Solutions contribution method, UNIQUAC

For molecules which differ in size or shape interactions between the surface of the molecules, different Gibbs excess models, such as NRTL [34] or UNIQUAC [35], are recommended, respectively. The predictive group contribution method UNIFAC [36] will fail if several polar groups compose a solvent or solute molecule. As a... 

The UNIFAC (Unified quasi chemical theory of liquid mixtures Functional-group Activity Coefficients) group-contribution method for the prediction of activity coefficients in non-electrolyte liquid mixtures was first introduced by Fredenslund et al. (1975). It is based on the Unified Quasi Chemical theory of liquid mixtures (UNIQUAC) (Abrams and Prausnitz, 1975), which is a statistical mechanical treatment derived from the quasi chemical lattice model (Guggenheim, 1952). UNIFAC has been extended to polymer solutions by Oishi and Prausnitz (1978) who added a free volume contribution term (UNIFAC-FV) taken from the polymer equation-of-state of Flory (1970). 

When it is necessary to estimate activity coefficients where no data or very limited data are available, estimates may be made by using a group contribution method. In this case, a molecule is divided into fimctional groups, or subgroups of the molecule. These subgroups are assumed to act independently of the molecule in which they appear. Molecular interactions are accounted for by properly weighted sums of group interactions. Fredenslund, Jones, and Prausnitz developed the method for UNIQUAC and named it as universal functional activity coefficient (UNIFAC). Smith, van Ness, and Abbott report the equations for the activity coefficients of multicomponent solutions and their parameters. These equations are very... 

The two most developed group contribution methods are the ASOG (Analytical Solution Of Groups) and UNIFAC (UNIquac Functional-group Activity Coefficient) " models, both of which are the subjects of books. We will consider only the UNIFAC model here. UNIFAC is based on the UNIQUAC model of Sec. 9.5. This model, you will remember, has a combinatorial term that depends on the volume and surface area of each molecule, and a residual term that is a result of the energies of interaction between the molecules. In UNIQUAC the combinatorial term was evaluated using group contributions to compute the size parameters, whereas the residual term had two adjustable parameters for each binary system that were to be fit to experimental data. 

Simple group-contribution methods based on UNIFAC, containing corrections for the FV effects, satisfactorily predict the solvent activities and vapor-liquid equilibria for binary and ternary polymer solutions. They are less successful for the prediction of liquid-liquid equilibria if the parameters are based on VLB. They are much more successful if the parameters are based on LLE data. The combination of a simple FV expression such as that employed in the Entropic-FV model and a local-composition energetic term such as that of UNIQUAC seems to be a very promising tool for both VLE and LLE in polymer solutions. We expect that such tools may find widespread use in the future for practical applications. 

If the mutual solubilities of the solvents A and B are small, and the systems are dilute in C, the ratio ni can be estimated from the activity coefficients at infinite dilution. The infinite dilution activity coefficients of many organic systems have been correlated in terms of stmctural contributions (24), a method recommended by others (5). In the more general case of nondilute systems where there is significant mutual solubiUty between the two solvents, regular solution theory must be appHed. Several methods of correlation and prediction have been reviewed (23). The universal quasichemical (UNIQUAC) equation has been recommended (25), which uses binary parameters to predict multicomponent equihbria (see Eengineering, chemical DATA correlation). 

The UNIFAC (UNIQUAC functional group activity coefficient) method is an extension of the UNIQUAC (Universal quasi chemical) method, which has been used widely in chemical process engineering to describe partitioning in organic systems as occur in petroleum and chemical processing (Fredenslund et al., 1975,1977). It has been applied less frequently to aqueous systems. It expresses the activity coefficient as the sum of a "combinational" component, which quantifies the nature of the area "seen" by the solute molecule, and a "residual" component, which is deduced from group contributions. Arbuckle (1983,1986), Banerjee (1985), Banerjee and Howard (1988), and Campbell and Luthy (1985) have tested the applicability of the method to water solubility. 

Modern theoretical developments in the molecular thermodynamics of liquid-solution behavior are based on the concept of local composition. Within a liquid solution, local compositions, different from the overall mixture composition, are presumed to account for the short-range order and nonrandom molecular orientations that result from differences in molecular size and intermolecular forces. The concept was introduced by G. M. Wilson in 1964 with the publication of a model of solution behavior since known as the Wilson equation. The success of this equation in the correlation of VLE data prompted the development of alternative local-composition models, most notably the NRTL (Non-Random-Two Liquid) equation of Renon and Prausnitz and the UNIQUAC (UNIversal QUAsi-Chemical) equation of Abrams and Prausnitz. A further significant development, based on the UNIQUAC equation, is the UNIFAC method,tt in which activity coefficients are calculated from contributions of the various groups making up the molecules of a solution. 

The Universal Quasi-chemical Theory or UNIQUAC method of Abrams and Prausnitz divides the excess Gibbs free energy into two parts. The dominant entropic contribution is described by a combinatorial part ( ). Intermolecular forces responsible for the enthalpy of mixing are described by a residual part ( ). The sizes and shapes of the molecule determine the combinatorial part, which is thus dependent on the compositions and requires only pure component data. Since the residual part depends on the intermolecular forces, two adjustable binary parameters are used to better describe the intermolecular forces. As the UNIQUAC equations are about as simple for multi-component solutions as for binary solutions, the UNIQUAC equations for multicomponent solutions are given below. Species are identified by subscript i, subscript j is a dummy index. Here, is a relative molecular surface area and r, is a relative molecular volume. Both of these quantities are pure-species parameters. 

Peihaps the most important teim in Eq. (S.2-3) is the liquid-phase activity coefficient, and methods for its prediction have been developed in many fomis and by many woricers. For binaiy systems the Van Laar (Eq. (1.4-18)], Wilson [Eq. (1.4-23)], NRTL [Eq. (1.4-27)], and UNIQUAC [Eq. (1.4-36)] relationships are usefiil for predicting liquid-phase nonidealities, they require some experimental data. When no data are available, and an approximate nonideality correction will suffice, the UNIFAC approach (Eq. (1.4-31)], which utilizes fiinctional group contributions, may be used. For special cases involving regular solutions (no excess entropy of mixing), the Scatchard-Hildebrand method provides liquid-phase activity coefficients based on easily obtained pure-component properties. 

---