J. R. Solana

Pair correlation function of short-ranged square-well fluids.

We have performed extensive Monte Carlo simulations in the canonical (NVT) ensemble of the pair correlation function for square-well fluids with well widths lambda-1 ranging from 0.1 to 1.0, in units of the diameter sigma of the particles. For each one of these widths, several densities rho and temperatures T in the ranges 0.1< or =rhosigma(3)< or =0.8 and T(c)(lambda) less or approximately T less or approximately 3T(c)(lambda), where T(c)(lambda) 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.

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.

Consistency conditions and equation of state for additive hard-sphere fluid mixtures

A number of consistency conditions for the contact values gij(σij) of the pair correlation function of species i and j in an additive hard-sphere fluid mixture are discussed. It is shown that most of the theoretically-based expressions, as well as other more empirical in character, existing for these functions, fail to satisfy at least one of the conditions. It is suggested that one could improve the performance of the expressions for gij(σij) and the equation of state by using the consistency conditions. This is illustrated by modifying the Boublik–Mansoori–Carnahan–Starling–Leland expressions for gij(σij), which results in better predictions for these functions as well as for the compressibility factor and the fourth and fifth virial coefficients.

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.

Heat capacity of square-well fluids of variable width

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 Baxters 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.

A NEW ANALYTICAL EQUATION OF STATE FOR ADDITIVE HARD SPHERE FLUID MIXTURES

A study has been made of the relation between the equation of state of additive binary hard sphere fluid mixtures and the equation of state of a pure hard sphere fluid for the same packing fraction. An analysis of the existing simulation data for a wide variety of compositions of the mixture and diameter ratios up to 1/0.2 makes it possible to conclude that the ratio of the excess compressibility factor of the mixture to that of the pure fluid is, to a very good approximation, a linear function of the packing fraction. This suggests the possibility of deriving the equation of state of the mixture from that of the pure fluid by using the second and third virial coefficients of the mixture, which are known analytically, to reproduce the linear relation mentioned above. When a suitable equation of state is chosen for the pure fluid, the results from the equation of state of the mixture thus obtained are in excellent agreement with simulation data. The predictions for the fourth and fifth virial coefficients ...

Comprehensive investigation about the second order term of thermodynamic perturbation expansion

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.

Behaviour of the internal pressure of liquids in accordance with variations in temperature, volume and cohesive energy density

Abstract A study is made of the variations to be found in the internal pressure of different types of liquid in accordance with variations in temperature and volume. These relationships are established through simple analytical equations. Variations in the cohesive energy density and the Hildebrand parameter in accordance with temperature variations are also calculated and it is shown that the internal pressure and the cohesive energy density are both analogous manifestations of the cohesion property of liquids and of the diminution of this property with falls in temperature.

Thermodynamic properties of double square-well fluids: computer simulations and theory.

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.

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.