Phonon Dispersion Curves of Some Liquid Metals Based on the Percus-Yevick Phonon Description

Abstract

Phonon dispersion curves are almost quantitatively predicted by a first-order theory based on a zeroth order model of independent density fluctuations. The temperature dependence of the liquid structure factor at constant volume is important for the present considerations.     

Temperature and density dependence of the structure of liquid lithium from an improved pseudopotential theory

Leribaux, H.R., and Lemarchand, J.L., 1978. Temperature and density dependence of the structure of liquid lithium from an improved pseudopotential theory. Fluid Phase Equilibria, 2: 79–90.The structure of liquid lithium and alloys has recently been measured more accurately near their melting point. We present for liquid lithium a modification of a previous pseudopotential for liquid metals, obtained by including explicitly the Xα exchange energy in the electron pseudopotential. The structure factor S(q), obtained from this model potential via the effective pair potential, and calculated by our solution of the Percus—Yevick equation, is found to have the right oscillations compared with the experimental structure factor, the first peak also having the right magnitude. A Percus—Yevick hard-sphere structure factor is also obtained via thermodynamic perturbation and is found to be surprisingly good even for lithium, except for the high-q oscillations. We present computed structures and radial distributions for several higher temperatures involved typically in the liquid lithium alloys, up to the highest temperatures at which saturated density is measured. Our model potential predicts also the correct cohesive energy for liquid lithium and liquid lithium—magnesium.     

Sound Velocity in Liquid Binary Alloys as Calculated via the Percus-Yevick Liquid Phonon Dispersion Relation

Abstract

In this note, we utilize the recently calculatd long wavelength limit of the “liquid virtual crystal” model of binary alloy liquid structure factor at the melting temperature, ST_M ^AB (0), to estimate the long-volume binary liquid alloys. We compare the calculate sound velocities to the available experimental sound velocities in these liquid binary alloys and find reasonable agreement.     

The significant structure theory applied to halobenzenes

Abstract

Just as molecular structure, as revealed by X-ray diffraction, can be interpreted in terms of intuitive models, so liquid structure can be interpreted in terms of a model which leads to a partition function giving the Helmholtz free energy in terms of volume, temperature, and composition. From this explicit expression for the Helmholtz free energy all thermodynamic properties are calculable and can be compared with experiment. Absolute Rate Theory permits the prediction of transport properties from this same model, providing still further insight into liquid structure. Here, Significant Liquid Structure Theory has been applied to twelve substituted benzenes and the results compared with experiment. A single equation is derived for the twelve substances differing in ten of the cases only in three parameters having to do with the solid-like part of the liquid. For simple liquids these properties are those of the solid at the melting point. These properties are the energy of sublimation, molar volume of the solid, and the Einstein characteristic temperature, θ. Hindered rotation is explained in terms of a barrier to rotation of one tenth the energy of sublimation     

Structure of classical fluid of charged hard spheres and point lons in the perturbation of a small non-responsive,uniform background density

Abstract

In liquid Te, the model of Cabane and Friedel is based on the coexistence of a network of strong covalent bonds with a metallic-like electron gas. We have attempted to simulate the gross features of this situation by studying a classical fluid of charged hard spheres, plus point charges (classical electrons!), all moving in a small neutralizing negative background density.

An exact solution of even this model will require computer simulation. We have therefore worked in the approximation of the mean spherical model. Also, we treat the neutralizing background only to first order in the background density.

The main effect of the background is to increase the height of the contact value of g(r) for the hard sphere pair correlations. This appears to correspond qualitatively with the high temperature behaviour of liquid Te.     

Interpretation of boundaries in the pressure–temperature diagram for liquid tellurium and their relationship to the melting-curve maximum

Research on liquid tellurium is reviewed and interpreted in an effort to obtain a consistent picture of the effect of pressure and temperature on the structure and properties of tellurium in the liquid state. Electrical resistance experiments on liquid tellurium support the existence of reaction boundaries in the p–T diagram. The boundaries are believed to identify stages in the reaction whereby the 2-coordinate covalent chain structure transforms to a 3-coordinate covalent network structure which eventually dissociates with pressure and temperature into a metallic system. The increasing liquid density associated with the molecular reaction is given as the cause of the maximum on the P–T melting curve. The melting curve maximum in tellurium is shown to be related to maxima in selenium and sulfur. Quenching tellurium from different liquid fields, delineated by reaction boundaries, resulted in materials with different x-ray spectra.     

