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.

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.

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,＋∞].

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 〈∞.

Temperature dependence of ratio between dielectric anisotropy and order parameter in fluorinated nematic liquid crystals

Temperature dependence of ratio between dielectric anisotropy and order parameter of fluorinated nematic liquid crystal is investigated by using a semi-empirical molecular orbital package that can accurately calculate an angle between molecular dipole moment and long axis. We optimize the molecular conformations with three semi-empirical Hamiltonians AM1, PM3 and PM5, and then make a comparison between computational results and experimental measurements. It is shown that the results obtained from AM1 method are in good agreement with the measurements. The present study offers an applicable method to predict the dielectric properties of liquid crystal material.

COMPENSATION EFFECT OF POLYIMIDE THIN FILMS ON NORMALLY WHITE TWISTED NEMATIC LIQUID CRYSTAL DISPLAYS

The disadvantages of Normally White Twisted Nematic Liquid Crystal Display (NW-TN-LCD) were discussed. The reason that the negative birefringent polyimide thin films were used to compensate NW-TN-LCD to decrease off-axis leakage, improve contrast ratios and enlarge viewing angles was explained in this paper. A certain polyimide thin film was taken as an example to show compensation effect on NW-TN-LCD.

Calculating the dielectric anisotropy of nematic liquid crystals:a reinvestigation of the Maier-Meier theory

This paper investigates the average dielectric permittivity （^-ε） in the Maier-Meier theory for calculating the dielectric anisotropy （△ε） of nematic liquid crystals.For the reason that ^-ε of nematics has the same expression as the dielectric permittivity of the isotropic state,the Onsager equation for isotropic dielectric was used to calculate it.The computed ^-ε shows reasonable agreement with the results of the numerical methods used in the literature.Molecular parameters,such as the polarizability and its anisotropy,the dipole moment and its angle with the molecular long axis,were taken from semi-empirical quantum chemistry （MOCPAC/AM1） modeling.The calculated values of △ε according to the Maier-Meier equation are in good agreement with the experimental results for the investigated compounds having different core structures and polar substituents.

Molecular theory of nematic liquid crystals viewed as effect of collective excitation in ferromagnetic systems

We develop a microscopic theory of the nematic phase with consideration of the effect of the collective excitation on properties of nematic liquid crystals. The model is based on the Heisenberg＇s exchange model of the ferromagnetic materials. Since the orientation of the molecular long axis and the angular momentum of the molecule rotating around its long axis have the same direction, operators can be introduced to research the nematic liquid crystals. Using the lattice model and the Holstein-Primakoff transformation, the Hamiltonian of the system can be obtained, which has the same form as that of the ferromagnetic substance. The relation between the order parameter and reduced temperature can be gotten. It is in good agreement with the experimental results in the low temperature region, the accordance is better than that of the molecular field theory and the computer simulation. In high temperature region close to the transition point, by considering the effect of the higher-order terms in the Hamiltonian, theoretical prediction is in better agreement with the experiment. That indicates the many-body effect is important to nematic liquid crystals.

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.

Lattice Boltzmann Simulation of 3D Nematic Liquid Crystal near Phase Transition

Phase transition between nematic and isotropic liquid crystal is a very weak first order phase transition.We avoid to use the normal Landau-de Gennes's free energy that reduces a strong first order transition, and set up adata base of free energy calculated by means of Tao-Sheng Lin's extended molecular field theory that can explain theexperiments of the equilibrium properties of nematic liquid crystal very well. Then we use the free energy method oflattice Boltzmann developed by Oxford group to study the phase decomposition, pattern formation in the flow of theliquid crystal near transition temperature.

Asymmetric dynamic phase holographic grating in nematic liquid crystal

A new scheme for recording a dynamic phase grating with an asymmetric profile in C60-doped homeotropically aligned nematic liquid crystal（NLC） was presented.An oblique incidence beam was used to record the thin asymmetric dynamic phase holographic grating.The diffraction efficiency we achieved is more than 40%,exceeding the theoretical limit for symmetric profile gratings.Both facts can be explained by assuming that a grating with an asymmetric saw-tooth profile is formed in the NLC.Finally,physical mechanism and mathematical model for characterizing the asymmetric phase holographic grating were presented,based on the photo-refractive-like（PR-like） effect.

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.

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.

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.

Dynamic Rheological Characterization of A Thermotropic Liquid Crystalline Poly (aryl ether ketone)

The rheometries ARES rheometer was applied to determining the rheological behavior of a thermotropic liquid crystalline poly (aryl ether ketone). The viscosity of the material decreases with increasing temperature. reaching a minimum in the nematic state, then slightly increases with further raising the temperature in the biphase.

Rotational viscosity of a liquid crystal mixture: a fully atomistic molecular dynamics study

Fully atomistic molecular dynamics （MD） simulations at 293, 303 and 313 K have been performed for the four- component liquid crystal mixture, E7, using the software package Material Studio. Order parameters and orientational time correlation functions （TCFs） were calculated from MD trajectories. The rotational viscosity coefficients （RVCs） of the mixture were calculated using the Nemtsov-Zakharov and Fialkowski methods based on statistical-mechanical approaches. Temperature dependences of RVC and density were discussed in detail. Reasonable agreement between the simulated and experimental values was found.