The hard ellipsoid-of-revolution fluid I. Monte Carlo simulations

We present the results of Monte Carlo simulations on a system of hard ellipsoids of revolution with length-to-breadth ratios a/b = 3, 2.75, 2, 1.25 and b/a = 3, 2.75, 2, 1.25. We identify four distinct phases, viz. isotropic fluid, nematic fluid, ordered solid and plastic solid. The coexistence points of all first order phase transitions are located by performing absolute free energy computations for all coexisting phases. We find nematic phases only for a/b ≥ 2.75 and a/b ≤ 1/2.75. A plastic solid is only observed for 1.25 ≥ a/b ≥ 0.8. It is found that the phase diagram is surprisingly symmetric under interchange of the major and minor axes of the ellipsoids.     

Strain-induced matrix and droplets anisotropic deformation in liquid crystalline cellulose dispersed liquid crystal films

The present work deals with the preparation of new liquid crystalline cellulose dispersed liquid crystal films (100 μm) using a shearing casting technique. The matrix of the films presents the so-called band texture perpendicular to the shear direction. The nematic low molecular weight liquid crystal is encapsulated in micron and submicron size ellipsoids. The ratio between the lengths of the main axis and the short axis is around 1.23. The main axis is oriented, on average, 28° away from the shear direction. The evolution of the band texture and of the ellipsoidal liquid crystal droplets is investigated by polarizing optical microscopy and light scattering techniques as a function of the strain imposed along and perpendicular to the shear direction. Stretch along shear with strain equal to 0.8 seems to have no effect on the banded structure of the matrix, while the nematic liquid crystal ellipsoids slightly orient the main axis to the stress direction and their shape anisotropy increases by a factor of 2. Deformation in the direction transverse to the shear direction induces a deep change of the polymeric matrix and, at the end, a fibrillar structure is found. The nematic ellipsoids rotate their main axis and align along the stretch direction. Their shape anisotropy evolves from a value of 1.23 to 1 for intermediate deformations with strain equal to 0.5, to a final value of 5 with strain equal to 0.8, in the perpendicular direction.     

Biaxial nematic phase in model bent-core systems

We determine the bifurcation phase diagrams with isotropic (I), uniaxial (N(U)) and biaxial (N(B)) nematic phases for model bent-core mesogens using Onsager-type theory. The molecules comprise two or three Gay-Berne interacting ellipsoids of uniaxial and biaxial shape and a transverse central dipole. The Landau point is found to turn into an I-N(B) line for the three-center model with a large dipole moment. For the biaxial ellipsoids, a line of Landau points is observed even in the absence of the dipoles.     

Effects of molecular geometry on liquid crystalline phase behaviour: isotropic-nematic transition

The effects of range and geometry of a simple attractive square-well on the phase diagram of hard ellipsoids and hard spherocylinders is systematically studied using a simple van der Waals type theory. The orientational single particle distribution function is approximated using the Onsager trial function. The quantitative errors introduced by this are thought to be considerably smaller than the use of the van der Waals approximation, which has been shown to give qualitatively correct phase diagrams for similar models. The phase diagrams obtained for hard ellipsoids and hard spherocylinders of aspect ratios ranging between 3 and 10 with a variety of square-well attractions are found to fall into three general types. The first type shows liquid-vapour coexistence and an isotropic-nematic transition, which meet at a liquid-vapour-nematic triple point. The second type shows a marked widening of the isotropic-nematic biphasic region which pre-empts the liquid-vapour coexistence. The final phase diagram shows a strong destabilization of the nematic phase with respect to the isotropic, which results in a shift of the phase transition to higher densities and pressures as the temperature is lowered.     

Dynamical precursor of nematic order in a dense fluid of hard ellipsoids of revolution

We investigate hard ellipsoids of revolution in a parameter regime where no long range nematic order is present but already finite-size domains are formed which show orientational order. Domain formation leads to a substantial slowing down of a collective rotational mode which separates well from the usual microscopic frequency regime. A dynamic coupling of this particular mode into all other modes provides a general mechanism which explains an excess peak in spectra of molecular fluids. Using molecular dynamics simulation on up to 4096 particles and on solving the molecular mode coupling equation we investigate dynamic properties of the peak and prove its orientational origin. Received 19 September 2001 and Received in final form 19 March 2002     

Polarization anisotropy in the optical properties of silicon ellipsoids

A new real space quantum mechanical approach with local field effects included is applied to the calculation of the optical properties of silicon nanocrystals. Silicon ellipsoids are studied and the role of surface polarization is discussed in details. In particular, surface polarization is shown to be responsible for a strong optical anisotropy in silicon ellipsoids, much more pronounced with respect to the case in which only quantum confinement effects are considered. The static dielectric constant and the absorption spectra are calculated, showing that the perpendicular and parallel components have a very different dependence on the ellipsoid aspect ratio. Then, a comparison with the classical dielectric model is performed, showing that the model only works for large and regular structures, but it fails for thin elongated ellipsoids.     

