Further property of Lennard-Jones fluid: Thermal conductivity

In this paper, we calculate the thermal conductivity of noble gases, methane, and three noble gas mixtures including He+Kr, He+Xe, and Kr+Xe assuming they obey Lennard-Jones (LJ) (12-6) model potential. One of the required quantities to calculate the thermal conductivity of these systems is the pair correlation function. Therefore, we solve numerically the Ornstein-Zernike (OZ) integral equation using the mean spherical approximation (MSA) to obtain the pair correlation functions. We use these functions to obtain the thermal conductivity, then compare our results with the available data. According to the results obtained from the present work for pure and mixtures of LJ fluids reveals that the integral equations method is suitable for predicting the thermal conductivity of this class of fluid.     

Vapour pressure of non-polar fluids and their repulsive and attractive contributions

Using a simple equation of state, based on the Weeks-Chandler-Andersen separation of the intermolecular potential, we have obtained the contributions of repulsive and attractive intermolecular forces to the thermodynamic properties of coexisting vapour and liquid phases of a Lennard-Jones (LJ) fluid.

In order to obtain the vapour pressure of real non-polar fluids, we take the LJ fluid as a reference model, and propose a new perturbative contribution, which is dependant on the temperature and on the acentric factor of the substance. Using the complete perturbed equation, we determine the corresponding repulsive and attractive contributions to the vapour pressure of non-polar fluids. The results show that the attractive vapour pressure of non-polar fluids increases with increasing acentric factor, i.e., larger deviation of the molecular shape from spherical symmetry.

This procedure could be extended to separate the repulsive and attractive contributions of the intermolecular forces to other thermodynamic properties of non-polar fluids as well as of polar fluids and fluid mixtures.     

A SAFT model for associating Lennard-Jones chain mixtures

The recently proposed equation of state of statistical associated fluid theory (SAFT) is extended to associating Lennard-Jones (LJ) chain mixtures. In this extension, a new radial distribution function (RDF) for LJ mixtures is derived around the LJ potential size (σ _ij ). The RDF expression is completely analytical and real. Comparisons with computer simulation data under various conditions indicate that the RDF is very accurate up to its first peak. The new RDF, together with a previously established equation of state for LJ mixtures, is employed to study LJ chain mixtures by combining with Wertheim's first-order perturbation theory. The resulting equation of state is tested satisfactorily against computer simulation data for both non-associating and associating LJ chain mixtures, with a performance similar to its predecessors for pure LJ chains and LJ mixtures. The SAFT model is uniquely featured by being totally mixing-rule free and by being adjustable at both chain bonding and association sites. Moreover, the SAFT model is formulated very generally, so that it is applicable to both homonuclear and heteronuclear chain mixtures.     

Perturbation and variational approach for the equation of state for hard-sphere and Lennard-Jones fluids

The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state (EOS) for a mixture of hard sphere (HS), Lennard–Jones (LJ) fluids. A suitable flexible functional form for the radial distribution function G(R) is assumed for the mixture, with R as a variable. The function G(R) has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m = 0.75 and m = 0.83 results are close to molecular dynamics (MD) result for pure HS and LJ fluid respectively.     

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.     

Equation of state for pure fluids at critical temperature

In this paper, we employ the concept of probability for creating a cavity with diameter d in fluid along with the perturbation and variation approach, and develop an equation of state (EOS) for a hard sphere (HS) and Lennard– Jones (LJ) fluids. A suitable axiomatic form for surface tension S(r) is assumed for the pure fluid, with r as a variable. The function S(r) has an arbitrary parameter m. S(r) = A + B(d/r)/[1 + m(d/r)]. We use the condition in terms of radial distribution function G(λd, η) containing the self-consistent parameter λ and the condition of continuity at r = d/2 to determine A and B. A different EOS can be obtained with a suitable choice of m and the EOS has a lower root-mean-square deviation than that of Barker–Henderson BH2 for LJ fluids.     

