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.

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.

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.

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.

Singularity Formation forthe General Poiseuille Flow of Nematic Liquid Crystals

We consider the Poiseuille flow of nematic liquid crystals via the full Ericksen-Leslie model.The model is described by a coupled system consisting of a heat equation and a quasilinear wave equation.In this paper,we will construct an example with a finite time cusp singularity due to the quasilinearity of the wave equation,extended from an earlier resultonaspecial case.

Flat multifunctional liquid crystal elements through multi-dimensional information multiplexing

Flat optical elements have attracted enormous attentions and act as promising candidates for the next generation of optical components.As one of the most outstanding representatives,liquid crystal(LC)has been widely applied in flat panel display industries and inspires the wavefront modulation with the development of LC alignment techniques.However,most LC elements perform only one type of optical manipulation and are difficult to realize the multifunctionality and light integration.Here,flat multifunctional liquid crystal elements(FMLCEs),merely composed of anisotropic LC molecules with space-variant orientations,are presented for multichannel information manipulation by means of polarization,space and wavelength multiplexing.Specifically,benefiting from the unique light response with the change of the incident polarization,observation plane,and working wavelength,a series of FMLCEs are demonstrated to achieve distinct near-and far-field display functions.The proposed strategy takes full advantage of basic optical parameters as the decrypted keys to improve the information capacity and security,and we expect it to find potential applications in information encryption,optical anti-counterfeiting,virtual/augmented reality,etc.

A review of liquid crystal spatial light modulators:devices and applications

Spatial light modulators,as dynamic flat-panel optical devices,have witnessed rapid development over the past two decades,concomitant with the advancements in micro-and opto-electronic integration technology.In particular,liquid-crystal spatial light modulator(LC-SLM)technologies have been regarded as versatile tools for generating arbitrary optical fields and tailoring all degrees of freedom beyond just phase and amplitude.These devices have gained significant interest in the nascent field of structured light in space and time,facilitated by their ease of use and real-time light manipulation,fueling both fundamental research and practical applications.Here we provide an overview of the key working principles of LC-SLMs and review the significant progress made to date in their deployment for various applications,covering topics as diverse as beam shaping and steering,holography,optical trapping and tweezers,measurement,wavefront coding,optical vortex,and quantum optics.Finally,we conclude with an outlook on the potential opportunities and technical challenges in this rapidly developing field.

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.

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.

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.

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.

Synthesis and Characterization of Star-like Liquid Crystals Centered by Silicon

The synthesis and characterization of two new star-like liquid crystals are reported.They are made of a silicon core and four alkoxyazobenzene monomers in the periphery. Theirphase behaviors and the structures are determined by infrared absorption spectroscopy (IR),nuclear magnetic resonance spectroscopy (NMR), elemental analysis (EA), polarizing opticalmicroscope (POM) and differential scanning calorimetry (DSC).

Monodomain Liquid Crystals of Two-Dimensional Sheets by Boundary-Free Sheargraphy

Eliminating topological defects to achieve monodomain liquid crystals is highly significant for the fundamental studies of soft matter and building long-range ordered materials.However,liquid crystals are metastable and sensitive to external stimuli,such as flow,confinement,and electromagnetic fields,which cause their intrinsic polycrystallinity and topological defects.Here,we achieve the monodomain liquid crystals of graphene oxide over 30 cm through boundary-free sheargraphy.The obtained monodomain liquid crystals exhibit large-area uniform alignment of sheets,which has the same optical polarized angle and intensity.The monodomain liquid crystals provide bidirectionally ordered skeletons,which can be applied as lightweight thermal management materials with bidirectionally high thermal and electrical conductivity.Furthermore,we extend the controllable topology of two-dimensional colloids by introducing singularities and disclinations in monodomain liquid crystals.Topological structures with defect strength from−2 to+2 were realized.This work provides a facile methodology to study the structural order of soft matter at a macroscopic level,facilitating the fabrication of metamaterials with tunable and highly anisotropic architectures.

