M. J. Maeso

Equations of state for hard spheres fluid in the metastable fluid region

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.

Equation of state for hard convex body fluids from the equation of state of the hard sphere fluid

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.

Equation of state for fluids of hard heteronuclear diatomic and symmetric triatomic molecules

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.

Equations of state for D-dimensional hard sphere fluids

Abstract An equation of state, a kind of generalized Pade approximant, first proposed for the hard-sphere fluid in three dimensions is extended to the two-, four-, and five-dimensional cases in addition to the trivial one-dimensional case (hard rods). The corresponding equations of state show good to excellent agreement with existing simulation data.

An accurate equation of state for fluids of linear homonuclear fused hard spheres

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.

Instabilities in the equations of state of hard-disk and hard-sphere fluids from the virial expansions

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.

Equation of state for the soft‐sphere fluid from a direct summation of the virial series

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.

Equation of state for repulsive models of n-alkane pure fluids and mixtures

Theoretically-based equations of state previously developed for hard models of molecular pure fluids and mixtures are extended in this paper to repulsive models of pure n-alkane fluids and mixtures. For pure fluids, the compressibility factor is expressed in terms of a scaling of the excess compressibility factor of a hard-sphere fluid with a packing fraction equal to the effective packing fraction of the true fluid. For mixtures, the excess compressibility factor is expressed as a similar scaling of the excess compressibility factor of a hard-sphere fluid mixture. The theory requires two parameters, namely the scaling factor and the effective (averaged) molecular volume of the fluid (mixture), which can be determined from the molecular geometry. Results are in generally good agreement with available simulation data.

An accurate equation of state for hard Gaussian overlap fluids from a generalized Carnahan-Starling method

The Carnahan-Starling method for obtaining the equation of state of the hard-sphere fluid is generalized and used to derive an equation of state for hard Gaussian overlap fluids. The results are in excellent agreement with existing simulation data.

Bonded hard-sphere theory and computer simulation of the equation of state of linear fused–hard-sphere fluids

The bonded hard-sphere (BHS) theory is extended to fluids consisting of rigid, linear, homonuclear molecules, each of them formed by n fused hard spheres. The theory shows excellent agreement with the Monte Carlo NpT simulation data which are also reported for reduced bond lengths l*=0.5 and n=2, 3, 4, 6, 8, and 10. The accuracy of the BHS prediction in comparison to simulation is similar to that of generalized Flory-dimer theory and superior to that of thermodynamic perturbation theory.