Mean-Field Limit and Phase Transitions for Nematic Liquid Crystals in the Continuum

We discuss thermotropic nematic liquid crystals in the mean-field regime. In the first part of this article, we rigorously carry out the mean-field limit of a system of N rod-like particles as \(N\rightarrow \infty \), which yields an effective ‘one-body’ free energy functional. In the second part, we focus on spatially homogeneous systems, for which we study the associated Euler–Lagrange equation, with a focus on phase transitions for general axisymmetric potentials. We prove that the system is isotropic at high temperature, while anisotropic distributions appear through a transcritical bifurcation as the temperature is lowered. Finally, as the temperature goes to zero we also prove, in the concrete case of the Maier–Saupe potential, that the system converges to perfect nematic order.     

Phase Diagram of XY Model with Nematic Coupling on the Simple Cubic Lattice

Using cluster Monte Carlo method,we numerically investigate the criticality in the XY model with nematic coupling on the simple cubic lattice.We determine critical lines belong to the three-dimensional XY universality class in variable of θ(2θ) between the XY-ferromagnetic(nematic) and disordered states.Furthermore,the phase transition between the XY-ferromagnetic and the nematic states is found to be in the three-dimensional Ising universality class.The critical points are determined from the intersections of Binder ratios for various system sizes.With two sets of critical points obtained,we finally construct the phase diagram on the-J plane.     

向列相液晶沿面到垂面排列转变的分子场理论

以摩擦基板间的液晶薄层为研究对象,用分子场理论研究了向列相液晶分子排列转变行为.分子质心固定在简单立方晶格的格点上.液晶由极性分子构成,与基板相接触的一层分子同时受到色散和极性两类表面作用.通过自洽的数值计算,获得3种相图,清楚地展示了摩擦基板间向列相出现的从高温沿面到低温垂面排列的转变;获得实现这类转变所需要的两类表面作用的参数范围.结果表明:基板的摩擦会改变基板表面色散作用,但不会影响基板表面极性作用;表面极性相互作用能引起基板间向列相液晶发生沿面到垂面排列转变.     

Non-uniformities in polymer/liquid crystal mixtures

We theoretically model the nucleation of nematic droplets during phase ordering in mixtures of a flexible polymer and a low-molecular-weight liquid crystal. By appealing to classical nucleation theory (CNT), we calculate the energy barrier to nucleation and the size of a critical nucleus. We study the influence of a metastable intermediate phase on the nucleation of the nematic. Below a triple point in the phase diagram, there are two distinct mechanisms for the formation of a nematic nucleus: 1) direct nucleation from the isotropic phase and 2) nucleation via a precursor metastable isotropic phase. We calculate the crossover concentration as a function of temperature, delineating the regions of the phase diagram in which each mechanism prevails. In the latter case, the presence of a hidden metastable isotropic-isotropic binodal may either promote or delay the nucleation of a nematic phase. Received 9 August 2002 RID="a" ID="a"e-mail: matuyama@chem.mie-u.ac.jp     

利用单轴压强下的电阻变化研究铁基超导体中的向列涨落

铁基超导体中普遍存在着反铁磁、超导和向列相,因此研究向列相的性质及其与反铁磁、超导的关系对于理解铁基超导体的低能物理及高温超导电性具有非常重要的作用.所谓向列相是指电子态自发破缺了晶格的面内四重旋转对称性而形成的有序态,从而导致样品的某些物理性质出现了两重的各向异性.我们通过自主研发的单轴压强装置,可以在低温下原位改变压强,测量电阻的变化,从而得到向列极化率.本文介绍了我们利用该装置在最近几年研究铁基超导体的向列相和向列涨落所取得的一些成果,包括详细研究了BaFe_(2-x)Ni_xAs_2体系中的向列量子临界点及其量子临界涨落,并提出了基于向列涨落强弱调节的铁基超导体统一相图.这些结果表明,向列相及其涨落与反铁磁和超导均有很强的耦合,对于理解铁基超导体中磁性和超导电性非常关键.     

