Interionic pair potentials and partial structure factors of compound-forming quaternary NaSn liquid alloy: First principle approach

In this paper formulae for partial structure factors have been used to study partial structure factors of compound-forming quaternary liquid alloys by considering Hoshino’s m-component hard-sphere mixture, which is based on Percus-Yevic equation of Hiroike. Formulae are applied to NaSn (Na, Sn, NaSn, Na₃Sn) which is considered as a quaternary liquid mixture with the formation of two compounds simultaneously. We have compared the total structure factors for ternary and quaternary alloys with experimental total structure factors which are found to be in good agreement. This suggests that, for suitable stoichiometric composition, two compounds are formed simultaneously. The hard-sphere diameters needed have been calculated using Troullier and Martins ab-initio pseudopotentials.      

Equation of state and liquid–vapour equilibrium in a triangle-well fluid

The second-order thermodynamic perturbation theory formulation of Barker and Henderson is used to derive the equation of state of the triangle-well fluid. This is combined with the rational function approximation to the radial distribution function of the hard-sphere fluid. Results are obtained for the critical parameters and the liquid–vapour coexistence curve for various values of the range of the potential. A comparison with available simulation data is presented.     

Perturbation theory and the excess properties of mixtures of simple liquids

One of the most successful theories of single-component simple liquids is perturbation theory which is based on the assumption that the structure of a liquid is primarily determined by the repulsive forces between its molecules, so that a liquid may be regarded as a system of hard spheres with the attractive forces providing a uniform background energy. Our earlier extension of these ideas to liquid mixtures was only partially successful. In this paper we show that this problem was due to the use of a somewhat unsatisfactory equation of state for the reference hard-sphere mixture. If a more satisfactory equation of state is used, perturbation theory yields results in close agreement with Monte Carlo and experimental results, even when the molecules of the mixture differ appreciably in size.     

Universal cubic equation of state and contact values of the radial distribution functions for multi-component additive hard-sphere mixtures

A universal cubic equation of state (UC EOS) is proposed based on a modification of the virial Percus-Yevick (PY) integral equation EOS for hard-sphere fluid. The UC EOS is extended to multi-component hard-sphere mixtures based on a modification of Lebowitz solution of PY equation for hard-sphere mixtures. And expressions of the radial distribution functions at contact (RDFC) are improved with the form as simple as the original one. The numerical results for the compressibility factor and RDFC are in good agreement with the simulation results. The average errors of the compressibility factor relative to MC data are 3.40%, 1.84% and 0.92% for CP3P, BMCSL equations and UC EOS, respectively. The UC EOS is a unique cubic one with satisfactory precision among many EOSs in the literature both for pure and mixture fluids of hard spheres.     

A generalization of the Ashcroft-Lekner hard-sphere model for the structure factor

The Ashcroft-Lekner hard-sphere model for the calculation of the structure factor is generalized to take into account a correct hard-sphere equation of state. The model has one independent parameter which can be adjusted by a fit to the experimental data at one point.     

CO2气、液、固三相饱和态下pVT的计算

本文基于分子聚集理论和硬球引力场模型应用分子热力学方法导出CS-vdW状态方程,应用上述方程计算了CO2气-液和气-固平衡相的饱和态下pVT性质.取得了很满意的结果.本方法的优点是使用简便,可供工程计算使用.     

Thermodynamics of pure and multicomponent dipolar hard-sphere fluids

The thermodynamics of two recent models of hard-sphere polar fluids is investigated. The two models are the Onsager model developed by Nienhuis and Deutch and the mean spherical approximation results obtained by Wertheim. The equation of state, vapour pressure curve, and other pertinent thermodynamic properties are determined. These results for the pure hard-sphere polar fluid complement the results recently reported by Rushbrooke, Stell and Høye. The thermodynamics of simple multicomponent hard-sphere polar mixtures is examined for the case of equal hard-sphere radii. Results for the multicomponent MSM are based on the exact solution of this model by Adelman and Deutch. The Onsager model is generalized to the case of many components. For both multicomponent models it is demonstrated that a variety of regions of instability exist for the one-phase fluid. Finally a discussion is included of how well these models agree with experiment.     

An equation of state for the isotropic phase of linear,partially flexible and fully flexible tangent hard-sphere chain fluids

A new equation of state is developed that accurately describes the isotropic phase behaviour of linear, partially flexible and fully flexible tangent hard-sphere chain fluids and their mixtures. The equation of state is based on the equation of state of Liu and Hu [H. Liu and Y. Hu, Fluid Phase Equilibr. 122, 75 (1996)] for fully flexible chain fluids. The effect of molecular flexibility is described by a pure-component parameter that is introduced in the theory at the level of the cavity correlation function of next-to-nearest neighbour segments in a chain molecule. The equation of state contains a total of three adjustable model constants. The extension to partially flexible- and linear chain fluids is based on a refitting of the first model constant to numerical data of the second virial coefficient of partially flexible and linear tangent hard-sphere chain fluids. The numerical data were obtained from an analytical approximation for the pair-excluded volume. The other two parameters were adjusted to molecular simulation data for the pressure of linear tangent hard-sphere chain fluids. For both, pure component systems and mixtures of chains of variable flexibility, the pressure and second virial coefficient obtained from the equation of state, are in excellent agreement with the results from Monte Carlo simulations. A significant improvement to TPT1, TPT2, generalised Flory-dimer theory and scaled particle theory is observed.     

