Structure formation in binary carboxyl-containing rubber-epoxide oligomer mixtures

The rules governing the formation of network structures in carboxyl-containing nitrile butadiene rubber-epoxide oligomer were studied. It was shown that reactions between epoxide, carboxyl, and hydroxyl groups occurred in the chemical interaction of oligomers. These reactions caused elongation of macromolecular chains and the formation of branching points and a three-dimensional network structure. The influence of temperature and the ratio between oligomers on the characteristics of the structure formed was considered.     

Perturbation theory of polar hard Gaussian overlap fluid mixtures

A perturbation theory of polar hard Gaussian overlap fluid mixture is discussed. Explicit analytic expressions for the second and third varial coefficients are given. Numerical results are estimated for the thermodynamic properties of quadrupolar hard Gaussian overlap fluid and fluid mixture. It is found that the excess free energy and internal energy depend on concentrationsc ₁,c ₂, molecular diameter ratioR, shape parameterK and the quadrupole momentsQ*₁,Q*₂.     

A study of ionic solids by means of new density-functional theory techniques

Summary The lattice parameter, the bulk modulus and the dissociation energy of NaCl and MgO are calculated by a method which allows the direct determination of the total energy and of the charge density of a crystal. An extensive comparison with the results of standard band structure calculations is reported. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Phase behavior of binary hard-sphere mixtures from perturbation theory

Using a first-order perturbation theory, we have studied the phase diagram of a binary mixture of hard spheres for different values of the size ratio. Recent models for the two-body depletion potential between large spheres are used to take into account the role of the small spheres. The theory predicts a complex phase diagram including a fluid-solid transition at high packing fraction of small spheres, metastability of fluid-fluid demixing, an isostructural solid-solid transition at high packing fraction of the large spheres for sufficiently small values of the size ratio q of the spheres, and the tendency to sticky-sphere behavior in the limit q-->0. The agreement with recent simulation results is quite good. We also show that this phenomenology was already implicit in the pioneering work of Asakura and Oosawa.     

A comparative study of non-linearity parameter for binary liquid mixtures

The present investigation comprises of theoretical evaluation of acoustic non-linearity parameter,B/A for equimolar binary mixtures, viz. chlorobenzene or 1-chloronaphthalene with a series of normal alkanes (n-C_n,n = 6, 8, 10, 12, 14, 16), and with a series of highly branched alkanes (br-C_n,n = 6, 8, 12, 16), viz. 2,2-dimethylbutane (br-C₆), 2,2,4-trimethylpentane (br-C₈), 2,2,4,6,6-pentamethylheptane (br-C₁₂) and 2,2,4,4,6,8,8-heptamethylnonane (br-C₁₆). Tong and Dong method, thermoacoustical method, Hartmann relation and Ballou relation have been employed to evaluateB/A. A comparative study ofB/A values obtained from the aforementioned methods has been made. The results are discussed on the basis of structural orientations of normal and branched alkanes.     

Excitations in time-dependent density-functional theory

An approximate solution to the time-dependent density-functional theory response equations for finite systems is developed, yielding corrections to the single-pole approximation. These explain why allowed Kohn-Sham transition frequencies and oscillator strengths are usually good approximations to the true values, and why sometimes they are not. The approximation yields simple expressions for G?rling-Levy perturbation theory results, and a method for estimating expectation values of the unknown exchange-correlation kernel.     

Stability and mechanical properties of various Hf-H phases: A density-functional theory study

We performe first-principles density functional theory calculations to investigate the stability and mechanical properties of various Hf Hx(0 ≤ x ≤ 1) phases. For pure Hf phases, the calculated results show that the HCP and FCC phases are mechanically stable, while the BCC phase is unstable at 0 K. Also, as for various Hf Hx phases, we find that H location and concentration could have a significant effect on their stability and mechanical properties. When 0 ≤ x ≤ 0.25, the HCP phases with H at(tetrahedral) T sites are energetically most stable among various phases. The FCC and BCC phases with H at T sites turn to be relatively more favorable than the HCP phase when H concentration is higher than 0.25. Furthermore, our calculated results indicate that the H solution in Hf can largely affect their mechanical properties such as the bulk moduli(B) and shear moduli(G).     

