Ana Laura Benavides

Vapor-liquid equilibrium and critical behavior of the square-well fluid of variable range: A theoretical study

The vapor-liquid phase behavior and the critical behavior of the square-well (SW) fluid are investigated as a function of the interaction range, lambdain [1.25, 3], by means of the self-consistent Ornstein-Zernike approximation (SCOZA) and analytical equations of state based on a perturbation theory [A. L. Benavides and F. del Rio, Mol. Phys. 68, 983 (1989); A. Gil-Villegas, F. del Rio, and A. L. Benavides, Fluid Phase Equilib. 119, 97 (1996)]. For this purpose the SCOZA, which has been restricted up to now to a few model systems, has been generalized to hard-core systems with arbitrary interaction potentials requiring a fully numerical solution of an integro-partial differential equation. Both approaches, in general, describe well the liquid-vapor phase diagram of the square-well fluid when compared with simulation data. SCOZA yields very precise predictions for the coexistence curves in the case of long ranged SW interaction (lambda>1.5), and the perturbation theory is able to predict the binodal curves and the saturated pressures, for all interaction ranges considered if one stays away from the critical region. In all cases, the SCOZA gives very good predictions for the critical temperatures and the critical pressures, while the perturbation theory approach tends to slightly overestimate these quantities. Furthermore, we propose analytical expressions for the critical temperatures and pressures as a function of the square-well range.

Deviations from corresponding-states behavior in the vapor-liquid equilibrium of the square-well fluid

The vapor-liquid equilibrium of the square-well (SW) fluid of variable range is studied. The analysis focuses on the dependence on the SW range, which exhibits deviations from corresponding-states behavior. The study is based on a new, compact and accurate equation for the SW Helmholtz free-energy. This equation relies on the mean-field approximation and a scaled-particle theory of Boublik, and agrees well with available computer simulations. The position of the critical point, the vapor pressures and the width of the orthobaric curve are obtained in terms of the width of the well. They show non-trivial oscillatory departures from corresponding-states behavior as given by the augmented van der Waals theory.

Phase behavior of colloids and proteins in aqueous suspensions: Theory and computer simulations

The fluid phase behavior of colloidal suspensions with short-range attractive interactions is studied by means of Monte Carlo computer simulations and two theoretical approximations, namely, the discrete perturbation theory and the so-called self-consistent Ornstein-Zernike approximation. The suspensions are modeled as hard-core attractive Yukawa (HCAY) and Asakura-Oosawa (AO) fluids. A detailed comparison of the liquid-vapor phase diagrams obtained through different routes is presented. We confirm Noro-Frenkels extended law of scaling according to which the properties of a short-ranged fluid at a given temperature and density are independent of the detailed form of the interaction, but just depend on the value of the second virial coefficient. By mapping the HCAY and AO fluids onto an equivalent square-well fluid of appropriate range at the critical point we show that the critical temperature as a function of the effective range is independent of the interaction potential, i.e., all curves fall in a master curve. Our findings are corroborated with recent experimental data for lysozyme proteins.

The thermodynamics of molecules with discrete potentials

Fluids formed by molecules interacting with discrete potentials are examined in the context of perturbation theory and the reference hypernetted chain equation (RHNC) solution to the Ornstein—zernike equation. A perturbation theory for discrete-potential fluids (DPT) is presented, which only requires one to know the properties of a square-well fluid of variable range. Several potentials are studied: square-shoulder, a combination of a square-well and square-shoulder, and a discrete representation of a continuous potential model. We have found that the DPT approach reproduces the RHNC predictions in most of the cases.

Perturbation theory for mixtures of discrete potential fluids

A thermodynamic perturbation theory for mixtures of fluids composed of particles interacting via discrete potentials is presented, based on previous work for pure component systems. Square-well and square-shoulder mixtures are accurately described by this theory, giving the necessary information for studying a wide range of discrete potential fluids. As an example of this, the theory is applied to a discrete Lennard-Jones mixture, obtaining very good results when compared against computer simulation values. The scope of this work is to implement perturbation theory for discrete potential systems in modern theories for complex fluids.

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.

Thermodynamics of a long-range triangle-well fluid

The long-range triangle-well fluid has been studied using three different approaches: firstly, by an analytical equation of state obtained by a perturbation theory, secondly via a self-consistent integral equation theory, the so-called self-consistent Ornstein–Zernike approach (SCOZA) which is presently one of the most accurate liquid-state theories, and finally by Monte Carlo simulations. We present vapour–liquid phase diagrams and thermodynamic properties such as the internal energy and the pressure as a function of the density at different temperatures and for several values of the potential range. We assess the accuracy of the theoretical approaches by comparison with Monte Carlo simulations: the SCOZA method accurately predicts the thermodynamics of these systems and the first-order perturbation theory reproduces the overall thermodynamic behaviour for ranges greater than two molecular diameters except that it overestimates the critical point. The simplicity of the equation of state and the fact that it is analytical in the potential range makes it a good candidate to be used for calculating other thermodynamic properties and as an ingredient in more complex theoretical approaches.

Vapor-liquid equilibrium of a multipolar square-well fluid

A simple polar fluid is modelled by square-well particles with point dipoles and quadrupoles at their centers. An equation for the free energy is derived by perturbation theory, obtaining the explicit dependence on the potential parameters, and allowing to study the effects of the strength of the multipoles on the vapor-liquid (V-L) equilibrium. It is found that the critical temperature is the property most sensitive to the values of the dipolar and quadrupolar moments, μ and Q, increasing with increasing moments although the effect of Q is much stronger. The shape of the coexistence curve is mostly affected on the liquid side and the coexistence diameters are found to be far from rectilinear. Comparison with simulation results shows that a multipolar SW fluid, for an attractive range equal to 1.5 times the diameter, is remarkably similar to the multipolar Lennard-Jones fluid.

Thermodynamic and structural properties of confined discrete-potential fluids

The thermodynamic and structural behaviors of confined discrete-potential fluids are analyzed by computer simulations, studying in a systematic way the effects observed by varying the density, temperature, and parameters of the potentials that characterize the molecule-molecule interactions. The Gibbs ensemble simulation technique for confined fluids [A. Z. Panagiotopoulos, Mol. Phys. 62, 701 (1987)] is applied to a fluid confined between two parallel hard walls. Two different systems have been considered, both formed by spherical particles that differ by the interparticle pair potential: a square well plus square shoulder or a square shoulder plus square well interaction. These model interactions can describe in an effective way pair potentials of real molecular and colloidal systems. Results are compared with the simpler reference systems of square-shoulder and square-well fluids, both under confinement. From the adsorption characterization through the use of density profiles, it is possible to obtain specific values of the interparticle potential parameters that result in a positive to negative adsorption transition.

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.