Thermophysical properties of ionic liquids and their mixtures from a new equation of state

In our previous work, a perturbed hard-trimer-sphere equation of state (PHTS EOS) was developed for modeling the phase equilibria of pure ionic liquids (ILs) (M.M. Alavianmehr et al., Ionics 22 (2016) 2447–2459). In this work, we have successfully extended the model to the mixtures of IL + IL and IL + solvent. Two temperature-dependent parameters appearing in the EOS are correlated with two microscopic scaling constants σ, the effective hard-sphere diameter, and ε, the non-bonded interaction energy. The overall average absolute deviation (AAD) of the estimated densities from the literature data using the proposed model with and without non-additivity parameter (λ _ij) was found to be 0.44 and 0.79%, respectively. A modified Enskog equation and rough hard-sphere (RHS) theory are combined with our proposed equation of state to calculate the viscosity coefficient of ionic liquids and their mixtures. Finally, from the results obtained, a linear relation between logarithm of surface tension and viscosity property of ionic liquid was developed.     

The viscosity of dilute solutions of hard-sphere macromolecules

The Thorne-Enskog theory for the viscosity of dense hard-sphere mixtures is analysed for a dilute suspension of macromolecules. The resulting equation, analogous to the Einstein viscosity equation, shows a dependance of intrinsic viscosity on molecular size which is in accord with observed experimental findings.     

Selective-pivot sampling of radial distribution functions in asymmetric liquid mixtures

We present a new method for selectively sampling radial distribution functions and effective interaction potentials in asymmetric liquid mixtures using a Monte Carlo simulation. We demonstrate its efficiency for hard-sphere mixtures, and for model systems with more general interactions, and compare our simulations with several analytical approximations. For interaction potentials containing a hard-sphere contribution, the algorithm yields the contact value of the radial distribution function.     

The approach to hard-sphere brownian motion: Variational eigenfunctions and evaluation of the Rayleigh-Fokker-Planck equation

We present detailed tabulations of the first few eigenfunctions of the hard-sphere energy scattering kernel for a test-particle in a background heat-bath. Calculations, for a range of heat bath/test particle mass-ratios between $\text{1}\text{8}$ and $\text{1}\text{1024}$, were carried out by a Rayleigh-Ritz method using the exact solutions of the hard-sphere Fokker-Planck equation as a basis set and supplement our previously-published results for the eigenvalues alone. The results, given as expansion coefficients in this representation thus also serve to verify the accuracy of the Fokker-Planck equation itself, the departure from this equation being reflected in the off-diagonal contributions in the Rayleigh-Ritz expansion eigenvectors.As expected, the tendency towards brownian motion behaviour with decrease in the mass-ratio parameter shows itself in a progressive convergence of a larger and larger subset of the true eigenfunctions to the corresponding Fokker-Planck set, beginning with the eigenvalue of lowest index. The class of probability distributions whose evolution is satisfactory predicted by the Fokker-Planck equation is then precisely the class that can be adequately expanded in terms of this incomplete subset. In keeping with the approximations introduced in the derivation of the Fokker-Planck equation and the qualitative nature of the hard-sphere eigenvalue spectrum, the results confirm quantitatively the considerable restrictions which the former imposes upon acceptable solution functions, excluding in particular both short-time behaviour and solutions of insufficient smoothness. A mean-square criterion for accuracy of the Fokker-Planck solutions is suggested and examined in the light of our numerical results.     

On the generalization of the Enskog equation to the case of steep repulsive potentials

For a classical homogeneous system of particles interacting via steeply repulsive potentials a generalization of the Enskog equation is proposed. This kinetic equation has the properties that it reduces to the usual Enskog equation in the limit of hard-sphere potentials and that the total instead of the kinetic energy is conserved in the system. The expression for the potential energy obtained is correct at arbitrary densities in equilibrium.     

Equation of state for a hard-sphere mixture

The equation of state for a multicomponent hard-sphere system is derived using the method of accelerated convergence of the perturbation series. In the asymptotic limit of small densities, this equation reproduces the virial coefficients known for the systems in question. In the case of a one-component system, the equation transforms into a form that adequately describes both the stable and metastable phases of the substance.     

Hard-sphere-like dynamics in a non-hard-sphere liquid

The collective dynamics of liquid gallium close to the melting point has been studied using inelastic x-ray scattering to probe length scales smaller than the size of the first coordination shell. Although the structural properties of this partially covalent liquid strongly deviate from a simple hard-sphere model, the dynamics, as reflected in the quasielastic scattering, are beautifully described within the framework of the extended heat mode approximation of Enskog's kinetic theory, analytically derived for a hard-sphere system. The present work demonstrates, therefore, the applicability of Enskog's theory beyond simple liquids.     

Equation of state for the Lennard-Jones truncated and shifted fluid with a cut-off radius of 2.5 σ based on perturbation theory and its applications to interfacial thermodynamics

ABSTRACT

An equation of state is presented for describing thermodynamic properties of the Lennard-Jones truncated and shifted (LJTS) potential with a cut-off radius of 2.5 σ. It is developed using perturbation theory with a hard-sphere reference term and labelled with the acronym PeTS (perturbed truncated and shifted). The PeTS equation of state describes the properties of the bulk liquid and vapour and the corresponding equilibrium of the LJTS fluid well. Furthermore, it is developed so that it can be used safely in the entire metastable and unstable region, which is an advantage compared to existing LJTS equations of state. This makes the PeTS equation of state an interesting candidate for studies of interfacial properties. The PeTS equation of state is applied here in two theories of interfaces, namely density gradient theory (DGT) and density functional theory (DFT). The influence parameter of DGT as well as the interaction averaging diameter of DFT are fitted to data of the surface tension of the LJTS fluid obtained from molecular simulation. The results from both theories agree very well with those from the molecular simulations.