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The possible existence of low-density and high-density fluid phase equilibria in fluids with a simple potential consisting in a combination of a square shoulder and a square well is explored by means of perturbation theory and histogram-reweighting grand canonical Monte Carlo simulation. Theory is useful as a simple and computationally inexpensive way to explore large sets of potential parameters to search for potential shapes susceptible to present multiple fluid phases, later confirmed or discarded from computer simulation. It is found that some combinations of the length and energy parameters of the potential actually give rise to such behaviour. [ABSTRACT FROM AUTHOR]

Monte Carlo computer simulations have been performed to obtain the equation of state and internal energy of fluids with Mie n − m potentials, with m = 6 and n = 9, 12 and 15, for different supercritical temperatures and densities covering most of the fluid phase. These data have been used to test the performance of a third-order perturbation theory with the first three perturbation terms determined from computer simulation, giving rise to a very good agreement between theory and simulation. Next, the theory has been used to tune effective two-body Mie n − 6 potentials for the real fluids Ne, Ar, Kr, Xe and $\rm CH_4$ C H 4 at supercritical temperatures for wide range of densities and pressures. It has been shown that the theory is able to accurately fit the experimental data for the energy and pressure of these fluids within the temperature and density ranges considered. This theory might be useful to obtain the equation of state and the internal energy of real molecular fluids within the context of the SAFT-VR Mie theory. [ABSTRACT FROM AUTHOR]

Monte Carlo NVT simulations have been performed to obtain the thermodynamic and structural properties of fluids with a potential consisting in a hard-core and screened Coulomb plus power series (HC-SPS) interactions for three sets of the potential parameters. These 'exact' data are used to check the accuracy of two integral equation theories and a local excess chemical potential formula for very short-ranged potentials. The theories considered are the reference hypernetted-chain (RHNC) approximation and the local self-consistent OZ approximation (LSCOZA). The main conclusions of our study are described below. (i) The RHNC always underestimates the first peak of the radial distribution, which directly leads to an underestimation of the pressure and an overestimation of excess internal energy. In general, as the potential range becomes shorter ranged and the temperature decreases, the performance of the RHNC worsens and even becomes qualitatively incorrect. (ii) Local pressure self-consistency is of crucial importance to ensure that the hard sphere bridge function with an effective hard sphere diameter yields very accurate results for the pressure and excess internal energy even for very short-range potentials and at temperatures very close to the critical temperature. (iii) The accuracy of the excess chemical potential, obtained by thermodynamic integration of the excess internal energy, is also remarkable even for very short-ranged potentials and superior to that of a local excess chemical potential formula previously proposed [S. Zhou, Theor. Chem. Acc.117, 555(2007)]. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that the numerical differentiation method in performing the coupling parameter series expansion [S. Zhou, J. Chem. Phys. 125, 144518 (2006); AIP Adv. 1, 040703 (2011)] excels at calculating the coefficients a of hard sphere high temperature series expansion (HS-HTSE) of the free energy. Both canonical ensemble and isothermal-isobaric ensemble Monte Carlo simulations for fluid interacting through a hard sphere attractive Yukawa (HSAY) potential with extremely short ranges and at very low temperatures are performed, and the resulting two sets of data of thermodynamic properties are in excellent agreement with each other, and well qualified to be used for assessing convergence of the HS-HTSE for the HSAY fluid. Results of valuation are that (i) by referring to the results of a hard sphere square well fluid [S. Zhou, J. Chem. Phys. 139, 124111 (2013)], it is found that existence of partial sum limit of the high temperature series expansion series and consistency between the limit value and the true solution depend on both the potential shapes and temperatures considered. (ii) For the extremely short range HSAY potential, the HS-HTSE coefficients a falls rapidly with the order i, and the HS-HTSE converges from fourth order; however, it does not converge exactly to the true solution at reduced temperatures lower than 0.5, wherein difference between the partial sum limit of the HS-HTSE series and the simulation result tends to become more evident. Something worth mentioning is that before the convergence order is reached, the preceding truncation is always improved by the succeeding one, and the fourth- and higher-order truncations give the most dependable and qualitatively always correct thermodynamic results for the HSAY fluid even at low reduced temperatures to 0.25. [ABSTRACT FROM AUTHOR]

The first four perturbation coefficients in the expansion of the Helmholtz free energy in power series of the inverse of the reduced temperature for a number of potential models with hard-sphere cores plus core-softened and discontinuous tails are obtained from Monte Carlo simulations. The potential models considered include square-well, double square-well, and square-shoulder plus square-well, with different potential parameters. These simulation data are used to evaluate the performance of a traditional macroscopic compressibility approximation (MCA) for the second order coefficient and a recent coupling parameter series expansion (CPSE) for the first four coefficients. Comprehensive comparison indicates the incapability of the MCA for the second order coefficient in most non-stringent situations, and significance of the CPSE in accurately calculating these four coefficients. [ABSTRACT FROM AUTHOR]

