Alejandro Gil-Villegas

Statistical associating fluid theory for chain molecules with attractive potentials of variable range

A version of the statistical associating fluid theory (SAFT) is developed for chain molecules of hard-core segments with attractive potentials of variable range (SAFT-VR). The different contributions to the Helmholtz free energy are evaluated according to the Wertheim perturbation theory. The monomer properties are obtained from a high-temperature expansion up to second order, using a compact expression for the first-order perturbation term (mean-attractive energy) a1. Making use of the mean-value theorem, a1 is given as the van der Waals attractive constant and the Carnahan and Starling contact value for the hard-sphere radial distribution function in terms of an effective packing fraction. The second-order perturbation term a2 is evaluated with the local compressibility approximation. The monomer cavity function, required for the calculation of the free energy due to the formation of the chains and the contribution due to association, is given as a function of a1. We analyse the equation of state for ch...

A statistical associating fluid theory for electrolyte solutions (SAFT-VRE)

A general theory for electrolyte solutions is examined within the framework of the statistical associating fluid theory for potentials of variable range (SAFT-VR). A first extension of the theory (SAFT-VRE) has already been used to describe the thermodynamics and phase equilibria of aqueous solutions of alkali-halide salts [GALINDO, A., GIL-VILLEGAS, A., JACKSON, G. and BURGESS, A. N., 1999, J. phys. Chem., 103, 10272]. The approach incorporates separate contributions describing the monomer, associating and ionic interactions. In the spirit of the SAFT-VR approach the monomer contribution is written as a high-temperature perturbation expansion up to second order; the separate effects of solvent-solvent, solvent-ion and ion-ion interactions on the phase equilibria are studied. Water is taken to be the solvent throughout the study, with the same four-site model and parameters as in the previous work. The association contribution is essential to account for the hydrogen bonding interactions present in water. The effects of ion pairing and solvent-ion association are also examined. For the ionic contribution several levels of approximation are discussed. The effect of the different molecular parameters on the phase behaviour of a model aqueous solution is examined for the different choices.

Describing the Properties of Chains of Segments Interacting Via Soft-Core Potentials of Variable Range with the SAFT-VR Approach

We present a general development for the equation of state (EOS) of chain molecules composed of tangent spherical segments interacting with a soft repulsive potential and an attractive well. The method is based on a recent version of the statistical associating fluid theory for chain molecules with interaction potentials of variable range (SAFT-VR). In this communication we focus our attention on the properties of Lennard–Jones chains (LJC), using SAFT-VR and a sample recipe for the evaluation of the chain free energy that requires only a knowledge of the contact value of the cavity function of a Sutherland-6 system. We study the liquid–vapor coexistence properties for different values of the chain length. The results obtained are of similar accuracy to other EOS for LJC, but our approach is simpler and more general. We show that standard perturbation theories developed for simple liquids can also be used for chain molecules.

An analytical equation of state for chain molecules formed from Yukawa segments

We present an analysis of the thermodynamic properties of chain molecules formed from Yukawa segments using the statistical associating fluid theory with interactions of variable range (SAFT-VR) and the high-temperature expansion of the mean-spherical solution (MSA-HTE) to the Ornstein–Zernike equation for a simple Yukawa fluid. The SAFT-VR expressions derived previously for this system allow the MSA-HTE equation of state to be reformulated in terms of first-order perturbation quantities, thus improving its accuracy. Furthermore, the MSA-HTE solution provides a full theoretical derivation of the perturbation theory used in SAFT-VR, together with a completely analytical equation of state for chain molecules composed of segments which interact via the Yukawa potential.

THE THERMODYNAMICS OF HETERONUCLEAR MOLECULES FORMED FROM BONDED SQUARE-WELL (BSW) SEGMENTS USING THE SAFT-VR APPROACH

We broaden the scope of the statistical associating fluid theory for potentials of variable attractive range (SAFT-VR) to treat heteron uclear chain molecules formed from bonded square-well (BSW) segments. The ideas of the bonded hard sphere (BHS) treatment for distributed-site models composed of hard-sphere segments are applied to square-well sites with the SAFT-VR approach. The results of isothermal—isobaric Monte Carlo simulations are reported for heteronuclear square-well diatomics with different sets of energy and range parameters. The SAFT-VR approach provides an excellent description of the equation of state of the diatomic systems for a wide range of densities. The goal of the work is to provide a rigorous treatment of distributed-site models of fluids, and to establish a framework for a group contribution approach with SAFT-VR.