How do mosquito eggs self-assemble on the water surface?

This work reports a detailed numerical study of the behavior of ellipsoid-shaped particles adsorbed at fluid interfaces. Former experiments have shown that micrometer-sized prolate ellipsoids aggregate under the action of strong and long-ranged capillary interactions. The latter are due to nonplanar contact lines and to the resulting deformations of the interface in the vicinity of the trapped objects. We first consider the case of a single ellipsoid and examine in detail the influence of contact angle and ellipsoid aspect ratio on interfacial distortions. We then focus on two contacting ellipsoids and study the optimum packing configuration depending on their size and/or aspect ratio mismatch. We thoroughly explore the variety of contact configurations between both ellipsoids and provide corresponding energy maps. Whereas the side-by-side configuration is the most stable state for identical ellipsoids, we find that the mismatched pair adopts an “arrow” configuration in which a finite angle exists between the particles long axes. Such arrows are actually seen in experiments with micron-sized ellipsoids and similarly with millimeter-sized mosquito eggs. These results complement our previous work (J.C. Loudet, B. Pouligny, EPL 85, 28003 (2009)) and highlight the importance of geometrical factors to explain the morphology of aggregated structures at fluid interfaces.     

Simulation and Statistical Analysis of Random Packings of Ellipsoids

The paper describes an algorithm for the generation of random packings of ellipsoids of revolution, which is a natural generalization of an older algorithm for the case of spherical particles and belongs to the class of collective rearrangement algorithms. It yields packings with a broad spectrum of densities and geometrical properties, aspect ratio which depend on and the various parameters controlling the motions of ellipsoids during the simulation. The ellipsoid systems obtained are characterized by second‐order characteristics, namely pair correlation and orientation correlation functions. Furthermore, the constructed packings are described in a phase diagram taken from statistical physics.     

Corresponding states of nematic birefringence: an order parameter universality

In this work, experimental birefringence data of several nematic liquid crystals, which share the presence of a nematic–isotropic and a nematic–crystalline phase transition, are used to show that the birefringence presents a universal behaviour which encompasses the entire range of the nematic phase. The meaning and consequences of such behaviour are discussed; as the order parameter is proportional to the birefringence, this result implies that the order parameter has an extended universal profile, similar to a corresponding state law, which is independent of the liquid crystal compound and becomes determined once the temperature interval of the existence of the nematic compounds is obtained.     

On limit behavior of quasi-local mass for ellipsoids at spatial infinity

We discuss the spatial limit of the quasi-local mass for certain ellipsoids in an asymptotically flat static spherically symmetric spacetime. These ellipsoids are not nearly round but they are of interest as an admissible parametrized foliation defining the Arnowitt–Deser–Misner mass. The Hawking mass of this family of ellipsoids tends to-∞. In contrast, we show that the Hayward mass converges to a finite value. Moreover, a positive mass type theorem is established. The limit of the mass has a uniform positive lower bound no matter how oblate these ellipsoids are. This result could be extended for asymptotically Schwarzschild manifolds. And numerical simulation in the Schwarzschild spacetime illustrates that the Hayward mass is monotonically increasing near infinity.     

Comprehensive studies on dielectric properties of p-methoxy benzylidene p-decyl aniline with function of temperature and frequency in planar geometry: A potential nematic liquid crystal for display devices

The dielectric properties of the nematic mesophase, p-methoxy benzylidene p-decyl aniline(MBDA), measured in planar geometry with a function of frequency and temperature are investigated in detail. The complex dielectric permittivity(ε' and ε') is also studied at a bias voltage of 10 V for planar aligned sample cell of nematic mesophase. The dielectric permittivity with bias voltage attains a higher( 2 times) value than that without bias voltage at a temperature of 56℃,which is due to the fact that the linking group of nematic molecules is internally interacted with an applied bias voltage.This is supported by observing an enhanced dielectric permittivity of nematic liquid crystal(LC) in the presence of bias voltage, which can be fully explained as the increasing of the corresponding dipole moment. The dielectric relaxation behaviors of nematic LC are also demonstrated for planar aligned sample cell. The remarkable results are observed that the relaxation frequency shifts into low frequency region with the increase of the bias voltage applied to the planar aligned sample cells. The dielectric relaxation spectra are fitted by Cole–Cole nonlinear curve fitting for nematic mesophase in order to determine the dielectric strength.     

Disclinations in the nematic phase of a magnet with spin 1

Two-dimensional topological defects, spin disclinations, exist for a magnet with spin 1 and strong biquadratic interaction, in which the spin nematic state is realized. The spin disclinations have a nonsingular macroscopic core with a saturated magnetic moment and destroyed nematic order. These singular lines have common features with disclinations in nematic liquid crystals, singular disclinations in antiferromagnets, and magnetic vortices. However, significant differences of their properties from the above-mentioned topological defects also exist. The dynamic properties of a disclination in the spin nematic are characterized by the “freezing in the condensate” and by the gyroscopic force.     

