Effects of vibrational anharmonicity on 19F nuclear resonance in SF6

A Barker-Henderson like perturbation theory for polyatomic fluids is developed. The molecular interaction forces are assumed to be described by an interaction site model potential and the reference system is a fluid of hard interaction site model molecules.

The theory is used to study the equation of state of nitrogen, the theoretical results being compared with experimental data and with those coming from other theories. The agreement between theory and experiment is as good as that shown by Barker and Henderson theory for monoatomic systems.     

TPT2 and SAFTD equations of state for mixtures of hard chain copolymers

We present the second-order thermodynamic perturbation theory (TPT2) and the dimer statistical associating fluid theory (SAFTD) equations of state for mixtures consisting of hetero-nuclear hard chain molecules based on extensions of Wertheim's theory for associating fluids. The second-order perturbation theory, TPT2, is based on the hard sphere mixture reference fluid. SAFTD is an extension of TPT1 (= SAFT) and is based on the non-spherical (hard disphere mixture) reference fluid. The TPT2 equation of state requires only the contact values of the hard sphere mixture site-site correlation functions, while the SAFTD equation of state requires the contact values of site-site correlation functions of both hard sphere and hard disphere mixtures. We test several approximations for site-site correlation functions of hard disphere mixtures and use these in the SAFTD equation of state to predict the compressibility factor of copolymers. Since simulation data are available only for a few pure copolymer systems, theoretical predictions are compared with molecular simulation results for the compressibility factor of pure hard chain copolymer systems. Our comparisons show a very good performance of TPT2, which is found to be more accurate than TPT1 (= SAFT). Using a modified Percus-Yevick site-site correlation function SAFTD is found to represent a significant improvement over SAFT and is slightly more accurate than TPT2. Comparison of SAFTD with generalized Flory dimer (GFD) theory shows that both are equivalent at intermediate to high densities for the compressibility factor of copolymer systems investigated here.     

超临界二氧化碳和模型共聚物的相平衡和成核性质研究

在Weeks-Chandler-Andersen （WCA）微扰理论的基础上,建立了一个状态方程,研究了温度和压力以及模型共聚物分子链长对体系相平衡和临界胶束浓度的影响. 关键词： 超临界二氧化碳 模型共聚物 相平衡 临界胶束浓度     

Equation of state for fused-hard-sphere fluid mixtures

This paper develops a theoretically-based equation of state for fused-hard-sphere fluid mixtures on the basis of an equation of state previously derived for hard-convex-body fluid mixtures. The equation uses as a reference the equation of state for an equivalent hard-sphere fluid mixture in which each component has the same molecular volume as the effective molecular volume of one of the components of the fused-hard-sphere mixture. The two parameters required by the theory, namely the averaged effective molecular volume of the molecules in the mixture and the corresponding effective non-sphericity parameter, are obtained from the geometrical characteristics of the molecules that form the mixture. The results are, on the whole, in closer agreement with simulation data than those obtained with other theories developed for this kind of mixture.     

Perturbation theory for a mixture of polarizable liquids

Thermodynamic perturbation theory developed for pure polar liquids with significant polarizability is applied to a mixture with polar and nonpolar polarizable components. Expressions for the average and unperturbed dipole moments of the components of the mixture are presented and the dipole and induced contributions to the thermodynamic functions of the mixture are calculated. The equation of state is obtained and used to calculate the excess properties of a binary mixture of particles interacting with a stockmeyer potential. It is shown that the induced dipole moments contribute significantly to the thermodynamic properties of this model solution and that their effects must be taken into account in predicting the properties of real liquid mixtures containing polar components.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 69–73, March, 1985.     

The use of a non-spherical reference potential in statistical mechanical perturbation theory

A statistical mechanical perturbation theory for the pair correlation function and thermodynamic properties of molecular fluids is presented in which the reference potential function is non-spherical. With this choice the short-range molecular repulsive forces can be properly taken into consideration and attractive forces, such as those resulting from electric moments, treated as the perturbation. Calculations are presented for the first-order perturbation term to the Helmholtz free energy due to quadrupolar forces in models of liquid nitrogen and chlorine, and due to dipolar forces in liquid hydrogen chloride. For these calculations the rigid diatomic model and its modification appropriate to heteronuclear molecules were used for the reference potentials. It is found that the lowest-order perturbation terms here are proportional to the second power of the dipole or quadrupole moments, and not the fourth power as had been found previously using a spherical reference potential function. This second-order dependence on the electric moment is especially important in the case of mixtures, where it leads to an explanation for the occurrence of negative azeotropes in binary mixtures of species with quadrupole moments of opposite sign.     

水的非线性振动能谱的自陷理论计算

用非线性自陷方程的动力学理论计算了水分子、液体水和水蒸汽等的ＯＨ和ＨＯＨ键的非线性振动的量子振动能谱，所得结果与实验值符合得较好，也比简正模式和局域模式的结果较好． 关键词：     

An equation of state for nematic liquid crystals

A derivation of an equation of state for nematic liquid crystals is given based upon slightly non-spherical molecules interacting via anisotropic attractive forces. The results are in reasonable agreement with the experimental data for p-azoxyanisole.     

