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 approximation of interacting molecule surfaces. The model is, however, not fully thermodynamically consistent due to its two-liquid mixture approach. In this approach the local concentration around one central molecule is assumed to be independent from the local composition around another type of molecule. 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. Earlier activity coefficient models such as the Wilson equation and the non-random two-liquid model (NRTL model) only consist of enthalpy terms. Today the UNIQUAC model is frequently applied in the description of phase equilibria (i.e. liquid–solid, liquid–liquid or liquid–vapor equilibrium). The UNIQUAC model also serves as the basis of the development of the group contribution method UNIFAC, where molecules are subdivided into functional groups. 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.
Equations Like most local composition models, UNIQUAC splits excess Gibbs free energy into a combinatorial and a residual contribution:
G E = ( G E ) C + ( G E ) R {\displaystyle G^{E}=(G^{E})^{C}+(G^{E})^{R}}
The calculated activity coefficients of the ith component then split likewise:
ln γ i = ln γ i C + ln γ i R {\displaystyle \ln \gamma _{i}=\ln \gamma _{i}^{C}+\ln \gamma _{i}^{R}}
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 correction caused by the change in interacting forces between different molecules upon mixing.
Combinatorial 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 ri and surface areas qi of the pure chemicals:
G E R T = ∑ i x i ln V i + z 2 q i x i ln F i V i {\displaystyle {\frac {G^{E}}{RT}}=\sum _{i}\,x_{i}\ln {V_{i}}+{\frac {z}{2}}q_{i}\,x_{i}\ln {\frac {F_{i}}{V_{i}}}}
Differentiating yields the excess entropy γC,
ln γ i C = ( 1 − V i + ln V i ) − z 2 q i ( 1 − V i F i + ln V i F i ) {\displaystyle \ln \gamma _{i}^{C}=(1-V_{i}+\ln V_{i})-{\frac {z}{2}}q_{i}\left(1-{\frac {V_{i}}{F_{i}}}+\ln {\frac {V_{i}}{F_{i}}}\right)}
with the volume fraction per mixture mole fraction, Vi, for the ith component given by:
V i = r i ∑ j x j r j {\displaystyle V_{i}={\frac {r_{i}}{\sum _{j}x_{j}r_{j}}}}
The surface area fraction per mixture molar fraction, Fi, for the ith component is given by:
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