A bridge function approximation is proposed to close the Ornstein–Zernike (OZ) integral equation for fluids with purely repulsive potentials. The performance of the bridge function approximation is then tested by applying the approximation to two kinds of repulsive potentials, namely, the square shoulder potential and the triangle shoulder potential. An extensive comparison between simulation and the OZ approach is performed over a wide density range for the fluid phase and several temperatures. It is found that the agreement between the two routes is excellent for not too low temperatures and satisfactory for extremely low temperatures. Then, this globally trustworthy OZ approach is used to investigate the possible existence or not of a liquid anomaly, i.e., a liquid-liquid phase transition at low temperatures and negative values of the thermal expansion coefficient in certain region of the phase diagram. While the existence of the liquid anomaly in the square shoulder potential has been previously predicted by a traditional first-order thermodynamic perturbation theory (TPT), the present investigation indicates that the liquid-liquid phase transition disappears in the OZ approach, so that its prediction by the first-order TPT is only an artifact originating from the low temperature inadequacy of the first-order TPT. However, the OZ approach indeed predicts negative thermal expansion coefficients. The present bridge function approximation, free of adjustable parameters, is suitable to be used within the context of a recently proposed nonhard sphere perturbation scheme. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations are carried out for the second order term in the thermodynamic perturbation expansion around a hard sphere reference fluid. The sample potentials considered cover a wide spectrum: From two frequently employed, namely hard sphere plus square well potential and hard core attractive Yukawa potential, to two kinds of repulsive potentials, namely hard sphere plus square shoulder potential and hard sphere plus triangle shoulder potential; the investigated potential range also extends from extremely short range to rather long range. The obtained simulation data are used to evaluate performance of two theoretical approaches, i.e., a traditional macroscopic compressibility approximation (MCA) and a recent coupling parameter expansion. Extensive comparison shows that the coupling parameter expansion provides a reliable method for accurately calculating the second order term of the high temperature series expansion, while the widely accepted MCA fails quantitatively or even qualitatively for most of the situations investigated. [ABSTRACT FROM AUTHOR]

Computer simulations have been performed to obtain the thermodynamic properties of fluids with double square-well potentials, that is, potentials consisting of two adjacent square wells with different depths. The compressibility factor, excess energy, chemical potential, constant-volume excess heat capacity, and other derived properties have been obtained. These data have been used to test the performance of several perturbation theories for predicting the thermodynamic properties of this kind of fluids. Good agreement is found on the whole between theory and simulation at supercritical temperatures. The possible presence of anomalous behavior at high densities in the fluids considered has been also analyzed in light of the same theories, with the result that in general, they do not predict such anomalous behavior, with the possible exception of a Monte Carlo-based perturbation theory for relatively large potential widths at high densities and very low temperatures. [ABSTRACT FROM AUTHOR]

Computer simulations have been performed for fluids with van der Waals potential, that is, hard spheres with attractive inverse power tails, to determine the equation of state and the excess energy. On the other hand, the first- and second-order perturbative contributions to the energy and the zero- and first-order perturbative contributions to the compressibility factor have been determined too from Monte Carlo simulations performed on the reference hard-sphere system. The aim was to test the reliability of this “exact” perturbation theory. It has been found that the results obtained from the Monte Carlo perturbation theory for these two thermodynamic properties agree well with the direct Monte Carlo simulations. Moreover, it has been found that results from the Barker-Henderson [J. Chem. Phys. 47, 2856 (1967)] perturbation theory are in good agreement with those from the exact perturbation theory. [ABSTRACT FROM AUTHOR]

We have performed extensive Monte Carlo simulations in the canonical (NVT) ensemble of the pair correlation function for square-well fluids with well widths λ-1 ranging from 0.1 to 1.0, in units of the diameter σ of the particles. For each one of these widths, several densities ρ and temperatures T in the ranges 0.1≤ρσ3≤0.8 and Tc(λ)≤T≤3Tc(λ), where Tc(λ) is the critical temperature, have been considered. The simulation data are used to examine the performance of two analytical theories in predicting the structure of these fluids: the perturbation theory proposed by Tang and Lu [Y. Tang and B. C.-Y. Lu, J. Chem. Phys. 100, 3079 (1994); 100, 6665 (1994)] and the nonperturbative model proposed by two of us [S. B. Yuste and A. Santos, J. Chem. Phys. 101 2355 (1994)]. It is observed that both theories complement each other, as the latter theory works well for short ranges and/or moderate densities, while the former theory works for long ranges and high densities. [ABSTRACT FROM AUTHOR]

