UNIQUAC
In statistical thermodynamics, UNIQUAC (a portmanteau of universal quasichemical) is an activity coefficient model used in description of phase equilibria.
The model is, however, not fully thermodynamically consistent due to its two-liquid mixture approach.
The UNIQUAC model can be considered a second generation activity coefficient because its expression for the excess Gibbs energy consists of an entropy term in addition to an enthalpy term.
Today the UNIQUAC model is frequently applied in the description of phase equilibria (i.e. liquid–solid, liquid–liquid or liquid–vapor equilibrium).
In fact, UNIQUAC is equal to UNIFAC for mixtures of molecules, which are not subdivided; e.g. the binary systems water-methanol, methanol-acryonitrile and formaldehyde-DMF.
A more thermodynamically consistent form of UNIQUAC is given by the more recent COSMOSPACE and the equivalent GEQUAC model.
[4] Like most local composition models, UNIQUAC splits excess Gibbs free energy into a combinatorial and a residual contribution: The calculated activity coefficients of the ith component then split likewise: The first is an entropic term quantifying the deviation from ideal solubility as a result of differences in molecule shape.
The latter is an enthalpic[nb 1] correction caused by the change in interacting forces between different molecules upon mixing.
The combinatorial contribution accounts for shape differences between molecules and affects the entropy of the mixture and is based on the lattice theory.
The Stavermann–Guggenheim equation is used to approximate this term from pure chemical parameters, using the relative Van der Waals volumes ri and surface areas qi[nb 2] of the pure chemicals: Differentiating yields the excess entropy γC, with the volume fraction per mixture mole fraction, Vi, for the ith component given by: The surface area fraction per mixture molar fraction, Fi, for the ith component is given by: The first three terms on the right hand side of the combinatorial term form the Flory–Huggins contribution, while the remaining term, the Guggenhem–Staverman correction, reduce this because connecting segments cannot be placed in all direction in space.
This spatial correction shifts the result of the Flory–Huggins term about 5% towards an ideal solution.
It is based on the coordination number of an methylene group in a long chain, which has in the approximation of a hexagonal close packing structure of spheres 10 intermolecular and 2 bonds.
[nb 3] In the case of infinite dilution for a binary mixture, the equations for the combinatorial contribution reduce to: This pair of equations show that molecules of same shape, i.e. same r and q parameters, have
The interaction energy parameters are usually determined from activity coefficients, vapor-liquid, liquid-liquid, or liquid-solid equilibrium data.
can be expressed as follows : The C, D, and E coefficients are primarily used in fitting liquid–liquid equilibria data (with D and E rarely used at that).
Activity coefficients can be used to predict simple phase equilibria (vapour–liquid, liquid–liquid, solid–liquid), or to estimate other physical properties (e.g. viscosity of mixtures).
They are commonly used in process simulation programs to calculate the mass balance in and around separation units.
UNIQUAC requires two basic underlying parameters: relative surface and volume fractions are chemical constants, which must be known for all chemicals (qi and ri parameters, respectively).
In a quaternary mixture there are six such parameters (1–2,1–3,1–4,2–3,2–4,3–4) and the number rapidly increases with additional chemical components.
The empirical parameters are obtained by a correlation process from experimental equilibrium compositions or activity coefficients, or from phase diagrams, from which the activity coefficients themselves can be calculated.
Remark that the determination of parameters from LLE data can be difficult depending on the complexity of the studied system.
For this reason it is necessary to confirm the consistency of the obtained parameters in the whole range of compositions (including binary subsystems, experimental and calculated lie-lines, Hessian matrix, etc.).
Some selected derivatives are: UNIFAC, a method which permits the volume, surface and in particular, the binary interaction parameters to be estimated.
This eliminates the use of experimental data to calculate the UNIQUAC parameters,[3] extensions for the estimation of activity coefficients for electrolytic mixtures,[7] extensions for better describing the temperature dependence of activity coefficients,[8] and solutions for specific molecular arrangements.
By adding a "dispersive" or "random-mixing physical" term, it better predicts mixtures of molecules with both polar and non-polar groups.
However, separate calculation of the dispersive and quasi-chemical terms means the contact surfaces are not uniquely defined.
The GEQUAC model advances DISQUAC slightly, by breaking polar groups into individual poles and merging the dispersive and quasi-chemical terms.
