Monte Carlo simulations of biaxial structure in thin hybrid nematic film based upon spatially anisotropic pair potential

Hybrid nematic films have been studied by Monte Carlo simulations using a lattice spin model, in which the pair potential is spatially anisotropic and dependent on elastic constants of liquid crystals. We confirm in the thin hybrid nematic film the existence of a biaxially nonbent structure and the structure transition from the biaxial to the bent-director structure, which is similar to the result obtained using the Lebwohl--Lasher model. However, the step-like director's profile, characteristic for the biaxial structure, is spatially asymmetric in the film because the pair potential leads to K₁ ≠ K₃. We estimate the upper cell thickness to be 69 spin layers, in which the biaxial structure can be found.     

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.     

Monte Carlo模拟空间各向异性势向列相液晶微滴

基于分子两体势,用Monte Carlo方法计算向列相液晶微滴.两体势基于格点模型,是空间各向异性的且依赖于液晶的弹性常数.假定向列相液晶微滴具有自由表面,引入切向内禀强度定量描写表面引发的分子内禀易取向的强弱.通过各向异性势的两种方案,在低温下计算切向内禀强度和二阶序参数在微滴内不同区域的变化,与Lebwohl-Lasher模型作对比分析.结果表明:只有一种方案在微滴表面产生内禀易取向,且内禀强度值的大小与K₃₃/K₁₁值有关;空间不完整的向列相液晶使得微滴由内层到外层有序度越来越低.     

Molecular mean field theory for liquid water

Attractive bonding interactions between molecules typically have inherent conservation laws which influence the statistical properties of such systems in terms of corresponding sum rules. We have considered lattice water as an example, and we have enunciated the consequences of the sum rule through a general computational procedure called molecular mean field theory. Fluctuations about the mean field are computed and many of the liquid properties have been deduced and compared with Monte Carlo simulation, molecular dynamics, and experimental results. Large correlation lengths are seen to be a consequence of the sum rule in the liquid phase. Long-range Coulomb interactions are shown to have minor effects on our results.     

Blue phase liquid crystal phase transition for cyano compound chiral nematic liquid crystal mixtures with three two-ring core structures and chiral dopant concentrations

Blue phase (BP) temperature range of a chiral nematic liquid crystal (LC) mixture is dependent upon the host nematic LC chemical structure and chiral dopant concentration. In this study, we investigated BP phase transition behaviour and helical twisting power (HTP) using three chiral dopant concentrations of cyano compound chiral nematic LC mixtures incorporating three two-ring core structures in the host nematic LCs. The effect of the host nematic LC core structure, HTP and chiral dopant concentrations were considered on BP temperature ranges, for two types of complete BPI and BPII without isotropic phase (Iso) and two types of coexistence state of BPI+Iso and BPII+Iso.     

Surface electric-field-induced instabilities in a homeotropically oriented nematic liquid crystal sample

The effect of a surface electric field produced by ionic adsorption on the molecular orientation of a nematic liquid crystal sample is analyzed. The eigenvalue problem for a semi-infinite medium is analytically solved both for strong and weak anchoring situations. The threshold instabilities are numerically determined and it is shown that the homeotropic pattern can be destabilized also in the situation of strong anchoring. The dependence of the threshold field on the anchoring strength and on the surface polarization is determined by taking into account also the coupling of the quadrupolar component of the flexoelectric coefficient with the field gradient. Received 4 November 1999 and Received in final form 4 April 2000     

用Weiss分子场理论对有外电场时铁电体系相变特征的研究

Weiss分子场理论(WMFT)对晶体中顺磁-铁磁和顺电-铁电相变特征的定量描述是相当成功的. 由于是平均场理论,又可作为初步分析结构无序体系和复杂组分体系相变行为的理论依据. 但是迄今为止,并没有对有外场时WMFT的相变特征进行详细研究. 而对铁电体系,仅仅对分子取向为两个状态时WMFT的相变特征进行了研究. 另外,虽然铁磁与铁电体系的WMFT描述极为相似,但是由于两种体系中微观磁化和极化的单元不同,导致相应的数学描述与结果也有所不同. 本文首先对外电场中分子取向包含任意状态的铁电体系的WMFT相变特征, 包括自发极化、内能和比热以及静态极化率随温度变化进行严格推导, 然后对相变特征随外电场的演变进行了研究.结果表明: 1)无外场时,体系发生二级顺电-铁电相变,且随状态数的增加,相变温度减小, 这是与铁磁体系不同的地方,同时单分子的平均极化强度减小,而内能、比热和极化率增大; 2)外场的存在,使得体系原有的二级相变转化为弥散相变,且外场越强,弥散温区越大. 上述结果对深入研究铁电体系的相变,特别是弥散相变无疑是有益的.     