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.

Reaction-field and Ewald summation methods in Monte Carlo simulations of dipolar liquid crystals

The treatment of the long-range dipolar interactions in simulations of mesogens is examined. After a brief reformulation of the standard Ewald summation and reaction-field methods in the general context of electrostatics using Green functions, we report the results of Monte Carlo simulations of liquid crystalline phases for L/D = 5 hard spherocylinders (cylinder length Land diameter D) with central point dipoles oriented along the main axis of the cylinder. In the case of N = 1020 particles an equivalent description of the thermodynamic properties and the structure of the phases is obtained with both techniques. A good description of the dielectric constant of the surrounding continuum is achieved by using a simple selfconsistent iterative method based on the calculation of the dielectric constant within the cell. The reaction-field method allows a systematic study of the phase behaviour of the system to be made with relatively modest computational requirements. We make a preliminary assessment of the pha...

The liquid-crystalline phase behaviour of hard spherocylinders with terminal point dipoles

We examine the effect of dipolar interactions on the liquid-crystalline phase behaviour of L/D = 5 hard spherocylinders with a terminal point dipole. The hard spherocylinder consists of a cylinder of length L and diameter D with hemispherical caps on each end; the point dipole is located at the centre of the hemispherical cap (2.5D from the centre of the spherocylinder) and is oriented along the principal molecular axis. The phase transitions exhibited by this system are studied using the isothermal - isobaric Monte Carlo (MC-NPT) technique. As for systems with central dipoles, the terminal dipole is seen to slightly destabilize the nematic (orientationally ordered) phase relative to the isotropic phase when compared with the non-polar hard spherocylinders. More interestingly, the smectic (layered) phase is destabilized in the terminal dipole case, and is only seen at the very highest densities. This is in stark contrast to what is seen for systems with central point dipoles in which the smectic phase is stabilized relative to the nematic phase due to the strong anti-parallel dipolar interactions. We do not find any evidence for ferroelectric or anti-ferroelectric ordering in these systems.

Chain and ring structures in smectic phases of molecules with transverse dipoles

Abstract Systems of hard spherocylinders with central transverse point dipoles are studied by Monte Carlo simulation. The dipoles are seen to stabilise the formation of the smectic-A phase relative to the nematic phase; the nematic phase disappears altogether at low temperatures. In the smectic-A phase the cores of the molecules align parallel to the layer normal with the dipoles in the plane. At high temperatures the dipoles are orientationally disordered; as the temperature is lowered ring-like domains appear, and then elongated antiferroelectric chain-like domains form. We analyse these results in the context of recent studies on two-dimensional vortex-antivortex systems.

Predicting the High-Pressure Phase Equilibria of Binary Mixtures of n -Alkanes Using the SAFT-VR Approach

The phase behavior of selected alkane binary mixtures is studied using SAFT-VR, a version of the statistical associating fluid theory for potentials of variable attractive range (SAFT). We treat the n-alkane molecules as chains formed from united-atom hard-sphere segments with square-well potentials of variable range to describe the attractive interactions. We use a simple relationship between the number of carbon atoms in the n-alkane molecule and the number of segments in the united atom chains in order to predict the phase behavior of n-butane with other n-alkanes. The calculated vapor pressures and saturated liquid densities of the pure components are fitted to experimental data from the triple point to the critical point. These optimized parameters are rescaled by the respective experimental critical points and used to determine the critical lines and phase behavior of the mixtures. We use the Lorentz-Berthelot combining rule for the unlike interactions. We predict the phase behavior of n-butane + n-alkane binary mixtures, concentrating mainly on the critical region. The gas-liquid critical lines predicted by SAFT-VR for the n-alkane mixtures are in excellent agreement with the experimental data, and improve significantly on the results obtained with the simpler SAFT-HS approach where the attractive interactions are treated at the mean-field level.