Bayesian error estimation in density-functional theory

We present a practical scheme for performing error estimates for density-functional theory calculations. The approach, which is based on ideas from Bayesian statistics, involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies for molecules and solids. Fluctuations within the ensemble can then be used to estimate errors relative to experiment on calculated quantities such as binding energies, bond lengths, and vibrational frequencies. It is demonstrated that the error bars on energy differences may vary by orders of magnitude for different systems in good agreement with existing experience.     

Particle-vibrational coupling in covariant density-functional theory

A consistent combination of covariant density-functional theory and Landau-Migdal theory of finite fermi systems is presented. Both methods are in principle exact, but Landau-Migdal theory cannot describe ground-state properties and density-functional theory does not take into account the energy dependence of the self-energy and therefore fails to yield proper single-particle spectra as well as the coupling to complex configurations in the width of giant resonances. Starting from an energy functional, phonon energies and their vertices are calculated without any further parameters. They form the basis of particle-vibrational coupling leading to an energy dependence of the self-energy and an induced energy-dependent interaction in the response equation. A proper subtraction of the static phonon-coupling contribution from the induced interaction avoids double counting of this contribution. Applications in doubly magic nuclei and in a chain of superfluid nuclei show excellent agreement with experimental data. The text was submitted by the authors in English.     

Exact conditions in finite-temperature density-functional theory

Density-functional theory (DFT) for electrons at finite temperature is increasingly important in condensed matter and chemistry. The exact conditions that have proven crucial in constraining and constructing accurate approximations for ground-state DFT are generalized to finite temperature, including the adiabatic connection formula. We discuss consequences for functional construction.     

Derivative discontinuities in time-dependent density-functional theory

Based on the Runge-Gross theorem for ensembles we investigate the influence of particle-number-changes on the exchange-correlation potential in time-dependent density-functional theory. We show that the potential changes discontinuously when the particle number crosses an integer value. Real-time simulations of an atomic ionization process demonstrate that this discontinuity appears naturally in the theory of the time-dependent optimized effective potential. The importance of such a discontinuity for physical processes, even such ones in which the particle number is a constant, is discussed.     

On the theory of spinodal decomposition in solid and liquid binary mixtures

The kinetics of phase separation is discussed with emphasis on the transition between spinodal decomposition and nucleation. A reanalysis of the theory of Langer, Baron and Miller shows that it exhibits a spinodal line somewhat closer to the coexistence curve than the meanfield spinodal. There the same (as we think unphysical) critical singularities occur as in Cahn-Hilliard theory. The precise location of this spinodal line depends on the cell size of the coarse graining. For concentrations less than the spinodal one the structure factorS(k, t) converges then towards the structure factor of the metastable onephase state, implying an infinite lifetime of the latter.In order to include the effects of nucleation and growth we hence present an alternative treatment, extending our previous work on cluster dynamics. From a simple approximation for the radial concentration distribution function of clustersS(k, t) is computed numerically. Even at rather low concentrations the time evolution ofS(k, t) is then similar to what Langer et al. find at high concentrations, implying a very gradual transition from nucleation and growth to spinodal decomposition, at least for parameter values appropriate to the Ising model. This treatment, which is consistent with Lifshitz-Slyozov's coarsening law at late times, is extended to the early stages of phase separation in liquid mixtures.     