Effect of surface electric field on the anchoring of nematic liquid crystals

We analyse the influence of adsorbed ions and the resulting surface electric field and its gradient on the anchoring properties of nematics with ionic conductivity. We take into account two physical mechanisms for the coupling of the nematic director with the surface electric field: (i) the dielectric anisotropy and (ii) the coupling of the quadrupolar component of the flexoelectric coefficient with the field gradient. It is shown that for sufficiently large fields near saturated coverage of the adsorbed ions, there can be a spontaneous curvature distortion in the cell even when the anchoring energy is infinitely strong. We also discuss the director distortion when the anchoring energy of the surface is finite. Received: 29 September 1997 / Received in final from: 10 November 1997 / Accepted: 18 November 1997     

Comparison of optical compensations based on discotic liquid crystals with linear and non-linear orientation for wide viewing angle twisted nematic liquid crystal displays

Optical compensation film using discotic liquid crystals has been commercialized to suppress light leakage of twisted nematic (TN) liquid crystal (LC) cells in the dark state when the viewing directions are off-axes. In the conventional film, the tilt angle variation of the discotic LC layers is linear, whereas that of the rod-like LC layers in the TN cell is non-linear with twist alignment. We investigated the optical compensation effects in terms of iso-contrast ratio, gray scale inversion and color shift with linear and non-linear orientation in a tilt angle or twist and non-twist orientation on TN-LC cells. The results showed that the optical compensation with non-linear orientation exhibited an improved performance in suppressing light leakage in the dark state.     

Behaviour of nematic liquid crystals doped with ferroelectric nanoparticles in the presence of an electric field

A planar nematic liquid crystal cell (NLC) doped with spherical ferroelectric nanoparticles is considered. Polarisation of the nanoparticles are assumed to be along the NLC molecules parallel and antiparallel to the director with equal probability. The NLC molecules anchoring to the cell walls are considered to be strong, while soft anchoring at the nanoparticles surface is supposed. Behaviour of the NLC molecules and nanoparticles in the presence of a perpendicular electric field to the NLC cell is theoretically investigated. The electric field of the nanoparticles is taken into account in the calculations. Freedericksz transition (FT) threshold field in the presence of nanoparticles is found. Then, the director and particles reorientations for the electric fields larger than the threshold field are studied. Measuring the onset of the nanoparticles reorientation is proposed as a new method for the FT threshold measurement.     

Ternary phase-amplitude modulation with twisted nematic liquid crystal displays for Fourier-plane light homogenization in holographic data storage

Holographic data storage applications often use liquid crystal displays as spatial light-amplitude modulators for writing data images. The hologram created in the Fourier plane is usually applied to store the information, since this plane supplies optimal data density. A well known technique for homogenizing the light distribution in the Fourier plane is the application of external random phase modulating masks. The requirement for pixel by pixel matched positioning of the phase modulating mask and the pixels of the spatial light-amplitude modulator is hard to solve in the optical systems and any positioning error leads to significant signal degradations. The article analyses the possibilities of realizing the required simultaneous amplitude and phase modulation of light with the application of a single LCD. Twisted nematic LCDs with different maximal birefringence are numerically investigated using the Jones matrix method. Elliptical incident and exit polarizations are proposed, by which ternary phase-amplitude modulation (+1,–1,0) can be realized. Test measurements are also presented that demonstrate the validity of the calculated results.     

