Activity-coefficient models Flory-Huggins equation

Although the Wilson activity coefficient model has proven to be useful for solutions of small molecules, it has seen very limited use for polymer solutions most likely because of its increased complexity relative to the Flory-Huggins equation. 

The VSM-W isotherm equation is a four parameters model, A i, K and C s). The pairwise interaction constants Aj and A j have been found to be highly correlated. To avoid this problem, Cochran et al. (1985) used the Flory-Huggin equation for the activity coefficient instead of the Wilson equation ... 

The two VSM isotherm equations are given in eqs. (2.7-5) and (2.7-7) depending on whether the Wilson equation or the Flory-Huggin equation is used to calculate the activity coefficient. Observing the form of these equations, the vacancy solution model equation can be written in general form as follows ... 

The different equations are represented in detail in the literature. To derive a reliable g - resp. activity coefficient model using Eq. (4.85) the different excess properties (h . s, v ) should be taken into account Flory [16] and Huggins [17,18] independently derived an expression for g starting from the excess entropy... 

A final note for these classical activity coefficient models is that, despite the advent of advanced SAFT and other equations of state discussed next (Section 3.4), they are stiU quite popular aud widely used in practical applications. They are also well cited in literature. For example, the historical articles by Flory and Huggins (Refs. [32,33]) are cited 998 (13.5) and 1034 (14) and the citations of the articles by Elbro et al. 164 (6.6), Lindvig et al. 44 (3.4), Kontogeorgis et al." 121 (5.5), and Oishi and Prausnitz" 353 (9.5). The citations are per May 2014 and the numbers in parenthesis are citations per year. 

Haeany Solution Model The initial model (37) considered the adsorbed phase to be a mixture of adsorbed molecules and vacancies (a vacancy solution) and assumed that nonideaUties of the solution can be described by the two-parameter Wilson activity coefficient equation. Subsequendy, it was found that the use of the three-parameter Flory-Huggins activity coefficient equation provided improved prediction of binary isotherms (38). 

The Flory-Huggins and Wilson equations for the activity coefficients of the components of the mixed solvent were employed to correlate 32 experimental data sets regarding the solubility of drugs in aqueous mixed solvents. The results were compared with the models available in literature. It was found that the suggested equation can be used for an accurate and reliable correlation of the solubilities of drugs in aqueous mixed binary solvents. It provided slightly better results than the best literature models but has also the advantage of a theoretical basis. 

The FH model for the activity coefficient, proposed in the early 1940s by Flory and Huggins, is a famous Gibbs free energy expression for polymer solutions. For binary solvent-polymer solutions and assuming that the parameter of the model, the so-called FH interaction parameter x,2, is constant, the activity coefficient is given by the equation ... 

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