F Del Rio

Theoretical prediction of multiple fluid-fluid transitions in monocomponent fluids

The authors use the analytical equation of state obtained by the discrete perturbation theory [A. L. Benavides and A. Gil-Villegas, Mol. Phys. 97, 1225 (1999)] to study the phase diagram of fluids with discrete spherical potentials formed by a repulsive square-shoulder plus an attractive square-well interaction (SS+SW). This interaction is characterized by the usual energy and size parameters plus three dimensionless parameters: two of them measuring the widths of the SS and the SW and the third the relative height of the SS. The matter of interest is that, for certain values of the interaction parameters, the SS+SW systems exhibit more than one first-order fluid-fluid transition. The evidence that several real substances (such as water, phosphorus, carbon, and silica, among others) exhibit an extra liquid-liquid transition has drawn interest into the study of interactions responsible for this behavior. The simple SS+SW fluid is one of the systems that, in spite of being spherically symmetric, shows multiple fluid-fluid transitions. In this work the authors investigate systematically the effect on the phase diagram of varying the interaction parameters. The use of an analytical free-energy equation gives a clear thermodynamic picture of the emergence of different types of critical points, throwing new light on the phase behavior of these fluids and thus clarifying previous results obtained by other techniques. The interplay of attractive and repulsive forces with several scale lengths produces very rich phase diagrams, including cases with three critical points. The region of the interaction-parameter space where multiple critical points appear is mapped for various families of interactions.

Discrete perturbation theory for the hard-core attractive and repulsive Yukawa potentials

In this work we apply the discrete perturbation theory [A. L. Benavides and A. Gil-Villegas, Mol. Phys. 97, 1225 (1999)] to obtain an equation of state for the case of two continuous potentials: the hard-core attractive Yukawa potential and the hard-core repulsive Yukawa potential. The main advantage of the presented equation of state is that it is an explicit analytical expression in the parameters that characterize the intermolecular interactions. With a suitable choice of their inverse screening length parameter one can model the behavior of different systems. This feature allows us to make a systematic study of the effect of the variation in the parameters on the thermodynamic properties of this system. We analyze single phase properties at different conditions of density and temperature, and vapor-liquid phase diagrams for several values of the reduced inverse screening length parameter within the interval kappa( *)=0.1-5.0. The theoretical predictions are compared with available and new Monte Carlo simulation data. Good agreement is found for most of the cases and better predictions are found for the long-range ones. The Yukawa potential is an example of a family of hard-core plus a tail (attractive or repulsive) function that asymptotically goes to zero as the separations between particles increase. We would expect that similar results could be found for other potentials with these characteristics.

The SP-MC computer simulation method for calculating the chemical potential of the square-well fluid

The efficient recently proposed SP-MC method for calculating the chemical potential of hardbody fluids at very high densities by computer simulation is extended to the case of the squarewell fluid. Results are obtained for the square-well fluid with energy width parameter λ = 1.5. The implementation of the method takes into account a discontinuity in the third derivative with respect to core size of the chemical potential at infinite dilution of a test particle in the fluid. We note the implications of this discontinuity for the SP-MC method for larger values of λ and for equations of state for square-well fluid mixtures. Chemical potentials have been simulated at two high densities over a range of temperatures. We additionally present new simulation results for the compressibility factor and the internal energies of the fluid at these state points, and perform thermodynamic consistency calculations involving these quantities and the chemical potentials. The results are also compared with those of a recen...

Vapour pressures of CCl3F, CCl2F2 and CClF3

Abstract We report measurement of the vapour pressures of CCI 2 F 2 and CCIF 3 in the temperature ranges 172–293 K and 188–273 K, respectively. The estimated uncertainties are 0.2 kPa, maximum, for pressure and 0.001 K for temperature. In addition, the most accurate vapourpressure measurements available for CCI 3 F, CCI 2 F 2 and CCIF 3 were represented by a Wagner-type equation from almost their triple points to their critical points. These equations are shown to provide adequate representations of the selected experimental results over the entire liquid range. The corresponding values of the Wagner parameters are reported.

