In
statistical thermodynamics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic b ...
, the UNIFAC method (
UNIQUAC Functional-group Activity Coefficients)
[Aage Fredenslund, Russell L. Jones and John M. Prausnitz, "Group-Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures", '']AIChE
The American Institute of Chemical Engineers (AIChE) is a professional organization for chemical engineers. AIChE was actually established in 1908 to distinguish chemical engineers as a profession independent of chemists and mechanical engineers ...
Journal'', vol. 21 (1975), p. 1086 is a
semi-empirical
Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences an ...
system for the prediction of non-electrolyte
activity in non-
ideal mixture
In chemistry, an ideal solution or ideal mixture is a solution that exhibits thermodynamic properties analogous to those of a mixture of ideal gases. The enthalpy of mixing is zero as is the volume change on mixing by definition; the closer to zer ...
s. UNIFAC uses the
functional group
In organic chemistry, a functional group is a substituent or moiety in a molecule that causes the molecule's characteristic chemical reactions. The same functional group will undergo the same or similar chemical reactions regardless of the rest ...
s present on the molecules that make up the liquid mixture to calculate
activity coefficient
In thermodynamics, an activity coefficient is a factor used to account for deviation of a mixture of chemical substances from ideal behaviour. In an ideal mixture, the microscopic interactions between each pair of chemical species are the same ( ...
s. By using interactions for each of the functional groups present on the molecules, as well as some binary interaction coefficients, the activity of each of the solutions can be calculated. This information can be used to obtain information on liquid equilibria, which is useful in many thermodynamic calculations, such as
chemical reactor
A chemical reactor is an enclosed volume in which a chemical reaction takes place. In chemical engineering, it is generally understood to be a process vessel used to carry out a chemical reaction, which is one of the classic unit operations in chem ...
design, and
distillation
Distillation, or classical distillation, is the process of separation process, separating the components or substances from a liquid mixture by using selective boiling and condensation, usually inside an apparatus known as a still. Dry distilla ...
calculations.
The UNIFAC model was first published in 1975 by Fredenslund, Jones and
John Prausnitz
John Michael Prausnitz (born January 7, 1928) is a professor of chemical engineering at the University of California, Berkeley, a position he has held since 1955.[University of California
The University of California (UC) is a public land-grant research university system in the U.S. state of California. The system is composed of the campuses at Berkeley, Davis, Irvine, Los Angeles, Merced, Riverside, San Diego, San Francisco, ...]
. Subsequently they and other authors have published a wide range of UNIFAC papers, extending the capabilities of the model; this has been by the development of new or revision of existing UNIFAC model parameters. UNIFAC is an attempt by these researchers to provide a flexible liquid equilibria model for wider use in
chemistry
Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
, the
chemical
A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., wi ...
and
process engineering
Process engineering is the understanding and application of the fundamental principles and laws of nature that allow humans to transform raw material and energy into products that are useful to society, at an industrial level. By taking advantage ...
disciplines.
Introduction
A particular problem in the area of liquid-state
thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
is the sourcing of reliable thermodynamic constants. These constants are necessary for the successful prediction of the
free energy state of the system; without this information it is impossible to model the
equilibrium phases of the system.
Obtaining this free energy data is not a trivial problem, and requires careful experiments, such as
calorimetry
In chemistry and thermodynamics, calorimetry () is the science or act of measuring changes in ''state variables'' of a body for the purpose of deriving the heat transfer associated with changes of its state due, for example, to chemical reacti ...
, to successfully measure the energy of the system. Even when this work is performed it is infeasible to attempt to conduct this work for every single possible class of chemicals, and the binary, or higher, mixtures thereof. To alleviate this problem, free energy prediction models, such as UNIFAC, are employed to predict the system's energy based on a few previously measured constants.
It is possible to calculate some of these parameters using
ab initio
''Ab initio'' ( ) is a Latin term meaning "from the beginning" and is derived from the Latin ''ab'' ("from") + ''initio'', ablative singular of ''initium'' ("beginning").
Etymology
Circa 1600, from Latin, literally "from the beginning", from ab ...
methods like
COSMO-RS COSMO-RS (short for COnductor like Screening MOdel for Real Solvents)"Conductor-like Screening Model for Real Solvents: A New Approach to the Quantitative Calculation of Solvation Phenomena", A. Klamt, J. Phys. Chem., 99, 2224-2235 (1995), DOI: 10 ...
, but results should be treated with caution, because ab initio predictions can be off. Similarly, UNIFAC can be off, and for both methods it is advisable to validate the energies obtained from these calculations experimentally.
UNIFAC correlation
The UNIFAC correlation attempts to break down the problem of predicting interactions between molecules by describing molecular interactions based upon the functional groups attached to the molecule. This is done in order to reduce the sheer number of binary interactions that would be needed to be measured to predict the state of the system.
Chemical activity
The
activity coefficient
In thermodynamics, an activity coefficient is a factor used to account for deviation of a mixture of chemical substances from ideal behaviour. In an ideal mixture, the microscopic interactions between each pair of chemical species are the same ( ...
of the components in a system is a correction factor that accounts for deviations of real systems from that of an
Ideal solution, which can either be measured via experiment or estimated from chemical models (such as UNIFAC). By adding a correction factor, known as the activity (
, the activity of the i
th component) to the liquid phase fraction of a liquid mixture, some of the effects of the real solution can be accounted for. The activity of a real chemical is a function of the thermodynamic state of the system, i.e. temperature and pressure.
