamic holographic display.

Liquid crystal-integrated metasurfaces for an active photonic platform

Metasurfaces have opened the door to next-generation optical devices due to their ability to dramatically modulate electromagnetic waves at will using periodically arranged nanostructures.However,metasurfaces typically have static optical responses with fixed geometries of nanostructures,which poses challenges for implementing transition to technology by replacing conventional optical components.To solve this problem,liquid crystals(LCs)have been actively employed for designing tunable metasurfaces using their adjustable birefringent in real time.Here,we review recent studies on LCpowered tunable metasurfaces,which are categorized as wavefront tuning and spectral tuning.Compared to numerous reviews on tunable metasurfaces,this review intensively explores recent development of LC-integrated metasurfaces.At the end of this review,we briefly introduce the latest research trends on LC-powered metasurfaces and suggest further directions for improving LCs.We hope that this review will accelerate the development of new and innovative LC-powered devices.

Dptic properties of bile liquid crystals in human body

AIM To further study the properties of bileliquid crystals,and probe into the relationshipbetween bile liquid crystals and gallbladderstone formation,and provide evidence for theprevention and treatment of cholecystolithiasis.METHODS The optic properties of bile liquidcrystals in human body were determined by themethod of crystal optics under polarizingmicroscope with plane polarized light andperpendicular polarized light.RESULTS Under a polarizing microscope withplane polarized light,bile liquid crystalsscattered in bile appeared round,oval orirregularly round.The color of bile liquidcrystals was a little lighter than that of the bilearound.When the stage was turned round,thecolor of bile liquid crystals or the darkness andlightness of the color did not change obviously.On the border between bile liquid crystals andthe bile around,brighter Becke-Line could beobserved.When the microscope tube is lifted,Becke-Line moved inward,and when lowered,Becke-Line moved outward.Under aperpendicular polarized light,bile liquid crystalsshowd some special interference patterns,called Malta cross.When the stage was turninground at an angle of 360°,the Malta cross showed four times of extinction.In the vibratingdirection of 45° angle of relative to upper andlower polarizing plate,gypsum test-board withoptical path difference of 530 nm was inserted,the first and the third quadrants of Malta crossappeared to be blue,and the second and thefourth quadrants appeared orange.When micatest-board with optical path difference of 147 nmwas inserted,the first and the third quadrants ofMalta cross appeared yellow,and the secondand the fourth quadrants appeared dark grey.CONCLUSION The bile liquid crystals weredistributed in bile in the form of global grains.Their polychroism and absorption were slight,but the edge and Becke-Line were very clear.Itsrefractive index was larger than that of the bile.These liquid crystals were uniaxial positivecrystals.The interference colors were the firstorder grey-white.The double refractive index ofthe liquid crystals was △n=0.011-0.015.

Synthesis and characterization of non-symmetrical liquid crystals containing a cholesteryl ester moiety

In this paper, a series of chiral non-symmetrical liquid crystals （nBA-chol） consisting of a cholesteryl ester moiety as chiral entity and a biphenyl aromatic core with different terminal alkyl chain has been synthesized and investigated for their liquid crystalline properties. Effects of numbers of methylene units in the terminal alkyl chain on the phase transition temperatures and on the temperature-dependent pitch lengths of the chiral liquid crystals have been studied. The long terminal alkyl chain tends to exhibit smectic A mesophases. The pitch lengths of the cholesteric mesophases of the chiral liquid crystals decrease with increasing temperature and with increasing numbers of methylene units in the terminal alkyl chain, respectively.

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.

Facile synthesis and characterization of novel thermo-chromism cholesteryl-containing hydrogen-bonded liquid crystals

Two series of novel cholesteryl-containing H-bonded liquid crystals were prepared through facile self-assembly between cholesteryl isonicotinate （proton acceptor） exhibiting a monotropic cholesteric phase, and the 4-alkoxy-benzoic acid or 4-alkoxy cinnamic acid （proton donor）. It was found that the increase of the conjugate length as well as the terminal length can contribute to enhance the interaction of molecules and thus significantly influenced the thermal behaviors of H-bonded LCs. The cholesteric reflection spectra of the induced mesogenic complexes were located in the visible region with the color tuneable thermo-sensitivity, which could be used for display application.

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.

High-Resolution Heat Transfer Coefficients Measurement for Jet Impingement Using Thermochromic Liquid Crystals

A high-resolution testing technique named liquid crystal thermography is used for the experimental study on jet array impingement to map out the distribution of heat transfer coefficients on the cooling surface. Effects of the impingement distance, the impinging hole arrangement and the initial crossflow on heat transfer characteristics are investigated. The thermal images show truly the features of local heat transfer for each jet impingement cooling. The applications of thermochromic liquid crystal are successful in the qualitative and quantitative measurement for heat transfer coefficients distribution.

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.

Liquid crystal droplets formation and stabilization during phase transition process

The study of phase transition processes in liquid crystals(LCs)remains challenging.Most thermotropic LCs exhibit a narrow temperature range and a rapid phase transition from the isotropic(ISO)to the nematic(N)phase,which make it difficult to capture and manipulate the phase transition process.In this study,we observed the evolution of small droplets during the ISO–N phase transition in ferroelectric nematic(NF)LC RM734.After doping with metal nanoparticles(NPs),the temperature range of the phase transition broadened,and the droplets formed during the phase transition remained stable,with their diameter increasing linearly with temperature.In addition,droplets doped with NPs can be well controlled by an external electric field.This discovery not only aids in understanding the fundamental mechanisms of LC phase transitions but also provides a simple alternative method for preparing droplets,which is potentially valuable for applications in optoelectronic devices and sensors.

Stability analysis of a liquid crystal elastomer self-oscillator under a linear temperature field

Self-oscillating systems abound in the natural world and offer substantial potential for applications in controllers,micro-motors,medical equipments,and so on.Currently,numerical methods have been widely utilized for obtaining the characteristics of self-oscillation including amplitude and frequency.However,numerical methods are burdened by intricate computations and limited precision,hindering comprehensive investigations into self-oscillating systems.In this paper,the stability of a liquid crystal elastomer fiber self-oscillating system under a linear temperature field is studied,and analytical solutions for the amplitude and frequency are determined.Initially,we establish the governing equations of self-oscillation,elucidate two motion regimes,and reveal the underlying mechanism.Subsequently,we conduct a stability analysis and employ a multi-scale method to obtain the analytical solutions for the amplitude and frequency.The results show agreement between the multi-scale and numerical methods.This research contributes to the examination of diverse self-oscillating systems and advances the theoretical analysis of self-oscillating systems rooted in active materials.

LOW MACH NUMBER LIMIT OF A COMPRESSIBLE NON-ISOTHERMAL NEMATIC LIQUID CRYSTALS MODEL

In this paper, we study the low Mach number limit of a compressible nonisothermal model for nematic liquid crystals in a bounded domain. We establish the uniform estimates with respect to the Mach number, and thus prove the convergence to the solution of the incompressible model for nematic liquid crystals.

INCOMPRESSIBLE LIMIT OF A COMPRESSIBLE LIQUID CRYSTALS SYSTEM

This article is devoted to the study of the so-called incompressible limit for solutions of the compressible liquid crystals system. We consider the problem in the whole space R^N and a bounded domain of R^N with Dirichlet boundary conditions. Here we set the number of dimension N = 2 or 3.

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.