BINARY MIXTURES WITH ASSOCIATING AND REACTING COMPONENTS:
MOLECULAR AND PHENOMENOLOGICAL THEORIES, AND SUPPORTING EXPERIMENTS
State-of-the-art
Determination of the thermodynamic properties of mixtures and prediction of their phase behavior is
one of the most important tasks of physical chemistry and chemical engineering. Among the most difficult
types of fluid systems from the point of view of thermodynamic theory are those of pure substances and
solutions containing associating components, and systems with chemical reaction. Whereas the importance
of the former systems (e.g. water and aqueous solutions, alcohols, etc.) has been recognized long time ago,
the latter systems with simultaneous phase and reaction equilibrium and that, nearly as a rule, contain at
least one associating component, are emerging as a perspective efficient technology.
Traditionally, one way that the thermodynamic properties of the above systems have been modeled
is by semi-empirical approaches based on phenomenological theories [1]. Another possibility has been the
use of so-called chemical models [2], within which distinct polymeric species are postulated to comprise
species of a multi-component mixture. The modern approach, which is still under development, explores the
results of modern statistical mechanical theories of liquids by relating the properties of mixtures to the
forces acting between the molecules. From this point of view the considered systems lie at one of current
frontiers of theoretical capability.
The concept of microscopic species has been quite fruitful. Although semi-empirical in nature, it
improves phenomenological description of given mixtures and may constitute an input to a true molecular
(statistical thermodynamic) description. Presence and amounts of such species can be studied using a
number of techniques, both experimental and
theoretical, such as quantum mechanic calculations,
measuring of low density volumetric behavior, studies of infrared spectra, or measuring phase equilibria
[3,4]. Unfortunately, none of the techniques gives unambiguous answers.
The other approach to modeling the properties of associated fluids is to use well-defined
intermolecular potential models, upon which the techniques of statistical mechanics are employed. These
models, incorporating point charges within a basic molecular core, however are, due to their complexity,
generally intractable in terms of theoretical approaches and they are typically studied by means of computer
simulation techniques only. The complexity of these models also makes any detailed study of their
predictions extremely problematic for multi-component mixtures.
A different approach to modeling associated fluids at the molecular level was developed in the early
part of the last decade [5-7]. This approach considers explicitly the H-bonding by constructing simple
models of the phenomenon of association. The original model of Bol [5] for water was reformulated by
Kolafa and Nezbeda [8] and extended to methanol and ammonia [8,9]. This model, called the ‘primitive’
model in a similar spirit to the use of this term in the case of primitive models of electrolytes, has become
the standard basic model used in studies of associating fluids and aqueous mixtures. It pictures the molecule
of an associating compound by a hard body with interaction sites of two kinds with a strong and shortranged attractive interaction between the unlike sites to mimic hydrogen bonding. A primary focus of the
pioneering studies was the model and its properties predicted by a thermodynamic perturbation theory of
Wertheim [10], rather than applications to real systems. An exception is an empirical equation of state,
called SAFT equation [11], that combines in an empirical way the main physical ingredients of the
intermolecular interactions: hydrogen bonding at short separations with weak (e.g. van der Waals
dispersion) forces. A similar equation has also been proposed by Nezbeda and Pavlicek [12] who examined
it from the point of its theoretical justification rather than for applications. This analysis along with recent
numerous applications point to certain defects in SAFT-type equations. It turns out that the formal addition
of terms corresponding to weak interactions may destroy the properties of the primitive models and,
consequently, the equations lose their theoretical justification. A more justified way to account for weak
interactions within the thermodynamic perturbation theory is therefore more than desirable.
Early primitive models accounted only for the attractive interaction between the unlike sites (to mimic
hydrogen bonding) and ignored completely the repulsive interactions between the like sites. Further recent
theoretical investigations have elaborated the original primitive models and removed this defect by
incorporating also this short-ranged repulsion [13-15]. Extensive and thorough investigations of the so
called extended primitive models have showed that they satisfy all requirements imposed on reference
systems in perturbation theories of fluids upon which a rigorous theory may be developed [16,17]. Such a
theory must ultimately yield also a molecular-based equation of state of associating fluids and their
mixtures. With respect to development of new technologies, properties of fluids in vicinity of their critical
point have attracted a good deal of attention in recent years. These applications involve mainly water and
carbon dioxide in their near-critical state and hydrocarbons as solutes. Consequently, suitable molecular
models of the latter compounds are also required.
