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Until now, all of the liquid-phase activity coefficient models are only suitable for the components condensable and inorganic salts, and the organic ions (e.g. ionic liquids) aren't concerned. In the recent years, CSMs (Dielectric continuum solvation models) and their revised versions (i.e. COSMO, COSMO-RS) have been developed, and can extend to predict the activity coefficient in the mixtures containing ions. In particular, COSMO-RS (conductor-like screening model for real solvents) model is a novel and fruitful concept, and avoids the questionable dielectric approach [50-55]. It is capable of treating almost the entire equilibrium thermodynamics of fluid systems and should become a power alternative to fragment-based models like UNIFAC. But the reports on the actual application of this model in predicting activity coefficients aren't so many.

When components are notably dissimilar and activity coefficients are large, two and even more liquid phases may coexist at equilibrium, which then leads to the vapor-liquid-liquid phase equilibrium for two liquid phases. For example, consider the binary system of methanol

(1) and cyclohexane (2) at 25°C [1, 56], an equilibrium plot of y, (mole fraction in the vapor phase) against x, (mole fraction in the liquid phase) assuming an isotherm condition is drawn in Fig. 1. By Eq. (35),

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