Perturbation theory for mixtures of simple liquids

The perturbation approach developed by Weeks, Chandler, and Andersen (WCA) and by Verlet and Weis (VW) for pure systems is here generalized to the case of mixtures. We study binary mixtures of molecules interacting with the 12–6 Lennard-Jones potential, for which Monte Carlo simulations are available for comparison. The work is divided into two parts: The first part presents results of Monte Carlo calculations on mixtures of hard spheres of 864 and 1000 particles. The radial distribution functions generated are used to test the VW representation for the correlation functions of hard-sphere mixtures. This representation is found to work satisfactorily within the expected error limits. The second part deals with the two-step perturbation procedure for calculating the thermodynamic quantities of the Lennard-Jones system. The Lennard-Jones potential is divided into a reference potential, which is strictly repulsive, and an attractive part. The system of the reference potential is represented by a system of hard-sphere mixture with equivalent diameters determined by the WCA rule. Analytical expressions are given for evaluating these equivalent diameters. The Lennard-Jones system is then recovered to the first order by a λ expansion over the reference system. Comparison with Monte Carlo results for a mixture of Lennard-Jones molecules, obeying the Berthelot rule, shows that the total thermodynamic properties are reproduced by the perturbation theory to 1 per cent, while the agreement in excess properties is only moderately successful, similar to some other analytical theories compared here. To reproduce these excess properties, which are extremely small, a precision of 0·1 per cent in the theory is required. The present theory is estimated to be accurate to 1 per cent in view of the successive approximations made.     

Perturbation theory for non-axial molecular fluids

The thermodynamic perturbation theory in which all angle-dependent interactions are considered as a perturbation of the central potential is applied to study the equilibrium properties of a fluid composed of non-axial molecules. The influence of a large number of anisotropic pair and three-body non-additive interactions have been taken into account. Using the same set of force parameters the calculation is made for gaseous pressure second and third virial coefficients and liquid phase thermodynamic properties (Helmholtz free-energy, configurational energy, pressure and entropy). It is shown that the non-axial approximation is an improvement over the axial one. Excellent agreement between theory and experiment is obtained for ethylene.     

Electric field dependence of phase equilibria of binary Stockmayer fluid mixtures

A perturbation theory based study of the effect of an external electric field on the phase equilibrium properties of binary Stockmayer fluids is presented. The dipole–dipole interaction and the applied field are treated as independent perturbations to a Lennard–Jones mixture, and the reference fluid is treated by the van der Waals one-fluid approximation. A third-order free energy expression in the electric field strength is established, and the dielectric constant is calculated for a needle-shaped sample parallel to the field direction. We present and discuss vapour–liquid and liquid–liquid equilibrium curves at a given temperature for some dipolar mixtures exposed to an electric field, including chlorodifluoromethane +?difluoromethane and acetonitrile +?methanol. A sufficiently high electric field may result in massive shifts of vapour pressures and critical or azeotropic points, and can considerably alter the properties of coexisting phases. The vapour pressure decreases with increasing field strength.     

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.     

Correlation in statistical theory of liquid crystals

A statistical theory which takes into account correlation between orientations of rod-like molecules in a liquid crystal is proposed. This theory is a variant of thermodynamical perturbation theory. The proposed representation of the distribution function in spherical functions enables us to introduce consistently long-range order parameters as well as to analyze the thermodynamics of a liquid crystalline phase described by a rotation-invariant Hamiltonian.     

The Feynman-Schwinger Representation in QCD

The proper time path integral representation is derived explicitly for Green's functions in QCD. After an introductory analysis of perturbative properties, the total gluonic field is separated in a rigorous way into a nonperturbative background and valence gluon part. For nonperturbative contributions the background perturbation theory is used systematically, yielding two types of expansions, illustrated by direct physical applications. As an application, we discuss the collinear singularities in the Feynman-Schwinger representation formalism. Moreover, the generalization to nonzero temperature is made and expressions for partition functions in perturbation theory and nonperturbative background are explicitly written down.     

Equilibrium properties of ferrocolloids

We consider a thermodynamic model of a stable macroscopically homogeneous ferrocolloid containing identical spherical particles with permanent moments suspended in a non-dissociated liquid on the basis of the hard sphere perturbation theory. Magnetostatic properties and the phase diagram of the ferrocolloid are shown to agree very well with experimental evidence. Dipole interparticle interactions result in an effective attraction between the particles which increase, as the strength of an externally applied magnetic field grows, favours the phase separation and cause a reduction in the coefficient of mutual Brownian diffusion of the particles.     

Statistical-mechanical perturbation theory for liquid metals

The techniques of statistical mechanical perturbation theory are applied to liquid metals. An ion-ion repulsive pair potential is determined from an experimental structure factor curve at a temperature β₀=1/kT₀. The theory then permits the prediction of radial distribution functions, structure factors, compressibilities, and other properties at all liquid temperatures. As a preliminary test of the theory, it has been used to calculate the isothermal compressibilities of Na, Hg and Ga. The results are in very good agreement with the experimental values, which for the last metals differ from earlier theoretical predictions by almost a factor of five.     