Liquid–vapour equilibrium of multipolar square-well fluids.Gibbs ensemble simulations and equation of state

Simulation results for a system comprising a square well plus either a point dipole or a point quadrupole are presented. The properties obtained are the vapour–liquid equilibrium densities and the critical properties. Critical densities are not very sensitive to the values of dipole or quadrupole, while critical temperatures increase significantly when the multipole strength rises. A comparison with a perturbation theory for multipolar square-well systems is presented. Overall agreement between simulated and theoretical values is good when comparison is restricted to quadrupoles or dipoles corresponding to the most relevant real polar substances but is only moderate for the largest multipolar strengths considered.

The mean distance of closest approach in the theory of liquids

Abstract The mean distance of closest approach, for two colliding particles, is defined as an average over their relative kinetic energies. It is shown that the mean distance of closest approach thus defined, is formally identical to the effective hard-sphere diameter in the Barker and Henderson perturbation theory of liquids.

Interaction potentials and thermodynamics of small polar molecules. The case of C1-Freons (halomethanes)

The recently proposed approximate nonconformal (ANC) theory has been very successful in determining effective interaction potentials for a large number of pure substances in the gaseous state: noble gases, homodiatomics, alkanes, perfluoroalkanes and some small polyatomic molecules, as well as many of their binary mixtures. ANC potentials are spherically symmetric Kihara-like functions involving an energy ϵ, a diameter δ and a form parameter s. In this work, we propose an effective-potential theory valid at finite densities. The basic assumption is that ANC potential functions represent effectively the thermodynamics of a substance over the isotropic fluid region given the appropriate state dependencies of ϵ, δ and s. The theory proposes a relation between the critical temperature of a substance and ϵ that is used here to predict effective potentials for the one-carbon Freons: CCl4, CCl3F, CCl2F2, CClF3, CHF3, CH2F2, CH3F, CH3Cl, CH2Cl2, CHCl3, CHClF2 and CHCl2F, a collection of small molecules that are all of similar geometry but varying degrees of polarity. As a test of the reliability of the theory the calculated second virial coefficients B(T ) are compared with experiment. For most of these substances, B(T ) is reproduced within experimental error. The relative contributions of the polar and nonpolar parts of the potential to the thermodynamics are discussed. The approach produces effective interactions and generalized Stockmayer potentials for this set of molecules to be used in predicting other thermodynamic properties.

Accurate Effective Potentials of Real Substances from Acoustic Virial Coefficients

Accurate second acoustic virial coefficients have been employed to determine parameters of an effective intermolecular potential for nine pure substances: argon, nitrogen, carbon dioxide, carbon tetrafluoride, and the first five alkanes (methane, ethane, propane, butane, and pentane). The values used for the second acoustic virial coefficients were taken from data reported in the literature. To obtain the form and parameters of the effective potential, we employed an inversion method recently introduced for volumetric second virial coefficients of nonconformal potentials. The potential parameters determined in this way are useful in predicting various gas properties. The model reproduces the experimental second virial data within their uncertainty, including volumetric second virial coefficients that were not used in the potential determination.

Extended mean spherical approximation for electrolyte solutions

The range of applicability of the mean spherical approximation to a primitive-model electrolyte is extended to allow for stronger Coulomb coupling. The new terms in the approximation are extracted from the HNC formalism, which is adequate for strongly coupled Coulomb systems. The new approximation satisfies the Stillinger-Lovett conditions. The new integral equation thus obtained is presented.

An interpretation of the mean spherical approximation

Abstract The mean spherical approximation is shown to be derivable from a perturbation expansion where the reference system follows the Percur-Yevick approximation. Then the MSA may be interpreted as a first-order expansion in which the perturbation is averaged with respect to the low-density reference distribution function. This represents a generalization of an equivalent interpretation previously made with respect to the free energy of a polar fluid.