Optimized Random Phase Approximation for the Structure of Liquid Alkali Metals as Electron-Ion Plasmas

Abstract

In a previous publication¹ we have shown that the model of the one-component classical plasma on an inert background (OCP) provides a basis for calculating the liquid structure factor of the alkali metals. This was achieved by allowing the conduction electrons to screen the structure of the OCP through the formalism of linear screening theory, but an empirical cut-off of the screening correction at the first node of the electron-ion pseudpotential in wavenumber space was found to be necessary. The purpose of this letter is to stress that the above results point the way towards an unconventional optimized-random-phase-approximation (ORPA) approach² to the structure of these liquid metals, and in fact provide already a good first-order solution for such an approach.     

On the temperature dependence of the order parameter of liquid crystals over a wide nematic range

Abstract

Based on the ideas of Landau-de Gennes theory applied to nematic liquid crystals, several forms for the variation of the order parameter as a function of temperature are investigated over a wide nematic range. These functional forms are used to fit the experimental order parameters, determined through the use of C-13 NMR, for 4-methoxybenzylidene-4′-butylaniline (MBBA) and 4-n-pentyl-4′-cyanobiphenyl (5CB), and the physical significance of the parameters is discussed. A comparison of the results shows that the functional form which fits the experimental data best is similar to the Haller equation, a useful relation which is usually regarded as empirical. In this case, the coefficients resulting from a semi-empirical approach based on the Landau-de Gennes treatment may be thought of as quantifying the importance of the structure and rigidity of the liquid crystal in determining the temperature dependence of the order parameter for that liquid crystal. In the process, we have also examined the pretransitional behaviour in the C-13 NMR chemical shifts of liquid crystals observed within a few tenths of a degree above the nematic to isotropic transition temperature.     

Structural differences between lonic and molecular fluid models of liquid UO2

Abstract

Though present evidence favours an ionic model of liquid UO₂, it seems of interest to compare and contrast structural predictions of such a model with those of a molecular fluid model.

Therefore, in this paper, we present partial structure factors on the basis of the reference interaction site model for liquid UO₂ just above its melting temperature. In this treatment, the “molecules” consist of rigid (linear) clusters of hard spheres.

In the absence of experimental information on the structure of liquid UO₂, comparison is made with the earlier work of Bhuiyan et al, for the mean spherical approximation (MSA) to the ionic model. Considerable resemblance with the MSA results appropriate to zero coupling constant is found.     

Nematic liquid crystal gyroids as photonic crystals

ABSTRACT

We demonstrate nematic and cholesteric liquid crystal (LC) gyroids and show their photonic properties as photonic crystals by using numerical modelling. The LC gyroids are designed as composite optical materials, where we take one labyrinth of passages to be a solid dielectric, whereas the other (complementing) labyrinth of passages is taken to be filled by chiral or achiral nematic LC, with the intermediate gyroid surface imposing homeotropic (perpendicular) surface anchoring. The nematic inside the gyroid matrix is shown to exhibit a variety of possible orientational profiles which are characterised by complex networks of topological defects – from ordered, semi-ordered, to completely disordered. The diversity of possible nematic states is shown to lead to a rich structure of photonic bands, which can be tuned by the LC volume fraction and the cholesteric pitch, including control over full – direct and indirect – band gaps.     

Accurate modelling of nematic liquid crystal under the combination of microwave signal and applied voltage

ABSTRACT

In this paper, a three-dimensional modelling of nematic liquid crystal (NLC) under the combined action of applied voltage and microwave signal is presented. The analytical method applied in the modelling is detailed. In previous research, the modelling of liquid crystal usually uses a small signal wave, and neglected its effect on the orientation of liquid crystal. In this paper, we take the microwave signal into consideration in the calculation of liquid crystal orientation, and get the influence of the power of microwave signal on the orientation. The variations of the relative permittivity of liquid crystal E7 with the power of microwave signals at 30 GHz are obtained. This method is applicable for the modelling of NLC under high power signals excitation.     

Critical Properties of Argon

Abstract

Measurements of P-V-T properties of argon in the critical region are reported. Isothermal compressibilities have been calculated from the data for liquid and vapor along the coexistence curve and for the gas above the critical temperature at the critical density. Densities of the liquid and vapor along the coexistence curve were measured, and the critical temperature, pressure and density of argon were redetermined. These data are compared with those of other workers; in addition critical indices which represent the manner in which these properties vary as one approaches the critical point were determined and compared with the predictions of several theoretical estimates of these quantities.     