Isotope effects on the microphase separation of paraffin mixtures

Isotopic sensitivity is reported in both the formation and the above ambient temperature annealing behaviour of lamellar microphases in C₃₀:C₃₆ paraffin solid solutions. The time resolved small angle neutron scattering from a 1:1 C₃₀H₆₂:C₃₆D₇₄ mixture and its complementary pair 1:1 C D :C H has been studied. Upon quenching such mixtures from the melt; the solid solution so formed nucleates spontaneously to a ‘long period’ microphase. The two systems differ in that for 1:1 C₃₀D₆₂:C₃₆H₇₄ there is also strong diffraction at Q = 0·136 A^-1 associated with C₃₆H₇₄ enrichment of the solid solution or a separate phase. Both processes are sensitive to the isotopic composition of the mixture. For both systems the long period scattering from a quenched liquid mixture develops in periods of hours at ambient temperature. Heating the aged microphase structures to temperatures above about 43°C causes them to disappear, but again isotropic sensitivity is noted. It is concluded that the effects are largely kinetic in origin, in agreement with earlier IR studies on intralamellar microaggregation in this system.     

X-ray diffraction study of cholesterol-cholesteryl oleate binary mixtures

Summary The phase transitions for binary mixtures of cholesteryl oleate (CO) and cholesterol (CH) have been investigated by X-ray diffraction, differential scanning calorimetry and optical microscopy. The phase diagrams on heating, involving the solid-solid and solid-isotropic liquid transitions, and on cooling, involving the cholesteric and smectic mesophases, have been derived. In particular, a strong supercooling effect of liquid cholesterol and a progressive decrease of the isotropic liquid-cholesteric and cholesteric-smectic transition temperatures were observed. Moreover, some structural modifications induced in the smecticA and in the cholesteric phase by the presence of CH in CO were detected. Finally the dependence of intermolecular distance in the isotropic liquid phase was studied as a function of temperature and mixture composition.

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Riassunto Mediante diffrazione dei raggi X, calorimetria differenziale e microscopia ottica sono state studiate le transizioni di fase per miscele binarie di colesteril oleato (CO) e colesterolo (CH). Sono stati ricavati in riscaldamento il diagramma di fase per le transizioni solido-solido e solido-liquido isotropo ed in raffreddamento un diagramma di fase comprendente le mesofasi colesterica e smettica. In particolare sono stati osservati un marcato effetto di sovraraffreddamento del liquido del colesterolo ed una progressiva diminuzione delle temperature di transizione delle fasi liquido-isotropo colesterico e colestericosmettico. Inoltre sono state trovate alcune modificazioni strutturali indotte nella fase smetticaA ed in quella colesterica dalla presenza del CH nel CO. Infine è stata studiata la dipendenza della distanza intermolecolare nella fase liquido isotropo in funzione della temperatura e della composizione della miscela.

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Резюме Исследуются фазовые переходы в бинарных смесях олеата холестерила (CO) и холестерола (CH) с помощью дифракции рентгеновских лучей, дифференциальной сканирующей калориметрии и оптической микроскопии. Получаются при нагревании фазовые диаграммы, вклюьающие переходы твердое тело-твердое тело и твердое тело-изотропная жидкость, а при охлаждении фазовая диаграмма, включающая холестерическую и смектическую мезофазы. В частности, наблюдается сильные эффект сверхохлаждения дия жидкого холестерола и постепенное уменьшение температур фазовых переходов изотропная жидкость-холестерик и холестерик-смектик. Кроме того, определяются структурные модификации, индуцированные в фазе смектикаА и в фазе холестерика наличием CH и CO. В эаключение, исследуется эависимость расстояния между молекулами в фазе изотропной жидкости, как функция температуры и состава смеси.

     

Excess properties of Lennard-Jones binary mixtures from computer simulation and theory