Equipped with the activity coefficients and a knowledge of the constituents and their relative amounts, phenomena such as
phase separation
Phase separation is the creation of two distinct phases from a single homogeneous mixture. The most common type of phase separation is between two immiscible liquids, such as oil and water. Colloids are formed by phase separation, though ...
and
vapour-liquid equilibria can be calculated. UNIFAC attempts to be a general model for the successful prediction of activity coefficients.
Model parameters
The UNIFAC model splits up the activity coefficient for each species in the system into two components; a combinatorial
and a residual component
. For the
-th molecule, the activity coefficients are broken down as per the following equation:
:
In the UNIFAC model, there are three main parameters required to determine the activity for each molecule in the system. Firstly there are the group surface area
and volume contributions
obtained from the
Van der Waals surface area and volumes. These parameters depend purely upon the individual functional groups on the host molecules. Finally there is the binary interaction parameter
, which is related to the interaction energy
of molecular pairs (equation in "residual" section). These parameters must be obtained either through experiments, via data fitting or molecular simulation.
Combinatorial
The combinatorial component of the activity is contributed to by several terms in its equation (below), and is the same as for the
UNIQUAC
In statistical thermodynamics, UNIQUAC (a portmanteau of universal quasichemical) is an activity coefficient model used in description of phase equilibria.
The model is a so-called lattice model and has been derived from a first order approxi ...
model.
:
where
and
are the molar weighted segment and area ''fractional'' components for the
-th molecule in the total system and are defined by the following equation;
is a compound parameter of
,
and
.
is the
coordination number
In chemistry, crystallography, and materials science, the coordination number, also called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it. The ion/molecule/atom surrounding the central i ...
of the system, but the model is found to be relatively insensitive to its value and is frequently quoted as a constant having the value of 10.
:
and
are calculated from the group surface area and volume contributions
and
(Usually obtained via tabulated values) as well as the number of occurrences of the functional group on each molecule
such that:
:
Residual
The residual component of the activity
is due to interactions between groups present in the system, with the original paper referring to the concept of a "solution-of-groups". The residual component of the activity for the
-th molecule containing
unique functional groups can be written as follows:
:
where
is the activity of an isolated group in a solution consisting only of molecules of type
. The formulation of the residual activity ensures that the condition for the limiting case of a single molecule in a pure component solution, the activity is equal to 1; as by the definition of
, one finds that
will be zero. The following formula is used for both
and
:
In this formula
is the summation of the area fraction of group
, over all the different groups and is somewhat similar in form, but not the same as
.
is the group interaction parameter and is a measure of the interaction energy between groups. This is calculated using an
Arrhenius equation
In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1 ...
(albeit with a pseudo-constant of value 1).
is the group mole fraction, which is the number of groups
in the solution divided by the total number of groups.
:
:
is the energy of interaction between groups ''m'' and ''n'', with
SI units of joules per mole and ''R'' is the
ideal gas constant
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...
. Note that it is not the case that
, giving rise to a non-reflexive parameter. The equation for the group interaction parameter can be simplified to the following:
:
Thus
still represents the net energy of interaction between groups
and
, but has the somewhat unusual units of
absolute temperature
Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.
Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic wor ...
(SI
kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phys ...
s). These interaction energy values are obtained from experimental data, and are usually tabulated.
See also
*
Chemical equilibrium
In a chemical reaction, chemical equilibrium is the state in which both the reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the sy ...
*
Chemical thermodynamics
Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. Chemical thermodynamics involves not only laboratory measurement ...
*
Fugacity
In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant. It is equal to the pressure of an ideal gas whic ...
*
UNIQUAC
In statistical thermodynamics, UNIQUAC (a portmanteau of universal quasichemical) is an activity coefficient model used in description of phase equilibria.
The model is a so-called lattice model and has been derived from a first order approxi ...
– UNIversal QUasi-chemical Activity Coefficients
*
UNIFAC Consortium The UNIFAC Consortium was founded at the Carl von Ossietzky University of Oldenburg at the chair of industrial chemistry of Prof. Gmehling to invite private companies to support the further development of the group-contribution methods UNIFAC and ...
*
PSRK PSRK (short for Predictive Soave–Redlich–Kwong)
is an estimation method for the calculation of phase equilibria of mixtures of chemical components. The original goal for the development of this method was to enable the estimation of properties o ...
– Predictive Soave–Redlich–Kwong
*
MOSCED – Modified Separation of Cohesive Energy Density Model (Estimation of activity coefficients at infinite dilution)
References
{{Reflist
Further reading
* Aage Fredenslund,
Jürgen Gmehling
Jürgen Gmehling (born January 13, 1946 in Duisburg) is a retired German professor of technical and industrial chemistry at the Carl von Ossietzky University of Oldenburg.
Biography
His career started with an apprenticeship as a laboratory assi ...
and Peter Rasmussen, ''Vapor-liquid equilibria using UNIFAC : a
group contribution method'', Elsevier Scientific, New York, 1979
External links
UNIFAC structural groups and parametersAIOMFAC online-modelUNIFAC-based group-contribution model for calculation of activity coefficients in organic–inorganic mixtures.
Thermodynamic models