Bichromatic coherent random lasing from dye-doped polymer stabilized blue phase liquid crystals controlled by pump light polarization

In this paper,we investigate the bichromatic coherent random lasing actions from the dye-doped polymer stabilized blue phase liquid crystals.Two groups of lasing peaks,of which the full widith at half maximum is about 0.3 nm,are clearly observed.The shorter-and longer-wavelength modes are associated with the excitation of the single laser dye（DCM） monomers and dimers respectively.The experimental results show that the competition between the two groups of the lasing peaks can be controlled by varying the polarization of the pump light.When the polarization of the pump light is rotated from 0？to 90？,the intensity of the shorter-wavelength lasing peak group reduces while the intensity of the longer-wavelength lasing peak group increases.In addition,a red shift of the longer-wavelength modes is also observed and the physical mechanisms behind the red-shift phenomenon are discussed.

Synthesis and mesomorphic properties of fluorinated Schiff's base liquid crystals containing vinyl end groups

Three kinds of fluorinated Schiff＇s base esters, 4-allyloxy-2-X-6-X-benzoic acid 4-[（2, 3, 4-trifluorophenylimino）methyl]phenyl ester, where X=H or F, were synthesized and characterized. Their chemical structures were identified by Fourier transform infrared spectroscopy （FTIR） and ^1H nuclear magnetic resonance （^1H NMR）. Their mesomorphic properties were studied by polarized optical microscopy （POM） and differential scanning calorimetry （DSC）. It was found that all the three compounds exhibited enantiotropic nematic phases only. And their cleating point temperature and thermal range of mesophase decreased with the number of fluorine atoms on the rigid core of the compounds; while their melting point temperature showed no distinct regularity.

Phase behaviors of binary mixtures composed of electron-rich and electron-poor triphenylene discotic liquid crystals

Disk-like liquid crystals（DLCs） can self-assemble to ordered columnar mesophases and are intriguing onedimensional organic semiconductors with high charge carrier mobility.To improve their applicable property of mesomorphic temperature ranges,we exploit the binary mixtures of electronic donor-acceptor DLC materials.The electron-rich2,3,6,7,10,11-hexakis（alkoxy）triphenylenes（C4,C6,C8,C10,C12） and an electron-deficient tetrapentyl triphenylene-2,3,6,10-tetracarboxylate have been prepared and their binary mixtures have been investigated.The mesomorphism of the1：1（molar ratio） mixtures has been characterized by polarizing optical microscopy（POM）,differential scanning calorimetry（DSC）,and small angel x-ray scattering（SAXS）.The self-assembled monolayer structure of a discogen on a solid-liquid interface has been imaged by the high resolution scanning tunneling microscopy（STM）.The match of peripheral chain length has important influence on the mesomorphism of the binary mixtures.

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

在这篇论文，一系列 chiral 作为 chiral 实体和联本基由 cholesteryl 酉旨一半组成的非对称的液体晶体(nBA-chol ) 有不同终端烷基链的芳香的核心被综合了并且为他们的液体调查了水晶的性质。在阶段转变温度上并且在 chiral 液体晶体的温度依赖者沥青长度上的终端烷基链的甲又单位的数字的效果被学习了。长终端烷基链趋于展出近晶的 A 中央阶段。chiral 液体晶体的 cholesteric 中央阶段的沥青长度与增加温度并且与分别地在终端烷基链增加甲又单位的数字减少。

Cellulose-based Polymeric Liquid Crystals as a Biomimetic Modifier for Suppressing Protein Adsorption

A novel biomimetic protein-resistant modifier based on cellulose-based polymeric liquid crystals was described（PLCs）. Two types of PLCs of propyl hydroxypropyl cellulose ester（PPC） and octyl hydroxypropyl cellulose ester（OPC） were prepared by esterification from hydroxypropyl cellulose, and then were mixed with polyvinyl chloride and polyurethane to obtain composite films by solution casting, respectively. The surface morphology of PLCs and their composite films were characterized by polarized optical microscopy（POM） and scanning electron microscopy（SEM）, suggesting the existence of microdomain separation with fingerprint texture in PLC composite films. Water contact angle measurement results indicated that hydrophilicity of PLC/polymer composite films was dependent on the type and content of PLC as well as the type of matrix due to their interaction. Using bovine serum albumin（BSA） as a model protein, protein adsorption results revealed that PLCs with protein-resistant property can obviously suppress protein adsorption on their composite films, probably due to their flexible LC state. Moreover, all PLCs and their composites exhibited non-toxicity by MTT assay, suggesting their safety for biomedical applications.