Switching of banana liquid crystal mesophases under field

Taking advantage of the great number of bent-core or “banana" compounds synthesized and studied in the laboratory, we describe their behaviour under the application of an external electric field. If the field were a static one, we would work within the frame of an equilibrium phase diagram in a (field E, temperature T) space where some phases would be simple dielectrics and others ferroelectric ones with a macroscopic polarization, either spontaneous or induced by the field. In this paper, we deal with the basic responses of “banana” liquid crystals under the application of a low frequency (1 to 100 Hz) AC field. Firstly square-wave voltages allow us to locate the phase boundary between dielectric (at lower field) and ferroelectric phases (higher field) at a given temperature and field threshold. Then we apply slowly varying AC voltages with shapes like triangle or “triple-plateau” to check out the stability of the induced ferroelectric phase versus field removal. Three behaviours are encountered, the unstable one (short lifetime of the high-field ferroelectric phase) where the macroscopic polarization is destroyed and then rebuilt in the opposite direction during each half period and usually called “antiferroelectric”; the stable one (long lifetime) with a polarization that rotates at constant modulus which is labeled as “ferroelectric” and a new one where the macroscopic polarization is proportional to the applied fied, we named this behaviour as “superparaelectric”. Let us stress that these observations apply to the ferroelectric phases of the (E, T) phase diagram not to the zero field (0,T) phases observed in the usual phase characterization experiments except for an eventual spontaneous ferroelectric phase. Received 18 April 2002 and Received in final form 17 January 2003 Published online: 16 April 2003 RID="a" ID="a"e-mail: marcerou@crpp.u-bordeaux.fr RID="b" ID="b"URL: http://www.crpp-bordeaux.cnrs.fr     

Effect of variation of dielectric constant on the magnetic field modulation of exciplex luminescence

The effect of variation of dielectric constant on the relative magnetic field effect in singlet luminescence has been studied using a typical exciplex system at a saturating field. The study indicates strong specificity in the perturbation of the magnetic field effect by alcoholic solvents. In contrast to alcohols where relative singlet magnetic field effect is of the order of 2% only, the magnetic field effect in non-alcoholic medium reaches as high as 9%. Moreover, dielectric constant variation in alcohols yields curves which are distinctly different from those in non-alcoholic media. It turns out that this dependence of magnetic field effect on dielectric constant is similar in all non-alcoholic solvent mixtures. An analytical study based on Hong and Noolandi’s solution of Smoluchowski equation has been made. Derived expressions can interpret experimental curves reasonably well.     

电磁场法向边值关系的严密数学理论

阐述了矢量场穿过2阶无穷小平面的通量虽然也是2阶无穷小量,但特殊情况下要求计算精度必须达到3阶无穷小量,为此目的需要把2阶无穷小平面分成无穷多个4阶无穷小面元来计算通量,并且给出如此计算所得结果遵循的规律——3阶无穷小精度下矢量场穿过2阶无穷小平面的通量定理.最后介绍了这个定理在散度理论和电磁场法向边值关系理论中的应用.     

Eliashberg theory with the external pair potential

Based on BCS model with the external pair potential formulated in a work Grigorishin (2017) [1], analogous model with electron-phonon coupling and Coulomb coupling is proposed. The generalized Eliashberg equations in the regime of renormalization of the order parameter are obtained. High temperature asymptotics and effect of Coulomb pseudopotential on them are investigated: as in the BCS model the order parameter asymptotically tends to zero as temperature rises, but the accounting of the Coulomb pseudopotential leads to existence of critical temperature. The effective Ginzburg-Landau theory is formulated for such model.     

Self-consistent field theory and calculation for gyromonotron

A self consistent field large signal theory of gyromonotron is studied in this paper. The RF field profile function satisfies a wave equation. The field is determined by cavity geometry and AC electron beam current. The RF field not only satisfies the boundary conditions at the ends of the cavity but also obeys conservation of energy for steady state interaction between electron beam and field. The parameters of a particular gyrotron are calculated numerically using present theory. Effect of some factors on gyrotron characteristic is discussed. Comparison is made between the results of the self consistent field calculations with and without conservation of energy.     

Orientational dependence of the potential of mean force for a discotic liquid crystal near a substrate

In this work we calculate the potential of mean force for a discotic liquid crystal (DLC) confined in a slab geometry. We have set the reaction coordinate as the distance between a DLC test particle with a fixed orientation and a wall with face-on anchoring. Five different orientations of the DLC test particle are explored, which correspond to parallel and perpendicular orientations with regard to the anchoring promoted by the walls, and three intermediate orientations between the parallel and perpendicular configurations. The potential of mean force reflects the strong effect of the system's anisotropy: particles with the wrong orientation are energetically penalised whilst the particles with the correct orientation are favoured.     

Einstein-aether theory with a Maxwell field: General formalism

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.