Liquid solutions group contribution methods

When both VLE and LLE data are missing, it is not possible to assume ideal solutions. The separation into two liquid phases indicates a strong deviation from ideality. Here, the remaining possibility is to use some of the existing group contribution methods, such as UNIFAC, for which the parameters are based on LLE data. 

This equation is quite accurate in comparison with group contributing methods [40] or other predictive LSER methods [41]. For compounds where the solvatochromic parameters are known, the mean absolute error in log Dy is about 0.16. It is usually less than 0.3 if solvatochromic parameters of the solute and solvent must be estimated according to empirical rules [42], In contrast to the prediction of gas-liquid distribution coefficients, which is usually easier, the LSER method allows a robust estimation of liquid-liquid distribution coefficients. However, these equations always involve empirical terms, despite their being physico-chemically founded thermodynamic models. However, this is considered due to the fundamental character of the solvatochromic scales. 

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). 

The procedure is based on the UNIFAC-Free Volume method developed by T. Oishi and J. M. Prausnitz, "Estimation of Solvent Activities in Polymer Solutions Using a Group-Contribution Method," Ind. Eng. Chem. Process Des. Dev., 17, 333 (1978). The UNIFAC-FV method is presented by Aa. Fredenslund, J. Gmehling, and P. Rasmussen, Vapor-Liquid Equilibria Using UNIFAC, Elsevier Scientific Publishing, New York (1977). The group... 

In Chapter 4, methods based on equations of state were presented for predicting thermodynamic properties of vapor and liquid mixtures. Alternatively, as developed in this chapter, predictions of liquid properties can be based on correlations for liquid-phase activity coefficients. Regular solution theory, which can be applied to mixtures of nonpolar compounds using only properties of the pure components, is the first type of correlation presented. This presentation is followed by a discussion of several correlations that can be applied to mixtures containing polar compounds, provided that experimental data are available to determine the binary interaction parameters contained in the correlations. If not, group-contribution methods, which have recently undergone extensive development, can be used to make estimates. All the correlations discussed can be applied to predict vapor-liquid phase equilibria and some, as discussed in the final section of this chapter, can estimate liquid-liquid equilibria. 

For other applications, like the selection of solvents for the liquid-liquid extraction of solutes from mixtures, solubility and related measures are determined on the basis of the liquid-phase activity coefficients, 7y, for solute-solvent pairs. Usually, for screening purposes, it is sufficient to estimate the liquid-phase activity coefficient at infinite dilution, 7,", using group-contribution methods. 

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. 

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. 

Predictive methods make possible to treat the non-ideality of a liquid mixture without the knowledge of binary interaction parameters fitted from experimental data. Obviously, the predictive should be used only for exploratory purposes. Here we present two approaches. The first one, called the regular solution theory, requires information only about pure components. The second one, UNIFAC, is based on group contributions, and makes use indirectly of experimental data. 

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