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Thefirst three coefficients of the high temperature series expansion(HTSE) of the Helmholtz free energy for a number of simple potentialmodels with hard-sphere cores plus continuous tails are obtained forthe first time from Monte Carlo simulations. The potential modelsconsidered include Square-well, Sutherland, attractive Yukawa, andtriangle-well with different potential ranges, as well as a modelpotential qualitatively resembling the depletion potential in colloidaldispersions. The simulation data are used to evaluate performanceof a recent coupling parameter series expansion (CPSE) in calculatingfor these coefficients, and a traditional macroscopic compressibilityapproximation (MCA) for the second-order coefficient only. A comprehensivecomparison based on these coefficients from the two theoretical approachesand simulations enables one to conclude that (i) unlike one commonexperience that the widely used MCA usually underestimates the second-ordercoefficient, the MCA can both overestimate and underestimate the second-ordercoefficient, and worsens as the range of the potential decreases;and (ii) in contrast, the CPSE not only reproduce the trends in thedensity dependence of the perturbation coefficients, even the thirdone, observed in the simulations, but also the agreement is quantitativein most cases, and this clearly highlights the potential of the CPSEin providing accurate estimations for the higher-order coefficients,thus giving rise to an accurate higher-order HTSE. [ABSTRACT FROM AUTHOR]

Some points about the search for analytical expressions for the equation of state of the hard-disc fluid are discussed in the light of the most recent advances in the field. New and accurate equations of state for this fluid are proposed. [ABSTRACT FROM AUTHOR]

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.

A simple model for a chiral molecule is proposed. The model consists of a central atom bonded to four different atoms in tetrahedral coordination. Two different potentials were used to describe the pair potentials between atoms: the hard sphere potential and the Lennard-Jones potential. For both the hard sphere and the Lennard-Jones chiral models, computer simulations have been performed for the pure enantiomers and also for the racemic mixture. The racemic mixture consisted of an equimolar mixture of the two optically active enantiomers. It is found that the equations of state are the same, within statistical uncertainty, for the pure enantiomer fluid and for the racemic mixture. Only at high pressures does the racemic mixture seem to have a higher density, for a given pressure, than the pure enantiomer. Concering the structure, no difference is found in the site-site correlation functions between like and unlike molecules in the racemic mixture either at low or at high densities. However, small differences are found for the site-site correlations of the pure enantiomer and those of the racemic mixtures. In the Lennard-Jones model, similar conclusions are drawn. The extension of Wertheim's first-order perturbation theory, denoted bonded hard sphere theory (ARCHER, A. L., and JACKSON, G., 1991, Molec. Phys., 73, 881; AMOS, M. D., and JACKSON, G., 1992, J. chem. Phys., 96, 4604), successfully reproduces the simulation results for the hard chiral model. Virial coefficients of the hard chiral model up to the fourth have also been evaluated. Again, no differences are found between virial coefficients of the pure fluid and of the racemic mixture. All the results of this work illustrate the quasi-ideal behaviour of racemic mixtures in the fluid phase. [ABSTRACT FROM AUTHOR]

A model previously developed for the equation of state of pure fluids consisting of hard convex body molecules is extended to mixtures. The parameters of the model can be determined from the geometrical characteristics of the molecules which form the mixture. The equation of state is in excellent agreement with simulation data for mixtures of hard spheres with hard spherocylinders. [ABSTRACT FROM AUTHOR]

This paper proposes a simple method for predicting the virial coefficients, up to the fifth, for hard linear homonuclear molecules. The method uses the virial coefficients for hard spherocylinders and hard linear tangent spheres to obtain the virial coefficients of linear fused hard spheres. The results are in very good agreement with the known values for the latter kind of molecules. Thus the method is suitable for predictive purposes when virial coefficients are not known, which makes it useful for the derivation of certain equations of state. [ABSTRACT FROM AUTHOR]

A procedure previously developed by the authors to obtain the equation of state for a mixture of additive hard spheres on the basis of a pure fluid equation of state is applied here to a binary mixture of additive hard disks in two dimensions. The equation of state depends on two parameters which are determined from the second and third virial coefficients for the mixture, which are known exactly. Results are compared with Monte Carlo calculations which are also reported. The agreement between theory and simulation is very good. For the fourth and fifth virial coefficients of the mixture, the equation of state gives results which are also in close agreement with exact numerical values reported in the literature.