Search

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.

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]

The equilibrium thermodynamic properties of binary Lennard–Jones mixtures are determined by means of a Monte Carlo-based perturbation theory for an effective single-component fluid. The results for the equation of state and the excess energy are compared with simulation data obtained for two equimolar binary Lennard–Jones fluid mixtures at different temperatures along a wide range of densities. The satisfactory accuracy achieved seems to suggest that this approach might be a useful tool to deal with mixtures with a wide variety of intermolecular interactions including mixtures of real fluids. [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]

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]

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]

A perturbation theory for square-well chain fluids is developed within the scheme of the (generalised) Wertheim thermodynamic perturbation theory. The theory is based on the Pavlyukhin parametrisations [Y. T. Pavlyukhin, J. Struct. Chem. 53, 476 (2012)] of their simulation data for the first four perturbation terms in the high temperature expansion of the Helmholtz free energy of square-well monomer fluids combined with a second-order perturbation theory for the contact value of the radial distribution function of the square-well monomer fluid that enters into bonding contribution. To obtain the latter perturbation terms, we have performed computer simulations in the hard-sphere reference system. The importance of the perturbation terms beyond the second-order one for the monomer fluid and of the approximations of different orders in the bonding contribution for the chain fluids in the predicted equation of state, excess energy and liquid-vapour coexistence densities is analysed. [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]

The thermodynamic properties of a fluid with an interaction potential consisting in a hard-sphere core plus a Lennard-Jones tail have been obtained by Monte Carlo (MC) NVT simulation as a function of the density along several isotherms. In addition, the liquid–vapour coexistence has been determined by means of histogram-reweighting MC. These data have been used to analyse the performance of perturbation theory. To this end, the first three perturbation terms of the inverse temperature expansion of the Helmholtz free energy have been obtained by means of MC NVT simulations to test the convergence of the perturbation series and to compare with the predictions of the coupling parameter series expansion. Then, the predictions of the latter theory for the thermodynamic properties have been compared with the simulations, revealing the overall excellent performance of this perturbation theory for this model fluid, except in the vicinity of the critical point. [ABSTRACT FROM PUBLISHER]

The article focuses on thermodynamic perturbation theories developed to obtain the thermodynamic properties of the fluid and solids. It explores the progress of perturbation theory in different fields such as bulk fluid and solid phases, density functional approximation, and in the Ornstein-Zernike integral equation theory. It suggests improvement of perturbation approach by combining it with other theoretical approach including computer simulation, integral equations and renormalization theory.

We have obtained by Monte Carlo NVT simulations the constant-volume excess heat capacity of square-well fluids for several temperatures, densities and potential widths. Heat capacity is a thermodynamic property much more sensitive to the accuracy of a theory than other thermodynamic quantities, such as the compressibility factor. This is illustrated by comparing the reported simulation data for the heat capacity with the theoretical predictions given by the Barker-Henderson perturbation theory as well as with those given by a non-perturbative theoretical model based on Baxter's solution of the Percus-Yevick integral equation for sticky hard spheres. Both theories give accurate predictions for the equation of state. By contrast, it is found that the Barker-Henderson theory strongly underestimates the excess heat capacity for low to moderate temperatures, whereas a much better agreement between theory and simulation is achieved with the non-perturbative theoretical model, particularly for small well widths, although the accuracy of the latter worsens for high densities and low temperatures, as the well width increases. [ABSTRACT FROM AUTHOR]