As regards investigations of simultaneous phase and reaction equilibria, an alternative to
phenomenological approaches may also be molecular-based methods. However, despite significant progress
achieved by these methods over the last two decades, they have not been employed yet extensively: (i)
purely theoretical methods are still too numerically unwieldy and inaccurate for mixtures of any complexity,
and (ii) computer simulation techniques have been limited to simplest of chemical systems. Whereas the
straightforward applicability of the former methods remains limited, a breakthrough took place recently as
regards the simulation methods. Efficient methods to calculate the chemical potential and hence the phase
equilibria has been put forward and implemented for a number of systems [18] and quite recently, Smith
and Triska [19] devised a reaction ensemble technique enabling one to simulate chemical systems
undergoing any combination of reaction and phase equilibria. So far only the basic theory of the method
was presented and its potential was illustrated by applications to several simple systems.
Experimental studies of associating and reacting mixtures besides their own indisputable role in research
may serve as severe tests of theoretical models and approximations. As regards experimental methods,
measurements of solid-liquid phase equilibria contributes considerably to the identification of the above
discussed microscopic species. The ability of the bulk components to form compounds can be extracted
from phase diagrams along with information on their stability in the liquid phase. In addition to this
‘identification’ role, solid-liquid equilibrium data make the determination of the activity coefficients and
excess Gibbs free energy possible. The region of temperatures is typically considerably distant from that of
the liquid-vapor equilibrium which is important in attempts of the numerically stable determination of
temperature derivatives of the excess Gibbs free energy, enthalpy, and heat capacity, i. e. the quantities
obtained standardly from calorimetric data. Additional accurate data are still needed to yield a better
understanding of the associating and/or reacting systems.
Main goals and details of the methods used
All the above mentioned results have provided a breakthrough to the molecular understanding of associating
fluids and their mixtures and have paved the way to the development of a true molecular theory. It must be
however understood that the primitive models by themselves cannot be used directly to estimate
quantitatively the properties of associating fluids and that they have been studied primarily from the point of
view of their viability: They have been designed to form only a reference term accounting for the most
important effects but which must be accompanied by other terms. The proposed project plans to go on along
this line ending up ultimately with practically applicable theoretically based formulas for the
thermodynamic properties of pure associated fluids and their mixtures. Specifically, the project will pursue
the following goals:
1. Development of primitive models for all classes of associated fluids
All theoretical considerations to date have considered only water, ammonia, and lower alcohols. The goal is
to develop extended primitive models for all associated fluids. As a part of our previous projects an attempt
has already been made to model also fatty acids but without success. Only quite recently a complex realistic
potential of lower fatty acids has been developed [20] which casts light on specific interactions between the
molecules of fatty acids which should make it possible now to develop also a primitive model.
2. Theory of the thermodynamic properties of the extended primitive models
Although the primitive models of associating fluids have been around for about a decade, their application
has been limited so far, in principle, only to systems without hetero-association. Using the original ideas of
the Wertheim theory [10], theoretical expressions for the thermodynamic functions of mixtures of two
different associating molecules must be developed. This extension must account as well for the nonspherical
shape of molecules which will require also the investigation of a new type of hard body fluids (pseudohard
body models) with respect to the availability of their necessary characteristics (site-site correlation functions
in an analytic form etc.). The research should provide a closed analytic expressions for the thermodynamic
functions.
3. Determination of the phase behavior, and phase and reaction equilibria
Using the recently developed general software, we plan to determine the phase behavior of several classes
of mixtures (water plus alcohols, water plus fatty acids, water plus n-alkanes, etc.) by calculating the global
phase diagram. The global phase diagrams provide a deep insight into the general behavior of mixtures and
allow one to make predictions as one component of the mixture varies. In addition to these diagrams, the
standard P-T and P-x (or T-x) projections will be calculated as well. These calculations will be based both
on a newly developed theoretical equations of state and on an engineering SAFT equation.
