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Here we will explain the results related with interfacil properties we have obtained using Monte Carlo simulations


Solid-fluid phase behavior in molecular systems is determined not only by packing considerations (as occurs in simple fluids, in which freezing can be understood in terms of the frezzing of hard spheres), but also accouting for shape, polarity and flexibility. Although it is generally assumed that flexibility is not crucial in determining the essential phase behavior of many chain-like fluids, this microscopic effect can proundly affect the phase equilibria of a given system. For instance, rigid non-spherical molecules can exhibit liquid crystalline phase behavior, which is never observed in fully flexible systems. In addition, vapor-liquid critical points of chain-like molecules with different degree of flexibility are different.

One of the most successful and studied molecular model accounting for chain-like systems is one in which the molecules are modelled as chains formed by connected spherical segments. In these models the pair potential between the monomers (either in the same or in different chains) that form the chains is given by a spherical potential. Such models incorporates two essential features: the excluded volume of the chains, and the connectivity between segments. Chain molecules of tangent segments can be considered: (1) fully flexible, in which bending and torsional potentials are not considered; (2) rigid, in which connected spherical segments have fixed bond angles and internal degrees of fredom; and (3) semi-flexible, in which bending and torsional potential are explicitly considered.

Very recently our group (in collaboration with the Statistical Thermodynamics of Molecular Fluids Group of Prof. Carlos Vega de las Heras, Universidad Complutense, Madrid, Spain, and the Multiphase Fluid Systems Group of Dr. Amparo Galindo, Imperial College London, UK) has shown that the Wertheim's thermodynamic perturbation theory approach (which constitutes the foundamental basis of the Statistical Associating Fluid Theory or SAFT formalism) can also be applied to the solid phase. This fundamental advance allows to predict fluid-solid equilibrium by using the SAFT formalism for both fluid and solid phases. One major advances on this field are summarized below:

  • Extension of the Soft-SAFT equation of state to deal with solid-liquid phase behavior.
  • Determination of the phase behavior (solid-liquid, vapor-liquid and vapor-solid) of fully flexible Lennard-Jones chains.
  • Global phase behavior of the two-center Lennard-Jones model.

  • Determination of the global phase behavior of fully flexible hard-sphere chains under the mean-field approximation.
  • Global phase beahviour of linear rigid hard-sphere chain under the mean-field approximation.
  • Global phase behaviour (solid-liquid, vapor-liquid and vapor-solid) of linear rigid Lennard-Jones chains.

Supercritical carbon dioxide (SC-CO2) is an useful and benign replacement for many organic solvents used in the traditional chemistry and oil industries. It is often considered as an ideal substitute to the standard organic solvents because it is non-flammable, essentially non-toxic, and the least expensive solvent after water. It has readily critical properties compared to those of water, being its critical density higher than that of most other supercritical solvents, and hence its solvent power can be enhanced several orders of magnitudes. In addition, it has a very low viscosity, low surface tension and low heat of vaporization, with highly tuneable properties by changes with pressure, and is readily recovered and recycled. It is, however, a poor solvent of many polar and organic compounds, including long-chain n-alkanes, water, polymers, and in general hydrophilic compounds, and this is reason becasue has not been used before.

This has led to an extensive search for effective surfactants that could be used to stabilize microdispersions of water or polymers in SC-CO2. In analogy to well-known surfactants which stabilize microdispersions in oil-water systems, surfactants for use in SC-CO2 would be amphiphiles with one part of the surfactant molecule being CO2-philic. Recent advances in surfactancy have shown that the most promising surfactants for use in SC-CO2 contain fluorinated chains as the CO2-philic part. Because surfactants in SC-CO2 form micelles in which the hydrophilic part of the surfactant is in the core, these micelles are generally referred to as reversed micelles by analogy to the nomenclature if convential oil-in-water systems.

Particularly interesting from industrial and practical point of view are surfactants that could be used to stabilize CO2 + water and CO2 + polymer binary mixtures. In the first case, fluoroalkane-polyoxyethylene diblock molecules constitute one the simplest non-ionic surfactants which stabilizes CO2 + water; in the second case, the ideal candidate could be fluoroalkane-alkane diblock non-ionic surfactants, which may stabilize CO2 + polymer mixtures. It has been demonstrated recently that these surfactants can emulsify insoluble solutes (water, polymers, etc.) into CO2, and hence, could be used as replacements for conventional solvent systems currently used in manufacturing and service industries, such as precision cleaning (metal finishing, microelectronics, optics or electroplanting), medical device fabrication and dry (garment) cleaning, as well as in the chemical manufacturing and coating industries. Unfortunately, these new surface active materials are relatively new, and hence, litle information on there properties is available. This is especially true for fluoroalkane-polyoxyethylene and fluoroalkane-alkane biblock surfactants, which are not commercially available and need to be synthesied specifically for there use and study.