Nematic and chiral order for planar spins on a triangular lattice

We propose a variant of the antiferromagnetic XY model which includes a biquadratic (J2) as well as the quadratic (J1) interaction on the triangular lattice. The phase diagram for large J2/J1 exhibits a phase with coexisting quasi-long-range nematic, and long-ranged vector spin chirality orders in the absence of magnetic order, which qualifies our model as the first instance of a classical spin model that exhibits a vector chiral spin liquid phase. The interplay of nematic and spin chirality orders is discussed. A variety of critical properties are derived by means of Monte Carlo simulation.     

H and C NMR studies of molecular orientation and dynamics in liquid crystal 6BA

The dynamics and orientation of dimers accompanying the formation and destruction of hydrogen bonds in the nematic phases of 4-n-hexylbenzoic acid (6BA) were studied by ¹³C and ²H NMR. The orientational order parameter S in the nematic phase was estimated from the quadrupole splitting of the ²H NMR spectrum. The intermolecular interaction energy for the molecular order in the nematic phase decreased with increasing temperature. The flexibility of dimers due to the destruction of the hydrogen bond is closely related to a decrease in the intermolecular interaction energy. The proportion of ²H NMR spin-lattice relaxation time (T₁) to S, which reveals the coupling of the orientational fluctuations with the hydrogen bonding processes, was observed.     

Crystal → nematic phase transition in the liquid crystalline system 1‐isothiocyanato‐4‐(trans‐4‐propylcyclohexyl) benzene (3CHBT) probed by temperature‐dependent micro‐Raman study and DFT calculations

Raman spectra of 3CHBT in unoriented form were recorded at 14 different temperature measurements in the range 25–55 °C, which covers the crystal → nematic (N) phase transition, and the Raman signatures of the phase transition were identified. The wavenumber shifts and linewidth changes of Raman marker bands with varying temperature were determined. The assignments of important vibrational modes of 3CHBT were also made using the experimentally observed Raman and infrared spectra, calculated wavenumbers, and potential energy distribution. The DFT calculations using the B3LYP method employing 6‐31G functional were performed for geometry optimization and vibrational spectra of monomer and dimer of 3CHBT. The analysis of the vibrational bands, especially the variation of their peak position as a function of temperature in two different spectral regions, 1150–1275 cm⁻¹ and 1950–2300 cm⁻¹, is discussed in detail. Both the linewidth and peak position of the ( C H ) in‐plane bending and ν(NCS) modes, which give Raman signatures of the crystal → N phase transition, are discussed in detail. The molecular dynamics of this transition has also been discussed. We propose the co‐existence of two types of dimers, one in parallel and the other in antiparallel arrangement, while going to the nematic phase. The structure of the nematic phase in bulk has also been proposed in terms of these dimers. The red shift of the ν(NCS) band and blue shift of almost all other ring modes show increased intermolecular interaction between the aromatic rings and decreased intermolecular interaction between two  NCS groups in the nematic phase. Copyright © 2009 John Wiley & Sons, Ltd.     

Transition order and dynamics of a model with competing exchange and dipolar interactions

We performed Monte Carlo simulation of phase transitions from isotropic stripe phase with short-range order to long-range stripe phase in a model with competing ferromagnetic exchange and antiferromagnetic dipolar interactions on triangular lattice. We calculated phase diagram for different values of exchange and dipolar interaction constants ratio, η. We also determined the order of the transitions to stripe phases AFh of different stripe widths h: first-order phase transition was found to transitions into AF1 and AF2 phases, while transitions to AF3 and AF4 phases were of the second order. In the phase diagram the tricritical point was determined at the AF2 and AF3 phase boundary. We observed the peak of nematic phase at the transition region to the AF1 phase, but found it metastable at low values of η. We have also found that in AF1 phase spin relaxation corresponds to the Ising model dynamics. In phases AF3 and AF4 the dynamics slows down, and stripe domain growth with time is proportional to logt.     

Effect of disorder and isotope on the properties of a two orbital double exchange system

A two-site single electron double exchange model incorporating orbital degeneracy, superexchange and electron-phonon (e-ph) interaction is studied using exact diagonalization method. The core spins are treated quantum mechanically. We study the ground state phase diagram as well as the magnetic susceptibility and the kinetic energy of the system as a function of temperature. Effect of difference in site energies, which mimics the role of site-diagonal disorder, is investigated. The susceptibility shows a peak at a characteristic temperature which we have referred to as T₀. The variation of T₀ with e-ph coupling and that of the isotope-shift exponent (α) with T₀ are obtained. We also investigate the field-induced change in the kinetic energy, which is related to the colossal magnetoresistance (CMR) of the system, and find that the disorder enhances the CMR even for the two-site system.     