The simultaneous phase and reaction equilibrium in selected systems will be studied mainly by computer
simulations using the potential models developed within this project. In principle, this equilibrium may also
be studied using the developed equations of state.
4. Experimental determination of the phase behavior
It is well known that only harmony of a given theory with real experimental results can furnish a proof of its
correctness. The phase behavior of the (octanol +lower fatty acid) reacting systems will therefore be studied
using all available experimental equipment. The choice of this relatively simple system involving
association and/or chemical reaction is the fact that it can mimic processes which take place in living beings
(octanol, for instance, shares some properties of the body fat).
Itemization of the project
As it follows from the above discussion, the goals pursued by the proposed project will require that the
following individual tasks be solved:
1. In the initial stage (1st year):
a. Develop extended primitive models for associating diatomics (HF, HCl).
b. Develop extended primitive models for lower fatty acids based on recently developed realistic
potential models.
2. Simultaneously with item 1 above:
Derive closed analytic expressions for the thermodynamic functions for all extended primitive models using
the Wertheim’s theory and
3. In the second and third years:
a. Develop an equation of state which incorporates from the very beginning also weak
intermolecular forces.
b. Using developed equations of state, to determine the global phase behavior of the considered
mixtures.
As regards experimental measurements, they will … for all three years PLUS with respect to demands of
justification of the developed theories.
References
Reid R. C., Sherwood T. K.: THE PROPERTIES OF GASES AND LIQUIDS. McGraw-Hill, 19???
Doležalek F., Z. phys. Chem. 64, 727 (1908).
IVA – REFERENCE NA NEJAKA MERENI
IVA - TOTEZ
Bol W., Mol. Phys. 45, 605 (1982).
Dahl L. W., Andersen H. C., J. Chem. Phys. 78, 1980 (1983).
Smith W. R., Nezbeda I.: J. Chem. Phys. 81, 3694 (1984).
Kolafa J., Nezbeda I.: Mol. Phys. 61, 161 (1987).
Kolafa J., Nezbeda I.: Mol. Phys. 72, 777 (1991).
Wertheim M. S.: J. Stat. Phys. 42, 477 (1986).
SAFT
Nezbeda I., Pavlicek J.: STAVOVKA.
Nezbeda I., Slovak J.: Mol. Phys.
Slovak J., Nezbeda I.: Mol. Phys.
Strnad M. Nezbeda I.: Mol. Phys
Nezbeda I.: Czech. J. Phys. B
Nezbeda I.: J. Molec. Liq.
Nezbeda I., Kolafa J.: Mol. Simul.
Smith W. R., Triska B.: J. Chem. Phys.
Jedlovski P.:
Research team and international cooperation
The research team consists of two groups with years-long experience in their respective fields. Dr. Nezbeda
and his coworkers are experts in the field of modeling intermolecular interactions, perturbation theories and
their applications, and computer simulations. Dr. Malijevska is a leading experimentalist in the Department
of Physical Chemistry which is internationally recognized for its long tradition in high quality
measurements of the phase equilibria of multi-component systems.
A project similar to that proposed here but focusing predominantly on industrial applications of
phase equilibria in mixtures made up of associating components is being pursued by Professor R. W.
Missen, University of Toronto, Toronto, Canada. Personal contacts have been established and it has been
agreed to closely coordinate our investigations. A possibility for a Canadian Ph.D. student to join E. Hála
Laboratory of Thermodynamics to directly collaborate on the proposed project has also been discussed.
Professor Jackson from the Chemistry Department, University of Sheffield, is one of the authors of
the SAFT equation of state which will be used to calculate the phase diagrams and reaction equilibria. He
already has expressed his interest in this part of the project and plans to send a graduate student to E. Hala
Laboratory to collaborate on the project. There is also a possibility for one member of the team to work for a
shorter period in Sheffield.