Polymer solutions Flory-Huggins theory

Comparison of these two equations shows that for dilute polymer solutions, Flory-Huggins theory predicts the excess contribution to be... 

POLYMER SOLUTIONS FLORY HUGGINS THEORY IN THE ATTRACTIVE CASE... 

Bodi the partial pressure and Henry s law eonstant depend on temperature, pressure, and solvent properties. This relationship does not eonsider interaetion between solute and solvent In the ease of polymers, the Flory-Huggins theory gives a simplified relationship for low eoneenlrations of solvent ... 

Thermodynamics of Polymer Blends and Solutions. Flory-Huggins Theory... 

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 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. 

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 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. 

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 ... 

The Flory-Huggins theory begins with a model for the polymer solution that visualizes the solution as a three-dimensional lattice of TV sites of equal volume. Each lattice site is able to accommodate either one solvent molecule or one polymer segment since both of these are assumed to be of equal volume. The polymer chains are assumed to be monodisperse and to consist of n segments each. Thus, if the solution contains TV, solvent molecules and TV2 solute (polymer) molecules, the total number of lattice sites is given by... 

The Flory-Huggins theory of polymer solutions has been documented elsewhere [26, 27]. The basic parameters necessary to predict polymer miscibility are the solubility parameter 6, the interaction parameter %, and the critical interaction parameter ( ) . 

Of course, within the general framework of the Flory-Huggins theory a small difference between yn in a swollen network and in a solution is always to be expected, because the crosslinks have four rather than two polymer segments as first neighbours. An estimate of this effect has been made by Rijke 147), based on Stavekman s extension of Guggenheim s formulation of y to branched chains. The result is... 

Flory-Huggins Theory. The simplest quantitative model for AGmx that includes the most essential elements needed for polymer blends is the Flory-Huggins theory, originally developed for polymer solutions (3,4). It assumes the only contribution to the entropy of mixing is combinatorial in origin and is given by equation 3, for a unit volume of a mixture of polymers A. and B. Here, pt and... 

It should also be mentioned that polymer-solvent interactions can be characterized by the second virial coefficients that appear in equations (8) and (13) and by the free energy of interaction parameter Z1 that appears in the Flory-Huggins theory of polymer solution thermodynamics.1,61... 

To apply the procedure outlined above to a polymer, it is necessary to use the Flory-Huggins theory of polymer solution, which takes into account the entropy of mixing of solutes in polymers caused by the large difference in molecular size... 

Figure 10 Coexistence curve of binary polymer solutions with chain length r2 = 18 and 60. Open squares MC data solid line this work dash line Flory-Huggins theory dotted line Freed theory.

Figure 14 Normalized internal energy of mixing for a binary polymer solutions with r2 = 64(Yang et al., 2006a) and 100. MC data kT/(E = 4 (open square) kT/r = 10 (open triangle) kT/

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