Activity coefficient-models Flory-Huggins

Since there had not been any measurements of thermal diffusion and Soret coefficients in polymer blends, the first task was the investigation of the Soret effect in the model polymer blend poly(dimethyl siloxane) (PDMS) and poly(ethyl-methyl siloxane) (PEMS). This polymer system has been chosen because of its conveniently located lower miscibility gap with a critical temperature that can easily be adjusted within the experimentally interesting range between room temperature and 100 °C by a suitable choice of the molar masses [81, 82], Furthermore, extensive characterization work has already been done for PDMS/PEMS blends, including the determination of activation energies and Flory-Huggins interaction parameters [7, 8, 83, 84],... 

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 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). 

This equilibrium concentration c, or the corresponding mole fraction x, of EG, water and DEG in the interface can be calculated from the vapour pressure and the activity coefficient y, derived from the Flory-Huggins model [13-17], Laubriet et al. [Ill] used the following correlations (with T in K and P in mm Hg) for their modelling ... 

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. 

Figure 4.6 Competitive isotherms of a ternary mixture of benzyl alcohol (BA), phenyl-2-ethanol (PE) and methyl-benzyl alcohol (MBA) on Cig-sUica with MeOH/H20 as the mobile phase, at different relative concentrations. Adsorbed amormts of (a) benzyl alcohol, (b) 2-phenylethanol, (c) 2-methyl benzyl alcohol, (d) activity coefficient in the mobile phase versus concentration. In Figures (a), (b), (c), the open circles are for equal parts of BA, PE and MBA, the diamonds for three parts of BA, 1 part PE and 1 part MBA), the triangles for one part of BA, one part of PE and three parts of MBA and the stars for the singlecomponent isotherms. The solid line is the Flory-Huggins model and the dashed lines are the IAS model isotherms. In Figures (d) and (e), the circles are for BA, the squares for PE, the triangles for MBA and the diamonds for the solvent. Reproduced from I. Quinones, J. Ford, G. Guiochon, Chem. Eng. Set, 55 (2000) 909 (Figs. 12,13 and 14).

Another possible extension is to consider an excess oil phase which is a mixtnre of two or more species. Provided that mixing within the micelle can still be considered ideal and that activity coefficients for all species in the bulk oil mixture are known, an expression for for each solnte is readily obtained. Micelles formed from surfactant mixtures can be treated provided that micelle composition is known or can be calculated from theories of mixed micelles such as regular solution theory and that solubilization is low enough not to affect micelle shape or composition. Finally, nonideal mixing in the micelles can be included if some model for the nonideality is available as well as data for evaluating the relevant parameters. Perhaps the simplest scheme for incorporating nonideality with nonpolar solutes is to use volume fractions instead of mole fractions in the spirit of Flory-Huggins theory. 

The Flory-Huggins (FH) model is a famous expression for the activity coefficient (generally for the Gibbs free energy of mixing) proposed in the early 1940s by Flory and Huggins, almost at... 

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 ... 

For good solvents (x < 0), the Flory-Huggins theory predicts that A2 is proportional to w and is independent of chain molecular weight. However the experimental data show that A2 Attempts to explain this molecular weight dependence of the second virial coefficient have been made by Flory and Krigbaum and others. " A complete theory will not involve a lattice model and treat the averages more carefully. It is still an active subject. 

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