Thermodynamic properties of the Lennard-Jones FCC solid: perturbation theory parameterisation and Monte Carlo simulation

This work is concerned with a valid representation of the solid-phase equation of state (EOS), the validity of which is evaluated by comparing to Monte Carlo (MC) simulation results. The proposed EOS has been developed by employing an optimal division of the Lannard-Jones (LJ) potential and an effective temperature- and density-dependent diameter into the framework of the simplified perturbation theory. Then, with the aim of extending to the chain systems, the conventional chain contribution (i.e. TPT1) is added to the proposed model (i.e. the atomic LJ system). Finally, the solid-state EOS based on Helmholtz free energy will be introduced for low temperature and high density conditions. To verify the accuracy of the proposed model, its performance is compared with the results of MC simulation. The comparison between the obtained results from the proposed model and the MC simulations shows that the EOS can satisfactorily predict the properties of the solid LJ system, both for the atomic system and for the chains.     

Structural properties of effective potential model by liquid state theories

This paper investigates the structural properties of a model fluid dictated by an effective inter-particle oscillatory potential by grand canonical ensemble Monte Carlo (GCEMC) simulation and classical liquid state theories.The chosen oscillatory potential incorporates basic interaction terms used in modeling of various complex fluids which is composed of mesoscopic particles dispersed in a solvent bath,the studied structural properties include radial distribution function in bulk and inhomogeneous density distribution profile due to influence of several external fields.The GCEMC results are employed to test the validity of two recently proposed theoretical approaches in the field of atomic fluids.One is an Ornstein-Zernike integral equation theory approach;the other is a third order + second order perturbation density functional theory.Satisfactory agreement between the GCEMC simulation and the pure theories fully indicates the ready adaptability of the atomic fluid theories to effective model potentials in complex fluids,and classifies the proposed theoretical approaches as convenient tools for the investigation of complex fluids under the single component macro-fluid approximation.     

Perturbation and variational approach for the equation of state for hard-sphere and Lennardben Jones fluids

The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state (EOS) for a mixture of hard sphere (HS), Lennard-Jones (LJ) fluids. A suitable flexible functional form for the radial distribution function G(R) is assumed for the mixture, with R as a variable. The function G(R) has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m= 0.75 and m= 0.83 results are close to molecular dynamics (MD) result for pure HS and LJ fluid respectively.     

Modelling the effect of methanol,glycol inhibitors and electrolytes on the equilibrium stability of hydrates with the SAFT-VR approach

In this work we integrate the statistical associating fluid theory for fluids interacting through potentials of variable range (SAFT-VR) into a traditional van der Waals and Platteeuw framework for modelling clathrate hydrates. We incorporate a new water–guest cell potential for the hydrate phase that can be related to the potential adopted in the familiar SAFT-VR equation of state for modelling fluids. We show how the ability of this equation of state to treat a wide range of complex fluids increases the scope of hydrate modelling to incorporate, in a single framework, the presence of various inhibitors (alcohols, glycols) or brines – or, indeed, any fluid for which a model is available (for use within SAFT-VR) or can be conveniently obtained. Agreement with experimental results is good throughout and, in many cases, excellent.     

Surface phase transitions of multiple-site associating fluids

Surface phase transitions of Lennard–Jones (LJ) based two- and four-site associating fluids have been studied for various associating strengths using grand-canonical transition matrix Monte Carlo simulations. Our results suggest that, in the case of a smooth surface, represented by a LJ 9-3-type potential, multiple-site associating fluids display a prewetting transition within a certain temperature range. However, the range of the prewetting transition decreases with increasing associating strength and increasing number of sites on the fluid molecules. With the addition of associating sites on the surface, a quasi-2D vapor–liquid transition may appear, which is observed at a higher surface site density for weaker associating fluids. The prewetting transition at lower associating strength is found to shift towards the quasi-2D vapor–liquid transition with increasing surface site density. However, for highly associating fluids, the prewetting transition is still intact, but shifts slightly towards the lower temperature range. Adsorption isotherms, chemical potentials and density profiles are used to characterize surface phase transitions.     

Equilibrium theories of simple liquids

In this article, the theory of equilibrium properties of simple classical fluids is reviewed. The various relationships between the pair potential φ(r) and the pair correlation function g(r) are explored, from the usual integral equations and the perturbation theories to the generalized random phase approximation proposed recently. Particular attention is devoted to the extraction of the intermolecular forces from a given experimental data on the structure and thermodynamics of fluids. In particular, the propagation of errors in these calculations arising due to uncertainties in the input data is discussed. Finally, the recent use of BGY integral equation and the vacancy-cell model in the study of solid-liquid transition and melting is discussed.     