Monte Carlo simulation and theory are used to calculate the excess thermodynamic properties of binary mixtures of spherical Lennard-Jones molecules. We study the excess functions of three binary mixtures characterized by the following size and dispersive energy ratios: (1) (σ₂₂/σ₁₁)³ = 2 and ?₂₂/?₁₁ = 2; (2) (σ₂₂/σ₁₁)³ = 1 and ?₂₂/?₁₁ = 1/2 and (3) (σ₂₂/σ₁₁)³ = 1/2 and ?₂₂/?₁₁ = 2. In all cases, the unlike size parameter, σ₁₂, is kept constant and equal to the value given by the Lorentz combining rule (σ₁₂ = (σ₁₁ + σ₂₂)/2). However, different unlike dispersive energy parameter values are considered through the following combining rules: (a) ?₁₂ = (?₁₁?₂₂)^1/2 (Berthelot rule); (b) ?₁₂ = ?₁₁ (association); and (c) ?₁₂ = ?₂₂ (solvation). The pressure and temperature dependence of the excess volume and excess enthalpy is studied using the NpT Monte Carlo simulation technique for all the systems considered. Additionally, the simplest conformal solution theory is used to check the adequacy of this approach in predicting the excess properties in a wide range of thermodynamic conditions and variety of binary mixtures. In particular, we have applied the van der Waals one-fluid theory to describe Lennard-Jones binary mixtures through the use of the Johnson et al. [1993, Molec. Phys., 78, 591] Helmholtz free energy. Agreement between simulation results and theoretical predictions is excellent in all cases and thermodynamic conditions considered. This work confirms the applicability of the van der Waals one-fluid theory in predicting excess thermodynamic properties of mixtures of spherical molecules. Furthermore, since binary mixtures of spherical Lennard-Jones molecules constitute the reference fluid to be used in perturbation theories for complex fluids, such as the statistical association fluid theory (SAFT), this work shows clearly the applicability of the conformal solution theory within the framework of SAFT for predicting excess functions.     

An evolutionary game theory model of binary opinion formation

A basic characteristic of most opinion models is that people tend to agree or compromise in the opinion interaction, which could be hopefully described by cooperative games in the evolutionary game theory framework. This paper presents game theory methods to model the formation of binary opinions: cooperative games are proposed to model the interaction rules of general people who tend to find an agreement; minority games are proposed to model the behaviors of contrarians; opinion preference is considered by varying the payoff values. The Majority Voter model could be restored from the proposed games. The game theory models show evolutionary results similar to traditional opinion models. Specially, the evolution of opinions with consideration of contrarians is in accordance with the Galam model. Furthermore, influences of evolving rule, network topology and initial distribution of opinions are studied through numerical simulations. Discussions about methods to promote or hinder the consensus state at the best equilibrium point are given.     

Ultrasonic study on organic liquid and binary organic liquid mixtures by using Schaaffs＇ collision factor theory

Based on Schaaff's collision factor theory (CFT) in liquids, the equations for nonlinear ultrasonic parameters in both organic liquid and binary organic liquid mixtures are deduced. The nonlinear ultrasonic parameters, including pressure coefficient, temperature coefficients of ultrasonic velocity, and nonlinear acoustic parameter B/A in both organic liquid and binary organic liquid mixtures, are evaluated for comparison with the measured results and data from other sources. The equations show that the coefficient of ultrasonic velocity and nonlinear acoustic parameter B/A are closely related to molecular interactions. These nonlinear ultrasonic parameters reflect some information of internal structure and outside status of the medium or mixtures. From the exponent of repulsive forces of the molecules, several thermodynamic parameters, pressure and temperature of the medium, the nonlinear ultrasonic parameters and ultrasonic nature of the medium can be evaluated. When evaluating and studying nonlinear acoustic parameter B/A of binary organic liquid mixtures, there is no need to know the nonlinear acoustic parameter B/A of the components. Obviously, the equation reveals the connection between the nonlinear ultrasonic nature and internal structure and outside status of the mixtures more directly and distinctly than traditional mixture law for B/A, e.g. Apfel's and Sehgal's laws for liquid binary mixtures.     

Adiabatic approximation in nonperturbative time-dependent density-functional theory

We construct the exact exchange-correlation potential of time-dependent density-functional theory and the approximation to it that is adiabatic but exact otherwise. For the strong-field double ionization of the Helium atom these two potentials are virtually identical. Thus, memory effects play a negligible role in this paradigm process of nonlinear, nonperturbative electron dynamics. We identify the regime of high-frequency excitations where the adiabatic approximation breaks down and explicitly calculate the nonadiabatic contribution to the exchange-correlation potential.