Equations
Like most local composition models, UNIQUAC splits excessCombinatorial contribution
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 ''r''''i'' and surface areas ''q''''i''It is assumed that all molecules have the same coordination number as the methylene group of an alkane, which is the reference to calculate the relative volume and surface area. 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. The coordination number, ''z'', i.e. the number of close interacting molecules around a central molecule, is frequently set to 10. It can be regarded as an average value that lies between cubic (''z'' = 6) and hexagonal packing (''z'' = 12) of molecules that are simplified by spheres. 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 .Residual contribution
The residual, enthalpic term contains an empirical parameter, , which is determined from the binary interaction energy parameters. The expression for the residual activity coefficient for molecule i is: : with : /molis the binary interaction energy parameter. Theory defines , and , where is the interaction energy between molecules and . The interaction energy parameters are usually determined from activity coefficients, vapor-liquid, liquid-liquid, or liquid-solid equilibrium data. Usually , because the energies of evaporation (i.e. ), are in many cases different, while the energy of interaction between molecule i and j is symmetric, and therefore . If the interactions between the j molecules and i molecules is the same as between molecules i and j, there is no excess energy of mixing, . And thus . Alternatively, in some process simulation software 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). The ''C'' coefficient is useful for vapor-liquid equilibria data as well. The use of such an expression ignores the fact that on a molecular level the energy, , is temperature independent. It is a correction to repair the simplifications, which were applied in the derivation of the model.Applications (phase equilibrium calculations)
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). Models such as UNIQUAC allow chemical engineers to predict the phase behavior of multicomponent chemical mixtures. They are commonly used inParameters determination
UNIQUAC requires two basic underlying parameters: relative surface and volume fractions are chemical constants, which must be known for all chemicals (''q''''i'' and ''r''''i'' parameters, respectively). Empirical parameters between components that describes the intermolecular behaviour. These parameters must be known for all binary pairs in the mixture. 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. An alternative is to obtain activity coefficients with a method such as UNIFAC, and the UNIFAC parameters can then be simplified by fitting to obtain the UNIQUAC parameters. This method allows for the more rapid calculation of activity coefficients, rather than direct usage of the more complex method. 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.).Newer developments
UNIQUAC has been extended by several research groups. 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, extensions for the estimation of activity coefficients for electrolytic mixtures, extensions for better describing the temperature dependence of activity coefficients,Wisniewska-Goclowska B., Malanowski S.K., “A new modification of the UNIQUAC equation including temperature dependent parameters”, Fluid Phase Equilib., 180, 103–113, 2001 and solutions for specific molecular arrangements.Andreas Klamt, Gerard J. P. Krooshof, Ross Taylor “COSMOSPACE: Alternative to conventional activity-coefficient models”, AIChE J., 48(10), 2332–2349,2004 The DISQUAC model advances UNIFAC by replacing UNIFAC's semi-empirical group-contribution model with an extension of the consistent theory of Guggenheim's UNIQUAC. 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.See also
* Chemical equilibrium *Notes
References
{{DEFAULTSORT:Uniquac Thermodynamic models