Derivation of a simple coordination number model using a given equation of state and the effective pair potential function

In this work, a simple coordination number (C.N.) model for the (9, 3) Lennard–Jones (LJ) fluid is obtained. It is based on the comparison of the internal pressure derived from a given equation of state (EoS) with the internal pressure derived from the (9, 3) LJ fluid as an effective pair potential (EPP). This model reproduces well the thermodynamic properties of the fluid such as internal energy, and the C.N. which is comparable with the Monte Carlo simulation data for the C.N. in the high-density region. In addition, the obtained C.N. can predict the first shell radial distribution function, g(r), of the fluid as well.     

Generalized van der Waals theory VIII. An improved analysis of the liquid/gas interface

We extend a preceding application of the GvdW theory to the prediction of interface profiles and surface tension in simple fluids by incorporating a variational determination of the effective hard-sphere diameter. This has previously been found to improve the predicted equation of state. Here we find that it also improves the prediction of interface profiles and surface tension in LJ(12-6) fluids. The agreement with experiment and simulation when these quantities are considered as functions ofT/T _c is to within about 5%. As in our earlier calculations the nonlocal entropie effects are found to reduce the surface tension by 5%–10%. In the present conceptually more accurate theory this significantly improves the agreement with experiment and simulation.     

Kinetic theory of dense fluids. II. The generalized Chapman-Enskog solution

In the second paper of this series we solve the kinetic equation proposed in the previous paper by a method following the spirit of Chapman and Enskog (generalized Chapman-Enskog method). The zeroth-order solution to the kinetic equation leads to the Euler equations in hydrodynamics for real fluids, and the first-order solution to the Navier-Stokes equations for real fluids. General formulas for transport coefficients such as viscosity and heat-conductivity coefficients are obtained for dense fluids, which are given in terms of time-correlation functions of fluxes conjugate to the thermodynamic forces. The results have the same formal structures as the time-correlation functions in linear response theory except for the collision operator appearing in place of the Liouville operator in the evolution operator for the system.     

A molecular dynamics study on the role of attractive and repulsive forces in excess heat capacity at constant volume of dense fluids

The curves of experimental heat capacity against density show a minimum around and below the critical temperature (Tc), but at higher temperatures, this minimum is not observed. In this study, the role of attractive and repulsive forces on excess heat capacity of Lennard–Jones (LJ) dense fluids has been investigated using a molecular dynamics simulation technique. LJ potential is divided into attractive and repulsive parts. From the molecular dynamics calculations, potential energy and heat capacities have been obtained for Argon at temperatures of 100–500?K. The repulsive forces play the main role in causing the heat capacities at temperatures greater than critical point. Around and below the critical temperature, the role of repulsion is dominant at high densities, but attraction has the main role at low densities, consequently at middle densities, a minimum is formed.     

Shear-horizontal waves in a rotated Y-cut quartz plate in contact with a viscous fluid

We study shear-horizontal (SH) waves in a crystal plate of rotated Y-cut quartz in contact with a semi-infinite viscous fluid. The crystal plate and the fluid are governed by the equations of anisotropic elasticity and the theory of Newtonian fluids. A transcendental equation that determines the dispersion relations of the waves is obtained. Approximate analytical solutions to the equation are presented for the case of low viscosity fluids and the case of long waves whose wavelength is much larger than the plate thickness. The effects of the fluid viscosity and density on the dispersion relations of the waves are examined. The results obtained are fundamental and useful to the understanding and design of acoustic wave fluid sensors for measuring fluid viscosity or density.     

Inhomogeneous 2D Lennard-Jones Fluid: Theory and Computer Simulation

In this work, thermodynamical properties of a two-dimensional (2D) Lennard-Jones (LJ) fluid are studied. Here, to increase the accuracy of our theoretical calculations, the correlation functions in three-particle level (triplet) are applied. To obtain the triplet correlation functions, the Attard's source particle method is extended to 2D systems. In the Attard's procedure, the inhomogeneous Ornstein-Zernike (OZ) equation is solved using the Treizenberg-Zwanzwig (TZ) expression and a closure relation like the hypernetted-chain (HNC) approximation. In the present work, we also have performed the Monte Carlo (MC) simulation. The theoretical results are in fairly agreement with the MC simulation. Also, our results show that the approach proposed here is suitable to study the 2D LJ fluid.