Superfluid 3He in Squeezed Nematic Aerogel

We present results of nuclear magnetic resonance (NMR) experiments in superfluid ³He in two samples of nematic aerogel consisting of nearly parallel mullite strands. The samples were cut from the same piece of the aerogel, but one of them was squeezed by 30% in the direction transverse to the strands. In both samples, the superfluid transition of ³He occurred into the polar phase, where no qualitative difference between NMR properties of ³He in these samples was found. The difference, however, has appeared on further cooling, after the transition to the polar-distorted A phase (PdA phase) with the orbital part of the order parameter in the 2D Larkin–Imry–Ma (LIM) state. In the squeezed sample, the 2D LIM state is anisotropic, which results in changes in the NMR, which can be used as an additional marker of the PdA phase and have allowed us to measure the value of the anisotropy.

     

Phase equilibria of confined liquid crystals

The differences between the phase diagram of the Gay-Berne potential confined by two identical walls versus the corresponding bulk phase diagram have been investigated. A wall-fluid interaction 9-3 Lennard-Jones potential was used. The study was performed in most cases by using the hybrid Monte Carlo method for the μVT ensemble. Several isotherms were analysed where vapour, liquid and smectic phases were observed. The smectic-isotropic coexistence region becomes wider, i.e. the isotropic coexistence line is shifted to lower densities but the smectic coexistence line remains nearly the same. The triple point temperature of the confined system is estimated to be in the vicinity of 0.45 versus 0.40 of the bulk system. For the isotherm at T? = 0.65 an orientational dependence was added to the 9-3 Lennard-Jones potential to model the wall-fluid interaction. For both kinds of walls, 9-3 LJ with and without orientational dependence, confinement was not found to stabilize a nematic phase as found by previous authors.     

Nematic liquid crystals exhibiting high birefringence

Two fluorinated isothiocyanato nematic liquid crystalline compounds, 4′-butylcyclohexyl-3, 5-difluoro-4-isothiocyanatobiphenyl and 4′-pentylcyclohexyl-3, 5-difluoro-4-isothiocynatobiphenyl are studied in detail to obtain their different physical parameters. Optical polarizing microscopy, differential scanning calorimetry, density and dielectric studies have been carried out for the two samples. Both the samples were found to have high clearing temperature (>100 °C) and exhibit small enthalpy of transition. The two samples exhibit high optical birefringence (Δn > 0.2). The values of order parameters for the two samples were obtained using different approaches, namely, Vuks’, Neugebauer’s, modified Vuks’ and direct extrapolation method from birefringence data. Experimentally obtained values of order parameters have also been compared with theoretical Maier–Saupe values. The parallel and perpendicular components of dielectric permittivity values of the two compounds were also calculated and their anisotropy values were found to be small. The effect of temperature on the molecular dipole moment μ and the angle of inclination β of the dipole axis with the director have also been investigated in this work.     

Theoretical analysis on phase behaviour of a liquid crystalline material – effect of molecular motions

Molecular structure, and phase behaviour of 2-Cyano-N-[4-(4-n-pentyloxybenzoyloxy)-benzylidene] aniline (CPBBA) has been reported with respect to translational and orientational motions. The atomic net charge and dipole moment components at each atomic centre have been evaluated using the complete neglect differential overlap (CNDO/2) method. The modified Rayleigh–Schrodinger perturbation theory along with multicentered–multipole expansion method has been employed to evaluate the long-range intermolecular interactions, while a ‘6-exp’ potential function has been assumed for short-range interactions. The interaction energy values obtained through these computations have been used as input to calculate the configurational probability at room temperature (300 K), and nematic–isotropic transition temperature (396.5 K). On the basis of stacking, in-plane, and terminal interaction energy calculations, all possible geometrical arrangements between the molecular pairs have been considered. Molecular arrangements inside a bulk of materials have been discussed in terms of their relative order. Further, translational rigidity parameter has been estimated as a function of temperature to understand the phase behaviour of the compound. The present model is helpful to understand the effect of molecular motions on ordering, and phase behaviour of the mesogenic compounds.     