Density expansions of the contact pair correlation functions for binary mixtures of additive hard spheres are obtained from the virial expansion of the equation of state. The procedure is based on the use consistency conditions. The resulting expansions are exact up to first order in the density. This corresponds to the third virial coefficient which is exactly known for these mixtures. Analytical expressions for the second and third order terms are obtained on the basis of very accurate approximate analytical expressions for the fourth and fifth virial coefficients. It is found that the series converge slowly, but the convergency can be accelerated by means of a resummation procedure. [ABSTRACT FROM AUTHOR]

Extensive Monte Carlo simulations have been performed to obtain the thermodynamic properties of binary square-well mixtures for different compositions, well depths, hard-core diameter ratios and temperatures. They are used in combination with a one-fluid theory based on perturbation theory to analyse the performance of several mixing rules proposed in the literature. A new density- and temperature-dependent mixing rule is proposed. The new mixing rule provides better agreement with simulations than those previously proposed, especially for very asymmetric mixtures. [ABSTRACT FROM AUTHOR]

A model previously developed for the equation of state of linear homonuclear fused hard sphere fluids is generalized to fluids with heteronuclear molecules. The model only requires two parameters, which can be determined from the geometrical characteristics of the molecules, for which analytical expressions are derived. Results for fluids with heteronuclear hard diatomic and symmetric triatomic molecules agree with simulation data within their accuracy for almost all the fluids considered. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A model relating the equation of state of two-dimensional linear hard-body fluids to the equation of state of the hard disk fluid is derived from the pressure equation in a similar way to that previously described for three-dimensional hard-body fluids. The equation of state reproduces simulation data practically within their accuracy for fluids with a great variety of molecular shapes. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A model relating the equation of state of linear homonuclear fused hard sphere fluids to the equation of state of the hard sphere fluid is derived from the pressure equation. The equation of state reproduces simulation data practically within their accuracy for diatomic and linear triatomic hard molecular fluids. © 1994 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A simple and accurate equation of state for fluids of hard convex molecules is derived from the pressure equation and the equation of state of the hard sphere fluid. The equation of state provides theoretical support to some equations of state used in perturbation theories for real molecular liquids. The equation of state reproduces the simulation data with an accuracy comparable to that derived from density functional theory. [ABSTRACT FROM AUTHOR]

Equations of state for hard-disk and hard-sphere fluids are obtained from a generalization of the Carnahan–Starling method of direct summation of the virial series. The equations of state thus obtained, besides reproducing all known virial coefficients, agree very accurately with simulation data for stable fluids. If appropriate values for the sixth and seventh virial coefficients are chosen within their uncertainty, the equations of state predict that the fluids become unstable at Kauzmann’s density. [ABSTRACT FROM AUTHOR]

An equation of state for the inverse-twelfth-power soft-sphere fluid is obtained by direct summation of the virial series. To do so, a generalization of the Carnahan–Starling method for obtaining the equation of state of the hard-sphere fluid is used. The equation of state obtained in this way reproduces accurately the simulation data for both the stable and metastable fluid regions. Agreement remains good up to the neighborhood of the glass transition where the equation of state predicts that the soft-sphere fluid becomes unstable. [ABSTRACT FROM AUTHOR]

A number of existing approximants are reviewed and tested for the equation of state of the hard spheres fluid in the metastable fluid region, namely, at densities higher than the normal freezing density: ρ*=0.943. This is a region which is particularly sensitive to the quality of a given equation of state; however, it is frequently ignored in the study of analytical equations of state. A new set of approximants is also discussed, including as particular cases several other currently used equations of state for the hard spheres fluid. [ABSTRACT FROM AUTHOR]

Monte Carlo NpT simulations have been performed to obtain the pressure, excess enthalpy, excess internal energy, isothermal compressibility coefficient, thermal expansion coefficient and constant-pressure excess heat capacity of fluids with several kinds of Lennard–Jones–Gauss potential models from subcritical to supercritical and from vapour to liquid states. These data have been used to assess the performance of a perturbation theory, namely the coupling parameter series expansion (CPSE) of the Helmholtz free energy, for continuous potential models without hard-sphere core. The main findings are summarised as follows: (1) The analysis of the results for the constant-pressure excess heat capacity shows that the CPSE is convergent until seventh order. (2) The seventh-order CPSE, when combined with the simple Barker–Henderson (BH) effective hard-sphere diameter, predicts rather accurately the thermodynamic properties, except at high densities and low temperatures. (2) The loss of accuracy in these situations is attributed to the inadequacy of the BH prescription that does not account for the density dependence of the effective hard-sphere diameter. (3) The CPSE performance is rather insensitive to the details of the potential model considered. [ABSTRACT FROM AUTHOR]