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.     

Intersubband cyclotron combined resonances in 2D systems with anisotropic and tilted valleys

Lineshape of intersubband transitions is calculated in a surface space-charge layer on semiconductor whose constant-energy surfaces are ellipsoids arbitrarily oriented with respect to the surface. The case when magnetic field is normal to the surface is considered. Combined intersubband cyclotron transitions are allowed when ellipsoids are tilted with respect to the surface. The depolarization effect affects the combined transition differently from the main transition.     

Diffusion-influenced reactions

We summarize three of our recent results on diffusion-influenced reactions in solutions. All deal with the concentration dependence of the reaction rate when the reactants must first diffuse together before reaction can occur. When one species (the sink species) is not dilute, the rate cannot be obtained by solution of a pair diffusion equation; the correlations among the sinks for the diffusing species must be accounted for. First, we consider fluorescence quenching when the quenchers are not dilute. For charged quenchers and fluorophores we discuss how the solution dielectric constant and ionic strength can strongly influence the deviations from the linear Stern-Volmer behavior (the dilute sink result) which arise due to the sink correlations. Second, we consider heterogeneous catalysis where a reactive species is adsorbed onto a surface and must surface diffuse to reactive sites (the sinks). We find that surface diffusion can be an important factor contributing to the rate of reaction; especially when surface diffusion is rapid relative to the adsorption/desorption rate. Third, we discuss diffusion influenced reactions with sinks which are long ellipsoids. Dilute long ellipsoids provide a large rate enhancement relative to a spherical sink; we show that this rate enhancement survives when nondilute ellipsoids are considered.     

Entropy-driven enhanced self-diffusion in confined reentrant supernematics

We present a molecular dynamics study of reentrant nematic phases using the Gay-Berne-Kihara model of a liquid crystal in nanoconfinement. At densities above those characteristic of smectic A phases, reentrant nematic phases form that are characterized by a large value of the nematic order parameter S?1. Along the nematic director these "supernematic" phases exhibit a remarkably high self-diffusivity, which exceeds that for ordinary, lower-density nematic phases by an order of magnitude. Enhancement of self-diffusivity is attributed to a decrease of rotational configurational entropy in confinement. Recent developments in the pulsed field gradient NMR technique are shown to provide favorable conditions for an experimental confirmation of our simulations.     

External field induced tricritical phenomenon in the isotropicnematic phase transition of hard non-spherical particle systems

The effect of static external field is studied on the isotropic–nematic phase transition of a system of hard non-spherical particles (rods or platelets) with negative anisotropic polarizability (susceptabilities). On the basis of Onsager theory, the phase coexistence curve is calculated numerically without any approximation. It is found that a weakly ordered nematic phase (uniaxial planar) is in coexistence with a highly ordered biaxial nematic phase which ends at a tricritical point. In the limit of infinite field strength, the orientations of the particles are confined in a plane perpendicular to the field and continuous isotropic–nematic phase transition takes place.     

Anisotropy induced in a silver chloride emulsion by two successive beams of white light perpendicularly polarized

This paper is a study of the anisotropy induced in a silver chloride photographic emulsion by two successive beams of white light, linearly polarized at right angle. After the first exposure, the colloidal medium contains silver ellipsoids e generated by the photolysis of silver chloride and silver ellipsoids e_b resulting of the partial destruction of some of the previous ones by long wavelengths. This medium is then illuminated by the second beam linearly polarized at right angle of the first beam. Short wavelengths induced silver ellipsoids e′ identical to the ellopsoids e but rotated through π/2 with respect to them. As in the first exposure, some of them are partly broken up and transformed into ellipsoids e′_b identical to ellipsoids e_b but the direction of their major axis. Moreover, the long wavelengths of second exposure transform some of the particles e and e_b generated during the first exposure, into smaller ellipsoids e_eb and e_bb. Finally, the colloidal medium resulting of these two exposures, contains silver chloride and six sorts of silver particles. By calculating the indices of the medium, we show that the wavelengths characterizing the zero birefringence and zero dichroism of the emulsion are dependent on the energies recorded during each of the exposures.     

Capillary interactions between anisotropic colloidal particles

We report on the behavior of micron-sized prolate ellipsoids trapped at an oil-water interface. The particles experience strong, anisotropic, and long-ranged attractive capillary interactions which greatly exceed the thermal energy k(B)T. Depending on surface chemistry, the particles aggregate into open structures or chains. Using video microscopy, we extract the pair interaction potential between ellipsoids and show it exhibits a power law behavior over the length scales probed. Our observations can be explained using recent calculations, if we describe the interfacial ellipsoids as capillary quadrupoles.