Electrical conductivity and thermopower of metallic helium

The pair effective interionic interaction, electrical resistance, and thermopower of liquid metallic helium have been calculated over wide temperature and density ranges using the perturbation theory for the potential of electron-ion interaction. For conduction electrons, the random-phase approximation has been used taking into account the exchange interaction and correlations in the local-field approximation. The nuclear subsystem has been described by the hard-sphere model. The sphere diameter is the only parameter of the theory. The diameter and the system density at which helium is transformed from the singly ionized to doubly ionized state have been estimated based on an analysis of the pair effective interaction between helium nuclei. The case of doubly ionized helium atoms has been considered. The numerical calculations have been performed taking into account the perturbation theory in terms up to the third order. In all cases, the role of the third-order correction is significant. In the case of metallic helium, the values of the electrical resistance and its temperature dependence are characteristic of divalent simple liquid metals, as well as the dependences of the thermopower on the density and temperature.     

Feynman integral and perturbation theory in quantum tomography

We present a definition for tomographic Feynman path integral as representation for quantum tomograms via Feynman path integral in the phase space. The proposed representation is the potential basis for investigation of Path Integral Monte Carlo numerical methods with quantum tomograms. Tomographic Feynman path integral is a representation of solution of initial problem for evolution equation for tomograms. The perturbation theory for quantum tomograms is constructed.     

Study of the solid-liquid-vapour phase equilibria of flexible chain molecules using Wertheim's thermodynamic perturbation theory

The phase diagram of flexible molecules formed by freely-jointed tangent spheres is studied using the first-order thermodynamic perturbation theory of Wertheim for both fluid and solid phases. A mean-field term is added to the free energy of the fluid and solid phase in order to account for attractive dispersion forces. The approach is used to determine the global (solid-liquid-vapour) phase diagrams and triple points of chain molecules of increasing chain length. It is found that the triple point temperature is not affected strongly by the length of the chain, whereas the gas-liquid critical temperature increases dramatically. The asymptotic limits of the phase diagram for infinitely long chains are discussed. The reduced critical temperature of infinitely long chains as given by the mean-field theory is 2/3, and the reduced triple point temperature is 0.048 56, so that an asymptotic value of T _t/T _c = 0.07284 for the ratio of the triple to critical point temperatures is obtained. This indicates that fully-flexible tangent chains present an enormous liquid range. The proposed theory, while being extremely simple, provides a useful insight into the phase behaviour of chain molecules, showing the existence of finite asymptotic limits for the triple and critical point temperatures. However, since n-alkanes present an asymptotic limit of about T _t/T _c, = 0.40, the agreement With experiment is not quantitative. This suggests that fully flexible models may not be appropriate to model the solid phases of real chain molecules.     

液氦冲击压缩特性的理论计算

 用量子力学修正的WCA液体变分微扰理论计算了液氦冲击压缩曲线，计算中体系分子间相互作用势选择EXP-6有效两体势模型，两体势参数通过对实验数据的拟和优选。计算结果在一次冲击压力范围内，冲击温度及压力与Nellis等人的实验数据符合很好，二次冲击数据与实验值稍有偏差，但也在其误差范围内，由于二次冲击只有一个实验点，因此实验数据不能提供更多的信息以供比较。计算结果表明与其他分子间相互作用势相比，选择α值为12.7的EXP-6势更为准确地反映了液氦分子间的相互作用。     

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.     

Thermodynamic properties for the triangular-well fluid

The thermodynamic properties of the triangular-well fluid with a well range of up to twice the hard sphere diameter were studied by means of a new developed equation of state and molecular simulation. This EoS is based on the perturbation theory of Barker and Henderson with the first and second-order perturbation terms evaluated by molecular simulation and then a fit with a simple function based on the radial distribution function of the reference fluid. The thermodynamic properties for the triangular-well fluid were also obtained directly by Gibbs ensemble and NPT Monte Carlo simulations. Good agreement is observed between the proposed EoS and the molecular simulation results. A model for the triangular-well solid is also presented; this has been used to calculate the solid–liquid transition line. Very good agreement is obtained with previously report values for this line and for the triple point temperature and pressure.     

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。     

高温高密度氩物态方程研究

用Exp-6有效两体势模型和液体变分微扰理论计算了液Ar冲击压缩曲线,在35 GPa以下的压力范围内计算的冲击压缩曲线与Thiel 及Nellis等人的实验数据进行了比较.液体分子间Exp-6有效两体势参数根据实验数据计算优选出最佳值,计算结果表明得到的优选参数较为准确地描述了液Ar分子间相互作用.由理论结合实验数据可以认为液氩体系在冲击压力36 GPa以下无相变现象.对较高冲击压力下理论计算的冲击曲线和实验结果之间的偏差作了分析,结合不透明度实验的结果,得到当压力超过35 GPa,温度在12 000 K     

高温高压金刚石单晶生长界面的研究

 利用扫描电镜及Auger电子谱技术研究了高温高压下金刚石单晶生长界面的特性，观察到了金刚石单晶表面及金属膜表面的沟槽结构及金刚石-金属、金属-石墨两个主界面间的过渡层结构及界面间C原子电子组态的变化。