Nematic order by disorder in spin-2 Bose-Einstein condensates

We show that quantum and thermal fluctuations in spin-2 Bose-Einstein condensates lift the accidental degeneracy of the mean-field phase diagram. Fluctuations select the uniaxial (square biaxial) nematic state for scattering lengths a4>a2 (a4相似文献   

Possible mechanism of charge stripe formation based on the ring exchange interaction

Using the numerical diagonalization of the finite-cluster t–J model, we investigate the mechanism of the charge stripes based on the ring exchange interaction. We calculate the many-hole correlation functions related with the two-types of charge stripes; the vertical and diagonal types of the charge stripe. As a result, we present a phase diagram including the two stripe phases and a phase separation phase.     

The Phase Transitions from Chiral Nematic Toward Smectic Liquid Crystals

A Chen-Lubensky energy is used to investigate phase transitions from chiral nematic to smectic C* and smectic A* liquid crystal phases. We consider a liquid crystalline material Ω confined between two parallel plates, where the dimensions of Ω are assumed to be large relative both to the width of a smectic layer and the material’s chiral pitch. We take boundary conditions so that the smectic phase melts at the plates’ surfaces and prove the existence of energy minimizers in an admissible set consisting of order parameters and molecular directors . Then under the physically observed assumption that the Frank elasticity constants become large near a phase transition, we establish estimates for the transition region separating phases. In particular we derive analytic estimates proving that chirality lowers the transition temperature regime above which minimizers are nematic and below which minimizers are in a smectic phase.Research supported by NSF grants DMS-0306516 and DMS-0456286.     

Influence of pressure on the electric-field-induced phase transitions in liquid crystals

Within the framework of Landau-de-Gennes formulation, we analyse the effect of pressure on electric-field-induced phase transitions in a liquid crystal which shows spontaneously an isotropic-smectic A transition. Inferring from the experimental pressure dependences on the layer spacing in smectic A phase, as well as the nematic-smectic A metastable temperature T^*_AN, we incorporated the pressure dependence in the free energy through (the surface energy term) and the coupling between the quadrupolar nematic ordering Q_ij and the smectic order parameter ψ. From the S-T phase diagram, we found that the stability of field-induced nematic phase increases with pressure, whereas the discontinuity of the transition decreases. Also, the region where paranematic phase transits directly to smectic A phase increases with pressure.     

Transitions between modulated phases in an Ising model with third-neighbour interactions (mean-field approximation)

We study order–disorder transitions in a three-dimensional Ising lattice in which all the spins belonging to the same xy plane have the same degree of disorder, so that the structure can be effectively reduced to a chain of layers. The layers interact with each other up to third neighbours. Employing the mean-field approximation, we find the different configurations that undergo the transition to total disorder in terms of the interaction constants and work out a diagram displaying the possible sequences of modulated phases that can be found when the temperature goes from 0 to the order–disorder transition point. At intermediate temperatures the average values of the spins of the layers for periodic structures are found by solving an equation system. Substitution of these values into the expression of the free energy allows one to determine the most stable structure for each set of interaction constants and for each temperature. The model predicts a transition between two modulated structures with the same wavelength but different unit cells, for suitable values of the interaction constants. The formalism is also applied to substances like UNi₂Si₂, with only a partial agreement with experiment.     

Fluid–triangular solid phase transitions in a system of two-dimensional nematic quadrupoles

Density functional theory of freezing is used to study the phase transitions in a system of spherical colloidal particles dispersed in nematic host confined to two dimensions. We have considered both the one-component and two-component systems of the colloidal dispersions. Particles are assumed to interact via director distortion-mediated purely repulsive potential which scales as the fifth power of the inverse interparticle separation. The pair correlation functions needed as input information in the density functional theory are calculated by solving Roger–Young integral equation theory. In one-component system, a triangular crystalline phase is found to be stable. On the other hand, considering the freezing of the fluid phase of the binary mixture into a substitutionally disordered triangular solid, the temperature–composition phase diagram is found to have spindle shape for the ratio of quadrupole moment of the particles of the components being 0.9 and 0.8. The phase diagram changes to an azeotrope at a ratio 0.7. The results are verifiable in real-space experiments on nematic quadrupoles confined to a two-dimensional plane.