Flory-Huggins theory modification

Early attempts to model polymer miscibility started with the Flory-Huggins theory. Modifications to the theory to account for the free volume effects have been proposed in the literature. The Flory interaction parameter, x, was allowed to assume negative values to explain observed polymer-polymer miscibility. This approach was not found to be satisfactory for four reasons ... 

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... 

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. 

The distribution of a solute from water into SOM can be represented by a modification of the Flory-Huggins theory, which describes solubility in amorphous... 

In the case of copolymer solutions, the melting temperature also depends on interactions between the different monomeric imits and the solvent. Considering the case in which the crystalline phase is pure (i.e., only monomeric units of a single type crystallize and no solvent is present in the lattice), the decrease in the melting temperature can be derived in a similar manner as for the homopolymer solution case using the Flory-Huggins theory with an appropriate modification [15]. To take into accoimt the interactions between both comonomers and solvent, the net interaction parameter for binary copolymers should be calculated as follows ... 

TS2 Tseng, H.-S., Lloyd, D.R., and Ward, T.C., Phase behavior studies of the system polystyrene-polybutadiene-chloroform. II. Modification of the Flory-Huggins theory,... 

The justification for using the original Flory-Huggins theory, in some cases with small modifications lies in the fact that we are often dealing with multicomponent systems which would be difficult to treat with Flory snew theory. Moreover it turns out that the lattice theory suffices to give a good qualitative and in most cases also a semi quantitative acceptable picture of the often large effects of the different parameters which are involved in the description of the systems. 

This method is also based on the Flory-Huggins lattice model (522,533). In a modification of the method, inverse cloud temperatmes are plotted against (530), again based on the Flory-Huggins theory ... 

In this chapter, we have seen how classical and statistical thermodynamics coupled with simple ideas of lattice theory can be used to predict the phase behavior of polymer solutions. For polymers dissolved in low-molecular-weight solvents, the Flory-Huggins theory and its various modifications can adequately explain data obtained for quiescent solutions. More recently, the theory has been applied to predict the shift in the binodal under the influence of an imposed shear deformation [33]. For macromolecular solvents, however, development of the theory has not reached the same stage of maturity as for low-molecular-weight solvents. This remains an area of current and active research. 

Nonideal thermodynamic behavior has been observed with polymer solutions in which A Hm is practically zero. Such deviations must be due to the occurrence ofa nonideal entropy, and the first attempts to calculate the entropy change when a long chain molecule is mixed with small molecules were due to Flory [8] and Huggins [9]. Modifications and improvements have been made to the original theory, but none of these variations has made enough impact on practical problems of polymer compatibility to occupy us here. 

Modifications to the MKA equation have been proposed to take into account the swelling pressure and the dependence of the interfacial tension (y) and the Flory-Huggins interaction parameter (/) on particle size [62, 63] as well as the presence of adsorbed surfactant on particle swelling [64, 65], These modifications have allowed to obtain better agreement between theory and experimental data for the swelling of polystyrene particles using reasonable parameter values. 

Flory-Huggins mean-field theory. A similar mean-field theory successfully describes thermodynamics of polymer blends and, with some modifications, diblock copolymers and their blends with homopolymers. 

Fortunately, most organic solvents are nonpolar and therefore their intermolecular forces are weak London or dispersion forces. Hildebrand used the term "regular solutions" to describe solutions of nonelectrolytes and their nonpolar solvents. Additional theories on the solubility of polymers were developed by Flory ( ) and Huggins O). Probably the most important publications leading to the practical use of solubility theories by polymer scientists were those published by Burrell in 1955 ( ) and 1966 ( ). Modifications in the Hildebrand solubility parameter concept for regular solutions to account for larger intermolecular forces were made by Liebermann ( ), Crowley (.7), Hansen and Beerbower ( ) and Nelson et al. (9). 

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