Flory-Huggins theory polymers

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). 

Bawendi MG, Freed KF (1988) Systematic corrections to Flory-Huggins theory polymer-solvent-void systems and binary blend-void systems. J Chem Phys 88 2741-2756 Chang TS (1939) Statistical theory of absorption of double molecules. Proc R Soc Ser A 169 512-531... 

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. 

In polymer solutions or blends, one of the most important thennodynamic parameters that can be calculated from the (neutron) scattering data is the enthalpic interaction parameter x between the components. Based on the Flory-Huggins theory [4T, 42], the scattering intensity from a polymer in a solution can be expressed as... 

We shall devote a considerable portion of this chapter to discussing the thermodynamics of mixing according to the Flory-Huggins theory. Other important concepts we discuss in less detail include the cohesive energy density, the Flory-Krigbaum theory, and a brief look at charged polymers. 

We concluded the last section with the observation that a polymer solution is expected to be nonideal on the grounds of entropy considerations alone. A nonzero value for AH would exacerbate the situation even further. We therefore begin our discussion of this problem by assuming a polymer-solvent system which shows athermal mixing. In the next section we shall extend the theory to include systems for which AH 9 0. The theory we shall examine in the next few sections was developed independently by Flory and Huggins and is known as the Flory-Huggins theory. 

Next we use the Flory-Huggins theory to evalute AG by Eq. (8.44). As noted above, the volume fraction occupied by polymer segments within the coi domain is small, so the logarithms in Eq. (8.44) can be approximated by the leading terms of a series expansion. Within the coil N2 = 1 and Nj = (1 - 0 VuNa/Vi, where is the volume of the coil domain. When all of these considertions are taken into account, Eq. (8.108) becomes... 

Flory-Huggins Theory. The simplest quantitative model foi that iacludes the most essential elements needed foi polymer blends is... 

Experimental values of X have been tabulated for a number of polymer-solvent systems (4,12). Unfortunately, they often turn out to be concentration and molecular weight dependent, reducing their practical utility. The Flory-Huggins theory quahtatively predicts several phenomena observed in solutions of polymers, including molecular weight effects, but it rarely provides a good quantitative fit of data. Considerable work has been done subsequentiy to modify and improve the theory (15,16). 

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... 

The formation mechanism of structure of the crosslinked copolymer in the presence of solvents described on the basis of the Flory-Huggins theory of polymer solutions has been considered by Dusek [1,2]. In accordance with the proposed thermodynamic model [3], the main factors affecting phase separation in the course of heterophase crosslinking polymerization are the thermodynamic quality of the solvent determined by Huggins constant x for the polymer-solvent system and the quantity of the crosslinking agent introduced (polyvinyl comonomers). The theory makes it possible to determine the critical degree of copolymerization at which phase separation takes place. The study of this phenomenon is complex also because the comonomers act as diluents. 

By using the liquid lattice approach to treat the random mixing of a disoriented polymer and a solvent, the so-called Flory-Huggins theory is often used to correlate the penetrant activity and the composition of the solution ... 

According to Flory-Huggins theory, the heat of mixing of solvent and polymer is proportional to the binary interaction parameter x in equation (3). The parameter x should be inversely proportional to absolute temperature and independent of solution composition. 

In practice, it is difficult to assign the number of repeating segments in solvent or polymer unambiguously. For this reason, it is usual in using Flory-Huggins theory to replace segment fraction (f) in equation (3) by volume fraction ( >). 

There Is a large body of experimental literature relating to polymer fractionation In liquid-liquid equilibria. In addition, numerous authors have analyzed polymer fractionation using Flory-Huggins theory. We have considered use of the corresponding states theory to model polymer fractionation for the ethylene/ polyethylene system at reactor conditions (18). Results of the... 

The corresponding-states theory of polymer solution thermodynamics, developed principally by Prigogine and Flory, has provided a reliable predictive tool requiring only minimal information. We have seen here several examples of the use of the corresponding-states theory. We have also seen that the corresponding-states theory is a considerable improvement over the older Flory-Huggins theory. 

The polymer solubility can be estimated using solubility parameters (11) and the value of the critical oligomer molecular weight can be estimated from the Flory-Huggins theory of polymer solutions (12), but the optimum diluent is still usually chosen empirically. 

Flory-Huggins theory for polymer solutions provides the classical expression for the polymer-solvent mixing term nmis [47] ... 

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... 

Futerko and Hsing presented a thermodynamic model for water vapor uptake in perfluorosulfonic acid membranes.The following expression was used for the membrane—internal water activity, a, which was borrowed from the standard Flory—Huggins theory of concentrated polymer solutions ... 

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. 

Note 1 The Flory-Huggins theory has often been found to have utility for polymer blends, however, there are many equation-of-state theories that provide more accurate descriptions of polymer-polymer interactions. 

Clark, A.H. (2000). Direct analysis of experimental tie line data (two polymer-one solvent systems) using Flory-Huggins theory. Carbohydrate Polymers, 42, 337-351. 

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