Flory-Huggins process

For multiple liquid phases (e.g. suspension processes) or increasing concentrations of polymers, some more realistic models are desirable (van Laar, Flory-Huggins, Wilson). ... 

According to the Flory-Huggins theory of polymer solutions, if the mixing process were driven only by an entropic gradient (nonpolar solvent) the solubility coefficient... 

With this in mind, some important adsorption isotherms were introduced, and we found that each of them describes important characteristics of the adsorption process (Table 6.10). Thus, the Langmuir isotherm considers the basic step in the adsorption process the Frumkin isotherm was one of the first isotherms involving lateral interactions the Temkin is a surface heterogeneity isotherm and the Flory-Huggins-type isotherms include the substitution step of replacing adsorbed water molecules by the adsorbed entities (Fig. 6.98). 

Taking into account the modes in which the water can be sorbed in the resin, different models should be considered to describe the overall process. First, the ordinary dissolution of a substance in the polymer may be described by the Flory-Huggins theory which treats the random mixing of an unoriented polymer and a solvent by using the liquid lattice approach. If as is the penetrant external activity, vp the polymer volume fraction and the solvent-polymer interaction parameter, the relationship relating these variables in the case of polymer of infinite molecular weight is as follows ... 

So far two models have been employed to rationalize the solvation process the classical solution model, either the mole-fraction scale or any other concentration scale, and the Flory-Huggins model. The question is where to use which theoretical model to interpret the results of partitioning experiments, in which solute molecules distribute between two phases, a and ft. If the two phases are at equilibrium at the same temperature and the same pressure, /z = /xf. After rearrangement and applying Eq. (11-8), we can write... 

This equation is not particularly useful in practice, since it is difficult to quantify the relationship between concentration and activity. The Flory-Huggins theory does not work well with the cross-linked semi-crystalline polymers that comprise an important class of pervaporation membranes. Neel (in Noble and Stern, op. cit., pp. 169-176) reviews modifications of the Stefan-Maxwell approach and other equations of state appropriate for the process. 

For polymers, x is usually defined on a per monomer basis or on the basis of a reference volume of order one monomer in size. However, x is usually not computed from formulas for van der Waals interactions, but is adjusted to obtain the best agreement between the Flory-Huggins theory and experimental data on the scattering or phase behavior of mixtures (Balsara 1996). In this fitting process, inaccuracies and ambiguities in the lattice model, as well as in the mean-field approximations used to obtain Eq. (2-28), are papered over, and contributions to the free energy from sources other than simple van der Waals interactions get lumped into the x parameter. The temperature dependences of x for polymeric mixtures are often fit to... 

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