Equation of state of a mixture of hard spheres with non-additive diameters

The equation of state of a mixture of hard spheres with non-additive diameters has been found by molecular dynamical simulation. The mixture undergoes a fluid-fluid phase transition at high densities. A perturbation equation of state using a multicomponent reference fluid was found to give good agreement with the simulation results.     

Survey of segregation alteration of hydrogen-helium mixtures via structure factor

In this study, thermodynamic instabilities in hydrogen-helium fluid mixture have been analyzed. These kinds of investigations are inevitable for indicating hydrodynamic transitions in Hydrogen-Helium fluid mixture. Therefore, first we have derived equation of state of mixture via Barker-Henderson statistical perturbation theory. Moreover, we have used Yiping radial distribution function in calculating perturbed terms. Via equation of state, we have calculated excess Gibbs free energy and the Gibbs free energy in the long wavelength limit. By means of this energy in hand we could estimate degree of hetero-coordination and segregations of this mixture which is a measure for defining thermodynamic instabilities. At last, these measurements have made us capable of anticipating thermodynamic instabilities and coordination of mixture in different concentrations.     

Equation of state of mixtures of simple fluids at high pressures

Recently Lee and Levesque have extended the Weeks-Chandler-Andersen pure fluid perturbation theory to mixtures and have compared the results to the Leonard-Henderson-Barker mixture theory. The results seem to favour the Leonard-Henderson-Barker theory. This and other previous comparisons of mixture theories have been mostly confined to the study of ‘zero pressure’ thermodynamic properties. In this paper we compare the Lee-Levesque, Leonard-Henderson-Barker and the van der Waals one-fluid theories to high pressure equation of state data for helium-xenon mixtures. This system is modelled by a binary mixture of Lennard-Jones fluids and the hard sphere reference system is characterized by the Grundke-Henderson hard sphere mixture radial distribution function. The Lee-Levesque theory compares favourably with experimental equation of state data up to pressures of 2000 atmospheres. The Leonard-Henderson-Barker and van der Waals one theories are satisfactory. Although the van der Waals one theory yields the poorest results, it does offer the advantage of having the greatest ease of computation.

Previous theoretical and Monte Carlo calculations of mixture properties have assumed the geometric mean rule for the mixed interaction energy parameter, ε ₁₂, with consequent disagreement with experimental results. We point out that ε ₁₂ can be determined from mixed second virial coefficient data and use such improved determinations of ε ₁₂. We show that this method yields significantly improved theoretical predictions.     

LJ模型的热力学特性、相平衡及用于真实分子的研究

结合描述硬球固体Helmholtz自由能的自由体积方法与描述硬球固体径向分布函数的拟合的分析表达式与一阶热力学摄动理论,用于描述Lennard Jones(LJ)固体的Helmholtz自由能.按照一个修正的WCA方法将LJ势分为短程排斥部分与长程吸引部分,将文献中一个用于求取液相的等价的硬球直径的简单的迭代法扩展到固相,用于求取固相的等价的硬球直径.在固体Helmholtz自由能的计算中,使用200壳层,以便获得精确的结果.体相LJ液体的热力学特性由一个最近提出的状态方程求取.该方法很好地描述了LJ固体的过量Helmholtz自由能与状态方程,满意地描述了Lennard Jones模型的相平衡;通过选取合适的LJ势参数,能很好地描述了真实分子的融化曲线.     

爆轰产物物态方程（Ⅱ）——爆轰的ZND理论不成立吗?（上）

 爆轰的ZND理论,作为一个理论是需要经过严格检验之后才能承认其成立的。美国科学家做了这样的检验,但由于缺乏对爆轰产物物态方程的了解,没有能得出肯定的检验结论。用分子间有强排斥作用与分子作完全自由平动的液态物态方程（R-T物态方程）所做的检验表明爆轰的ZND理论是成立的。     

Equation of state and stability of the helium-hydrogen mixture at cryogenic temperature

The equation of state and the stability of the helium-molecular hydrogen mixture at cryogenic temperature up to moderate pressure are studied by means of current molecular physics methods and statistical mechanics perturbation theory. The phase separation, segregation and hetero-coordination are investigated by calculating the Gibbs energy depending on the mixture composition, pressure and temperature. Low temperature quantum effects are incorporated via cumulant approximations of the Wigner-Kirkwood expansion. The interaction between He and H₂ is determined by Double Yukawa potentials. The equation of state is derived from the hard sphere system by using the scaled particle theory. The behavior of the mixture over a wide range of pressure is explored with the excess Gibbs energy of mixing and the concentration fluctuations in the long wavelength limit. The theory is compared to cryogenic data and Monte-Carlo calculation predictions. Contrary to previous similar works, the present theory retrieves the main features of the mixture below 50 K, such as the critical point and the condensation-freezing curve, and is found to be usable well below 50 K. However, the method does not distinguish the liquid from the solid phase. The binary mixture is found to be unstable against species separation at low temperature and low pressure corresponding to very cold interstellar medium conditions, essentially because H₂ alone condenses at very low pressure and temperature, contrary to helium.     

