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The research carried out by the Physics
of Complex Liquids group involves different systems and properties, being
the common theme of research the understanding of complex systems using
molecular modelling techniques. Some of the most important topics in which
the group is working include:
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UNDER CONSTRUCTION
The knowledge of thermodynamic properties
of complex mixtures used in chemical industry are of prime importance to
design and understand chemical engineering processes, such as distillation,
extraction, absorption, etc. Traditional methods used to correlate and
predict the thermodynamic behavior of such systems, although useful, usually
fail in predicting the behaviour of the system far away from state conditions
at which parameters has been adjusted. This is essential to study the thermodynamic
behavior of a system at extreme conditions (high temperatures and pressures),
at which experiments are very difficult and expensive to be performed.
In this context, molecular modelling techniques constitute a powerful tool
to understand and predict the thermodynamic properties and phase equilibria
of the target system.
The main goal of this research line is the use and development of statistical mechanical theories for describing thermodynamic properties, including phase behavior, of complex fluid mixtures, such as associating substances and chain-like molecules. Our group (in collaboration with the Molecular Modelling Group of Dr. Lourdes Vega, Instituto de Ciencia de Materiales, CSIC, Barcelona, Spain) has developed the Soft-SAFT equation of state, which is based on the Statistical Associating Fluid Theory (SAFT) formalism. The SAFT approach is nowadays considered one of the most sophisticated and versatile molecular-based equations of state for predicting the phase behavior of complex mixtures (hydrocarbons, surfactants, water, polymers, refrigerants, etc.).
One of the main results of the group has been the formulation of the Soft-SAFT equation of state, which provides a useful tool for predicting phase equilibria of mixtures of associating and non-associating chain-like molecules. The approach has been also applied to address some specific properties of substances of industrial interest. In this context, we have obtained trasnferable parameters for the n-alkane homologous chemical family, which allows to obtained the thermodynamic behavior of long-chain molecules in a purely predictive way. The most important contributions are summarized below:
The main goal of this research line is the use and development of statistical mechanical theories for describing thermodynamic properties, including phase behavior, of complex fluid mixtures, such as associating substances and chain-like molecules. Our group (in collaboration with the Molecular Modelling Group of Dr. Lourdes Vega, Instituto de Ciencia de Materiales, CSIC, Barcelona, Spain) has developed the Soft-SAFT equation of state, which is based on the Statistical Associating Fluid Theory (SAFT) formalism. The SAFT approach is nowadays considered one of the most sophisticated and versatile molecular-based equations of state for predicting the phase behavior of complex mixtures (hydrocarbons, surfactants, water, polymers, refrigerants, etc.).
One of the main results of the group has been the formulation of the Soft-SAFT equation of state, which provides a useful tool for predicting phase equilibria of mixtures of associating and non-associating chain-like molecules. The approach has been also applied to address some specific properties of substances of industrial interest. In this context, we have obtained trasnferable parameters for the n-alkane homologous chemical family, which allows to obtained the thermodynamic behavior of long-chain molecules in a purely predictive way. The most important contributions are summarized below:
- Development of the Soft-SAFT molecular-based equation of state.
- Vapor-liquid equilibria of associating and non-associating Lennard-Jones chains.
- Phase behavior of binary and ternary mixtures of alkanes.
- Critical behavior and partial miscibility phenomena of binary mixtures of n-alkanes.
- Tricritical phenomena in n-alkane mixtures.
- Extension of the SAFT-HS approach to deal with branched chains.
- Development of the Soft-SAFT Dimer approach for predicting the vapor-liquid equilibria of long-chain molecules.
Molecules confined within porous materials,
with pore widths of few molecular diameters, can exhibit a wide range
of physical behaviour. The presence of wall forces, in addition to the
competition between wall-fluid and fluid-fluid intermolecular forces,
can lead to different surface-driven phase changes including layering
and wetting phase transition (not seen in bulk fluids), as well as shifts
in transitions, such as freezing, gas-liquid and liquid-liquid phase transitions.
The study of the thermodynamic behavior of confined fluids is not only important from a fundamental point of view due to the interest in the understanding from a molecular perspective of the new physics from finite-size effects, varying dimensionality and the presence of surface-forces, but also from a practical point of view. Micro- and meso-porous materials are important in fields as chemical, oil and gas, food and pharmaceutical industries for pollution control, mixture separation, and as catalysts and catalyst supports for chemical reactions among others.
Our group has collaborated with other research groups (Molecular Modelling Group of Dr. Lourdes F. Vega at Instituto de Ciencia de Materiales, CSIC, Barcelona, and Keith E. Gubbins' Group at North Carolina State University, US) to understand the thermodynamic behavior of confined fluids of industrial interest substances, with special emphasis on the adsorption behavior.
The study of the thermodynamic behavior of confined fluids is not only important from a fundamental point of view due to the interest in the understanding from a molecular perspective of the new physics from finite-size effects, varying dimensionality and the presence of surface-forces, but also from a practical point of view. Micro- and meso-porous materials are important in fields as chemical, oil and gas, food and pharmaceutical industries for pollution control, mixture separation, and as catalysts and catalyst supports for chemical reactions among others.
Our group has collaborated with other research groups (Molecular Modelling Group of Dr. Lourdes F. Vega at Instituto de Ciencia de Materiales, CSIC, Barcelona, and Keith E. Gubbins' Group at North Carolina State University, US) to understand the thermodynamic behavior of confined fluids of industrial interest substances, with special emphasis on the adsorption behavior.
- Adsorption of ethane and ethylene on gamma-alumina for separation purpouses using computer simulation.
- Adsorption behavior of nitrogen on model gamma-alumina using Fundamental Measure Density Functional Theory and computer simulation.
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:
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).
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:
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.
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.
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.
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:
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.
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