On the structure and the chain conformation of side-chain liquid crystal polymers

Abstract

Backbone anisotropy and the structure of the mesophases of a series of side-chain liquid crystal polymers have been studied in the bulk by neutron scattering. The backbone conformation is obtained by small-angle neutron scattering on mixtures of hydrogenous polymers with deuteriated backbones. The components of the radius of gyration parallel, R _⊥ and perpendicular, R ∥ to the magnetic field are determined as a function of temperature for both the nematic phase and the smectic phase. It is shown that the polymer backbone is deformed in both phases. When the polymer exhibits only a nematic phase, it adopts a prolate conformation, where the average backbone direction is more or less parallel to the aligned mesogenic groups. Upon transition from the smectic phase to a nematic phase, the backbone in the nematic phase assumes a slightly oblate shape. This tendency towards oblate shape is due to the smectic fluctuations which are always present in such nematic phases. The exentricity of the oblate backbone conformation in the smectic phase is always larger than in the nematic phase. This is attributed to a periodic distribution of the backbone between the mesophase layers. Then, the backbone anisotropy depends not only on the smectic structure (S_A1, S_Ad), but also on the temperature dependence of the density of aligned mesogenic groups in the layers. On the other hand, it is shown that the isotopic mixtures are no longer ideal when polymers deuteriated in the mesogenic moieties are mixed with the corresponding hydrogenous polymers.     

Pretransitional electro-optic response of 6CB liquid crystal in the isotropic phase

Abstract

In this work, the electro-optic response of a 6CB liquid crystal layer is studied using a sensitive differential technique. The layer is held at a temperature just above the nematic to isotropic phase transition. Transverse magnetic (p) polarized light incident on the cell is coupled to guided modes in the liquid crystal layer using prism coupling. The modes manifest themselves as sharp dips in the reflectivity as the angle of incidence is scanned. When a low frequency sinusoidal voltage is applied to the cell, the resonant mode shapes and excitation angles are altered at a frequency which is twice that of the applied field, resulting in a modulation of the reflectivity for a given angle of incidence. By synchronous observation of the modulated signal, a differential signal is recorded. Comparing the data with modelling generated from multilayer optics theory, two effects are then quantified. The first of these is an induced birefringence, varying quadratically with applied voltage, which is well understood and can be expressed in terms of Landau-de Gennes theory. The second is a field induced perturbation in the imaginary part of the optical permittivity, δε_i, which implies a modification of the light scattering properties of the liquid crystal. The measurement of the latter effect is, as far as we know, a novel one, being only made possible by the remarkable sensitivity of the synchronous differential technique.     

Virtual Crystal Model of Melting and the Structure Factor of Liquid Alloys

Abstract

In this paper, we extend the theory of melting entropy of metals, of Omini, based on the Percus-Yevick collective coordinate theory of liquids, to binary liquid alloys. We reformalate Omini's use of the Percus-Yevick theory to include binary liquid alloys and calculate the long wavelength limit of the binary liquid alloy structure factor as a function of solute concentration for the systems: Li-Na, K-Rb. Rb-Cs, Al-Zn, Zn-Ca and AI-Ga which are the most nearly equi-valent and equi-volumeatom pairs Omini worked with.     

Influence of the Screening Function on Theoretical Calculations of the Structure Factor of Liquid Aluminum

Abstract

The structure factor S(k) of liquid aluminum is calculated using the Metropolis Monte Carlo method. The effective two-body ion-ion interaction used in the calculations are the Shaw optimized model and the local approximation suggested by Harrison calculated using two screening function in each case, the screening function of Vashishta and Singwi and that of Utsumi and Ichimaru. The calculated structure factors from each case are compared with experiment.     

Synthesis and thermophysical properties of two new protic long-chain ionic liquids with the oleate anion

This work reports the synthesis of 2-hydroxy ethylammonium oleate and bis(2-hydroxy ethyl)ammonium oleate ionic liquids, which have a long aliphatic chain as well as the study of some of their physical properties, in particular the effect of temperature on their density, speed of sound, viscosity, and refractive index. ¹H and ¹³C NMR spectra were used to characterize the chemical structure of the species in concordance with FT-IR spectra. DOSY NMR spectra were used to determine the self-diffusion coefficients of 2-hydroxy ethylammonium oleate ionic liquid, which were consistent with the formation of a lamellar or micellar liquid crystal phase; due the similar structure, a similar aggregation in the bis(2-hydroxy ethyl)ammonium oleate ionic liquid it is expected.     

An Optical Density Thermometer

Abstract

An optical density thermometer is described for determining the temperature of centrifuge rotors. Quantitation is based on the change in the concentration of the vapor phase of a volatile substance, such as bromine, with temperature. Centrifugal force holds the liquid phase away from the light path and removes condensation from the optical windows.