Intermolecular interactions and excess thermodynamic properties of argon-krypton and krypton-xenon mixtures

Recently, reliable pair-potentials have been obtained for argon, krypton and xenon. Pair-potentials of similar form are obtained for the argon-krypton and krypton-xenon interactions. Three parameters are adjusted to give experimental values for the long-range r ^-6 term and the excess free energy and excess volume for an equimolar liquid mixture at zero pressure and a specified temperature. The excess thermodynamic properties are calculated from the Barker-Henderson perturbation theory, which has been shown to give good values for the excess thermodynamic properties of mixtures of 6:12 molecules, with the contributions of three-body forces and quantum effects included. Excellent agreement with the excess properties of argon-krypton and krypton-xenon mixtures is found at all concentrations.     

Vapour-liquid and gas-gas equilibria in simple systems: IV. The system argon-krypton

The vapour-liquid equilibrium of the system argon-krypton has been investigated. The co-existing liquid and gas phases have been determined as a function of pressure and temperature. The experimental critical line is compared with theoretical results obtained from perturbation theory and the Van der Waals equation of state.     

水高温高密度状态方程理论研究

 采用MCR方法计算由exp-6势描述的水分子作用体系的pVT状态方程。与MD数值模拟结果比较后发现，由于水分子间强烈的吸引作用有利于分子有序化过程的发生，在较高温度（2 000~4 000 K）条件下，水分子作用体系仍呈现出固态特征。该物相区内体系的热力学性质不能用MCR理论描述但MCR理论准确预言了水分子作用体系高温液相区pVT状态方程。     

Equation of state of initially liquid carbon monoxide and nitrogen mixture

The modified liquid perturbation variational theory and the improved vdW-1f model were applied to calculating the equation of the state of liquid CO-N₂ mixture with the ratio of 1:1, 4:1 and 1:4, respectively, in the shock pressure range of 9–49 GPa. It was shown that the calculated result for CO-N₂ mixture with the ratio of 1:1 is well consistent with the earlier experimental data. The thermodynamics equilibrium, chemical equilibrium and phase equilibrium were all considered in detail. It was found that Hugoniot of liquid CO-N₂ mixture is moderately softened in the pressure range of 20–30 GPa and 30–49 GPa for different initial proportions, and that the Hugoniot is more softened in the latter pressure range, which means that the structural phase transition occurs near 20 GPa and 30 GPa. Since the shock productions may absorb a plenty of systematic energy, the shock temperature and pressure decline compared with the case of no chemical reaction. Pressures and temperatures increase gradually with the increase in the mole fraction of nitrogen composition. The results for the 1:1 CO-N₂ mixture lie in the middle of two others. Therefore, it was shown that the modified Lorentz-Berthelor rule used in the scheme is effective to study shock-compression properties of liquid CO-N₂ mixture under high temperatures and high pressures. Supported by the National Natural Science Foundation of China (Grant No. 10576020)     

Thermodynamics of mixtures of non-spherical molecules

Thermodynamic properties of liquid mixtures in which strong anisotropic intermolecular forces exist are studied using the Padé approximant method used by Stell et al. for pure fluids. Equations for the third-order perturbation term are derived for a general intermolecular potential of multipolar type. Using a mixture of Lennard-Jones molecules as the reference system, the effects of adding point dipole, quadrupole and anisotropic overlap potentials are calculated. Numerical results are presented (at low pressures) for the effect of these forces on the excess functions, and on the vapor-liquid equilibrium curves. These anisotropic forces lead to positive deviations from Raoult's law. Strong polar and quadrupolar forces may cause liquid-liquid immiscibility to occur. Numerical calculations are presented to illustrate such behaviour; these systems have upper critical solution points.     

Thermodynamics of a long-range triangle-well fluid

The long-range triangle-well fluid has been studied using three different approaches: firstly, by an analytical equation of state obtained by a perturbation theory, secondly via a self-consistent integral equation theory, the so-called self-consistent Ornstein–Zernike approach (SCOZA) which is presently one of the most accurate liquid-state theories, and finally by Monte Carlo simulations. We present vapour–liquid phase diagrams and thermodynamic properties such as the internal energy and the pressure as a function of the density at different temperatures and for several values of the potential range. We assess the accuracy of the theoretical approaches by comparison with Monte Carlo simulations: the SCOZA method accurately predicts the thermodynamics of these systems and the first-order perturbation theory reproduces the overall thermodynamic behaviour for ranges greater than two molecular diameters except that it overestimates the critical point. The simplicity of the equation of state and the fact that it is analytical in the potential range makes it a good candidate to be used for calculating other thermodynamic properties and as an ingredient in more complex theoretical approaches.