Flory-Huggins theory application

The well-known Flory treatment [50-52] of the en-thropic contribution to the Gibbs energy of mixing of polymers with solvents is still the simplest and most reliable theory developed. It is quite apparent, however, that the Flory-Huggins theory was established on the basis of the experimental behavior of only a few mixtures investigated over a very narrow range of temperature. Strict applications of the Flory-Huggins approach... 

For more than two decades researchers have attempted to overcome the inadequacies of Flory s treatment in order to establish a model that will provide accurate predictions. Most of these research efforts can be grouped into two categories, i.e., attempts at corrections to the enthalpic or noncombinatorial part, and modifications to the entropic or combinatorial part of the Flory-Huggins theory. The more complex relationships derived by Huggins, Guggenheim, Stavermans, and others [53] required so many additional and poorly determined parameters that these approaches lack practical applications. A review of the more serious deficiencies... 

Chiou, C.T. and Manes, M. Application of the Flory-Huggins theory to the solubility of solids in glyceryl trioleate, / Chem. Soa, Faraday Trans. 1, 82(l) 243-246, 1986. 

According to Flory-Huggins theory, in the limit of x the critical x parameter is 0.5.(H) Below this value the polymer and solvent will be miscible in all proportions. Above this value, the solvent will not dissolve the polymer, but will act only as a swelling solvent. Thus, the pure solvent may not dissolve the polymer even though it is not crosslinked. If x is not , the critical value of x is larger, but the same qualitative arguments regarding mutual solubility of the solvent and polymer hold. Thus, the application of Equation 1 does not require that the pure solvent be able to completely dissolve the polymer, only that the solvent dissolve into the polymer by an amount that can be measured. 

Application of the Flory-Huggins theory to the melting point depression gives the relationship1... 

Geveke, D.J. Danner, R.P., "Application of the Flory-Huggins Theory to the System Chloroform-Polystyrene-Butadiene Rubber," Polym. Eng. Sci., 31, 1527 (1991). 

Robledo-Muniz, J. G. Tseng, H. S. Lloyd, D. R., "Phase Behavior Studies of the System Polystyrene-Polybutadiene- Chloroform. I. Application of the Flory-Huggins Theory," Polym. Eng. Sci., 25, 934 (1985). 

The closest approach to successful applications of polymer solution theory to humic substances was made by Chiou et al. (1983) when studying the binding of small organic chemicals by soils. They considered the soil sorbent substances to be amorphous macromolecular humic substances, and they adapted the Flory-Huggins theory to a study of the sorbate species solubilized in the amorphous macromolecules. 

This brings us to the question about the applicability of the Flory-Huggins theory for food polymers. For polyelectrolytes, the theory is invalid, unless ionic strength is very high. In Section 7.3 the solubility of proteins will be discussed. Very few polysaccharides are simple homo-... 

In the first stage, the Flory-Huggins theory derives an expression for AS mix when Zkffniix = 0. This involves the application of Eq. (3.16), but this time with... 

The free volume theory, which was developed subsequently by Flory and coworkers, is much more elaborate in its innate construction. It attempts to rectify the omissions of the Flory-Huggins theory whilst retaining certain important elements therefrom. Whereas the Flory-Huggins theory has found wide application in the development of theories of polymeric stabilization, the free volume theory has not yet proved to be quite so productive, although it remains crucial to the understanding of the effects of temperature. Both theories will therefore be outlined in this chapter. 

Maier, T. R., Jamieson, A. M., and Simha, R., Phase equilibria in SBR/polybutadiene elastomer blends application of Flory-Huggins theory, J. Appl. Polym. Sci., 51 (6), 1053-1062 (1994). 

A further approach to the determination of the molecular weight of coal invokes the concept of the time-dependent response of bituminous coals to constant stress and presents indications that these coals are cross-linked, three-dimensional molecules. There have also been attempts to apply the Flory-Huggins theory to coal but there is some question about the validity of such an approach. But coal is most unlikely to be a simple polymer netwoik its heterogeneity, its mineral content (e.g., clays might act as fillers in the polymer inunobilizing any layers), and other factors indicate that a simple application of polymer theory is not justified. If some of the problems of the application of polymer theory to coals could be resolved, the method could provide a valuable aid to chemical methods of molecular weight determination. 

This equation is the well-known Flory-Huggins Equation. The power of a theory is reflected by its capability for further applications in various situations. In the next section, we will introduce how the assumptions of Flory-Huggins theory can be amended for its broad applications. 

Although Flory-Huggins theory does not give an accurate description of polymer blends, it identifies the origins of polymer-polymer immiscibility and usually forms the basis of discussions interaction parameters are usually calculated assuming its applicability. For a more accurate description of the thermodynamics of mixing it is necessary to use a more complete equation-of-state theory [37,38]. 

The thermodynamic properties of concentrated polymer solutions were studied by Floryi and independently by Huggins. The Flory-Huggins theory of polymer solutions still forms the basis for much discussion of these solutions in industry and even in academic research. Understanding this model is important for making coimections to much of the literature. Flory also substantially improved this model to include compressible fluids. The Flory-OrwoU theory of polymer solutions is still transparent and easily applicable, predicting both upper and lower critical solution temperatures. More-empirically adequate theories of concentrated solutions do not lend themselves to simple lecture presentation and often require detailed computer calculations to obtain any results. Concentrated solutions also introduce the phenomenon of viscoelasticity. An extensive treatment of the full distribution of relaxation times necessary to imderstand the dynamic properties of polymers in concentrated solution is presented. 

ROB Robledo-Muniz, J.G., Tseng, H.S., Lloyd, D.R., and Ward, T.C., Phase behavior studies of the system polystyrene-polybutadiene-chloroform. I. Application of the Flory-Huggins theory, Polym. Eng. ScL, 25, 934,1985. 

Plasticizer-polymer systems form concentrated macromolecular solutions and no particular theory has been proposed yet to treat their thermodynamic behavior. The best treatment is to use the well-known Flory-Huggins theory, which is applicable to concentrated solutions of perfectly disordered homogeneous... 

In this section we consider a general model that has broad applicability to phase transitions in soft materials the Landau theory, which is based on an expansion of the free energy in a power series of an order parameter. The Landau theory describes the ordering at the mesoscopic, not molecular, level. Molecular mean field theories include the Maier-Saupe model, discussed in detail in Section 5.5.2. This describes the orientation of an arbitrary molecule surrounded by all others (Fig. 1.5), which set up an average anisotropic interaction potential, which is the mean field in this case. In polymer physics, the Flory-Huggins theory is a powerful mean field model for a polymer-solvent or polymer-polymer mixture. It is outlined in Section 2.5.6. 

---