Our group is involved in a preliminar study of this kind of systems using the SAFT-VR formalim which involves the understanding of the phase behavior of the corresponding binary and ternary mixtures. Different parts of the project are carried in collaboration with several groups: Multiphase Fluids System Group of Dr. Amparo Galindo at Imperial College London, UK; Dr. Clare McCabe at Vanderbilt University, US; and Dr. Eduardo J. M. Filipe at Instituto Superior Técnico, Lisbon.

  • Critical behavior of CO2 + n-alkane binary mixtures.
  • Determination of the vapor-liquid and liquid-liquid selected mixtures of CO2 + n-alkane and CO2 + perfluoroalkane binary mixtures.
  • Extension of the SAFT-VR approach to deal with pure diblock surfactant molecules.


There has been a great deal of effort in developing equations of state that can be used to describe the thermodynamics and bulk phase equilibria of fluids nand fluid mixtures. Analytical theories have now been developed to provide a quantitative description of bulk fluids comprising molecules which interact with more complex interactions, such associating systems, amphiphiles, polymers, and electrolytes. The SAFT-type theories clearly show how modern equations of state are able to describe the fluid phase behavior of systems ranging from small strongly assocating molecules such as water, to long-chain alkanes, polymers, and electrolytes.

Though the study of inhomogeneous fluids has a long history from the early mechanical models of Laplace and Young to the present day molecular density functional theory, a quantitative description of the interfacial properties of inhomogeneous fluids such as the interfacial thickness, adsorption, wetting and the surface tension is relatively rare, espcially in the case of moelcules with more complex interactions. Interfacial systems are ubiquitous in living systems (cell membranes which control molecular transport and biological functions) and are of fundamental industrial importance in areas as diverse as detergency (surfactants and solubilization), food production (emulsions and colloids), cosmetics (structured phases), and optoelectronic devices (liquid crystals).

The most successful modern theory of inhomogeneous classical fluids is undeniably the density functional (DFT) method, in which the free energy of the system is expressed as a functional of the spacially varying single particle density. The equilibrium density profile of an inhomogeneous system corresponds to the profile which leads to the minimum of the free energy of the system. Once the density profile is known, the interfacial properties may be determined from simple thermodynamic identities.

Our group (in collaboration with the Multiphase Fluid Systems Group of Prof. George Jackson, Imperial College London, UK) has developed new density functional theories based on the SAFT free. In particular, we have studied the effect of the potential range, chain length, association energy and volume and different association schemes on the interfacial properites. Our main achievements are described below:

  • Development of a DFT based on the free energy of the SAFT-HS.

  • Effect of the molecular parameters on the interfacial properties of chainlike associating molecules.
  • Development of a DFT based on the SAFT-VR free energy.

  • Application of the SAFT-VR DFT formalims to deal with the interfacial properties of systems of industrial interest.

The excess functions constitute the usual way to express the extent to which real liquid mixtures deviate from ideality. These properties are used extensively in a wide variety of scientific and technical fields, including chemistry, spectroscopy and chemical engineering. From a theoretical point of view, the excess functions are also a valuable information since equations of state, particularly those based in statistical mechanics, lead naturally to the prediction of excess properties. Since they are more sensitive than phase equilibria to the molecular details, the prediction of the excess properties provides an excellent way to check if theoretical approaches are suitable for describing accurately the behaviour of a given system.

A great advance in the field of the equations of state has been made in last years, motivated partially by the industrial interest, and also by the rapid development of modern molecular theories. These approaches provide a realistic description of the free energy of the system, as they are able to make quantitative predictions for the phase behaviour of complex systems. Most of the thermodynamic studies undertaken during last years concentrate in obtaining the phase equilibria, including the high-pressure phase behaviour and the critical properties, of systems of industrial interest. However, descriptions of the excess thermodynamic properties of these mixtures, such as excess volume, heat, and Gibbs free energy are less common.

Our group has applied the well known Soft-SAFT equation of state to predict the excess thermodynamic properties of some model binary mixtures. The key point to succesfully determine the excess properties of complex mixtures is to include the most important microscopic features of the system, such as chain connectivity, association, etc. Prelimiar results indicate that the SAFT approach is able to capture all the essential features of systems considered (see the list below).

In particular, we have addressed the following problems:

  • Excess thermodynamic properties of binary mixtures of spherical Lennard-Jones molecules.
  • Excess bahvior of binary mixtures of non-associating Lennard-Jones chains (n-alkane + n-alkane model).
  • Excess properties of self-associating binary mixtures of Lennard-Jones chains (n-alkane + 1-alcohol model).

Currently, we are working in collaboration with several experimental groups (Platon Group, University of Zaragoza, Spain, and Eduardo Filipe's Group, Instituto Superior Tecnico, Lisbon, Portugal) in order to apply the SAFT approach to deal with thermodynamic properties, and in particular excess thermodynamic functions, of complex mixtures.













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    Departamento de Física Aplicada
    Facultad de Ciencias Experimentales
    Universidad de Huelva
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