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.

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.

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.

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.

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.

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.

Odd-even Effect on Liquid Crystalline Behavior for C_3-Cyclotriveratrylene(CTV) Derivatives Containing Alkoxies with Different Lengths as Peripheral Groups

A series of bowlic cyclotriveratrylenes（CTV） with peripheral groups with different lengths were synthesized.These compounds were investigated by diferential scanning calorimetry and hot stage coupled polarizing microscopy.Several CTV derivatives show thermotropic liquid crystalline properties.The experimental results of their thermotropic liquid crystalline behavior indicate that the clear points,the entropy changes of melting points,the crystallization temperatures,and their entropy changes all exhibited an evident odd-even effect except the melting points,which decreased monotonously with the increase of the length of the alkoxy groups.The parameter values of CTVs with even number carbon atoms were larger than those of CTVs with odd number.When the length of alkoxyl chains was even longer,a monotonous decrease occured.Nevertheless,in the case of the entropy changes of both melting points and crystallization temperatures,the effect was valid for all the six species,and therefore,the whole curves presented as a zig-zag form.

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.

Fixation for the helical structure of a glassy cholesteric liquid crystal reflective film

The planar texture of glassy cholesteric siloxane cyclic side-chain liquid crystals was fixed by quenching initially. Then the polymer network formed by the optically active polymerizable monomers imposed additional constraints on the motion of chain segments of the glassy liquid crystal and then further stabilized the molecule arrangement. A cholesteric liquid crystal film with stable optical properties was developed by this method.

MECHANICAL PERTURBATION INDUCED MOLECULAR ALIGNMENTS IN A SIDE-CHAIN LIQUID CRYSTALLINE POLYACETYLENE, POLY{10-[4-(4'-METHOXYPHENOXY-CARBOML)PHENOXYCARBONYL]-1-DECYNE}

A new liquid crystalline polyacetylene containing a phenyl benzoate mesogen (5) is synthesized,whose mesomorphic properties are found to be easily 'tunab1e' by simple mechanical perturbation. Thepolymerization of 10- [ 4 - (4' -methoxyphenoxycarbonyl )phenoxycarbonyl] - 1 -decyne (4 ) in itiated by theWCl_6-Ph_4Sn/dioxane complex yields polymer 5 with a M_w of 28400. The molecular structure of 5 ischaracterized by NMR, IR, and UV spectroscopy and its liquid crystalline behavior is investigated by DSC,POM, and XRD analysis. Upon mechanical perturbation, 5 exhibits unusual agitation-induced high-strengthdisclinations, shear-induced inversion walls, and solidification-induced banded textures. Such phenomenahave been observed in the main-chain liquid crystalline polymers with rigid backbones, but have seldom beenreported for the side-chain liquid crystalline polymers with flexible backbones, suggesting that the rigidpolyacetylene backbone of 5 plays a constructive role in inducing the novel molecular alignments.

Temperature-tunable lasing in negative dielectric chiral nematic liquid crystal

In this work, negative dielectric nematic liquid crystal SLC 12V620-400, chiral dopant S811, and laser dye DCM are used to prepare dye-doped chiral nematic liquid crystal laser sample. In order to investigate temperature-tunable lasing in negative dielectric chiral nematic liquid crystal, we measure the transmission and lasing spectrum of this sample. The photonic band gap （PBG） is observed to red shift with its width reducing from 71.2 nm to 40.2 nm, and its short-wavelength band edge moves 55.3 nm while the long-wavelength band edge only moves 24.9 nm. The wavelength of output laser is found to red shift from 614.4 nm at 20 ~C to 662.8 nm at 67 ~C, which is very different from the previous experimental phenomena. The refractive indices, parallel and perpendicular to the director in chiral nematic liquid crystal have different dependencies on temperature. The experiment shows that the pitch of this chiral nematic liquid crystal increases with the increase of temperature. The decrease in the PBG width, different shifts of band edges, and the red shift of laser wavelength are the results of refractive indices change and pitch thermal elongation.

SYNTHESIS OF DIACETYLENE-CONTAINING COPOLYESTERS AND THEIR DFFECT ON ELECTRO-OPTICAL PROPERTIES OF LIQUID CRYSTALS

Some diacetylene-containing copolyesters with different ratios of dipropargyl 1,10-decanate anddipropargyl terephthalate were synthesized. Properties of these copolymers were characterized by differentialscanning calorimetry and polarizing optical microscopy. The copolymer could be cross-linked easily by UVirradiation in a liquid crystal matrix without adding any photoinitiator. The preliminary studies showed thatthe diacetylene-containing polymer network can assist liquid crystal molecules to align with the externalelectric field, thus reducing the response time of display devices.

Synthesis and Characterization of ChiralLiquid Crystal CMPPCDP

novel chiral liquid crystal4'-( 2-chloro-4methylpentanoyloxy ) phenyl 2-cyano-3-(4' -n-dodecyloxyphenyl)propenoate (CMPPCDP ) was synthesized. The compound was characterized usingIR, ￣1H NNIR, elementary analysis. The liquid crystalline pliasc transition wasstudied using optical polarized micrography and differential scanning calorimetry.

SYNTHESIS AND PHASE BEHAVIOUR OF CHIRAL COMBINED MAIN/SIDE CHAIN LIQUID CRYSTALLINE COPOLYMERS

The synthesis and phase behaviour of chiral combined main/side chain liquid crystallinecopolymers containing pendant group constituted by chiral side group and trans-azobenzenemoiety with nitro end group are described. The formation of liquid crystalline polymorphism ofcopolymers is influenced by various contents of achiral side group.

Ferroelectric Liquid Crystal Optical Switches

The dynamic response of molecular orientation, and the temperature and pulse shape dependences of the switching behavior in ferroelectric liquid crystal are described. The switching speed and the surface energy of ferroelectric liquid crystal are given.

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.

Mechanical model study of relationship of molecular configuration and multiphase in liquid crystal materials

A mechanical model of liquid crystals （LCs） is applied to study the polymorphism of homologous series of terphenyl compounds. With a senti-experimental molecular orbit method, we calculate the moment of inertia which represents the rotation state to describe the phase transition temperature obtained from experimental data. We propose a novel explanation of the phase sequence or polymorphism of LC materials using the two key parameters, the moment of inertia and critical rotational velocity. The effect of molecular polarity on the appearance of liquid crystalline is also discussed.

Synthesis and Liquid Crystal Properties of Transition Metal Complexes of Meso-tetra(4-n-myristyloxyphenyl)porphyrin

Transition metal complexes of meso-tetra(4-myristyloxyphenyl)porphyrin TMPPM [M =Mn, Fe, Co, Ni, Cu, Zn; TMPP=mesotetra(4-myristyloxyphenyl)porphyrin] have been synthesized and characterized by means of elemental analyses, UV-Vis spectra, infrared photoacoustic spectra, 1H NMR spectra, molar conductance and differential scanning calorimetry(DSC). The ligand and the Zn complex show liquid crystalline behavior. According to the DSC thermogram of the Zn complex, it exhibits a lower phase transition temperature -7.453 ℃ and a wide mesophase temperature span, 77 ℃.

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.