Flory-Huggins theory phase equilibria

It is simply a measure of how the free energy changes with composition and is the driving force for the two phases to come to equilibrium (i.e., for their compositions to adjust until Equation 11-46 is satisfied). The chemical potentials in the Flory-Huggins theory can be simply obtained by differentiating the free energy of mixing, which for... 

The shape of the binodal near the critical point is not predicted correctly by the mean-field (Flory-Huggins) theory as demonstrated in Fig. 5.3(a). The difference in the two concentrations coexisting at equilibrium in the two-phase region is called the order parameter. This order parameter is analogous to the order parameter of van der Waals for the liquid-vapour phase transition, that is proportional to the density difference between the two coexisting phases. This order parameter is predicted to vary as a power law of the proximity to the critical point ... 

Using Flory-Huggins theory it is possible to account for the equilibrium thermodynamic properties of polymer solutions, particularly the fact that polymer solutions show major deviations from ideal solution behavior, as for example, the vapor pressure of solvent above a polymer solution invariably is very much lower than predicted from Raoult s law. The theory also accounts for the phase separation and fractionation behavior of polymer solutions, melting point depressions in crystalline polymers, and swelling of polymer networks. However, the theory is only able to predict general trends and fails to achieve precise agreement with experimental data. 

In the second approximation of Flory-Huggins theory (state equation 3.6 1), the phase equilibrium relationships have the form (Sole et al., 1984)... 

Let s compute the vapor pressure of a solvent over a polymer solution by using the Flory-Huggins theory. Let component A represent the pohnner and B represent the small molecule. To describe the equilibrium, follow the strategy of Equation (16.2). Use Equation (31.20), and set the chemical potential of B in the vapor phase equal to the chemical potential of B in the polymer solution. The vapor pressure of B over a polymer solution is... 

At equilibrium, the chemical potential of the solute must be equal in the two phases Pi(A) = Flory-Huggins theory Equation (31.20) gives the two... 

The general theory of the interphase was developed by Kammer, with allowance for a density gradient in the layer. Rammer s theory relies on Gibbs s conditions of an equilibrium between two phases with an interphase region existing between both phases. Rammer derived, within the framework of the Flory-Huggins theory, a theoretical expression for the interphase region thickness ... 

The Flory-Huggins theory has been used extensively to describe phase equilibria in polymer systems. It can, for example, qualitatively describe the lower phase boundary (UCST) in Figure 7.1, although it rarely gives a good quantitative fit of experimental data. Partial differentiation of Equation 7.13 with respect to iti (keeping in mind that and are functions of i) gives the chemical potential of the solvent. This is, of course, a key quantity in phase equilibrium that also makes x experimentally accessible. Further development is beyond the scope of this chapter, but the subject is well treated in standard works on polymer solutions [12-15]. 

Flexible polymers in poor solvent show a quasi-ideal behavior at a certain compensation point 0. At a slightly lower solvent quality, phase separation occurs, and there is an equilibrium between a nearly pure solvent phase (containing a few chains, each being severely contracted) and a polymer-rich phase. The latter can be described by the Floiy-Huggins theory. At the onset of phase separation (at the critical point) each polymer coil behaves like one individual argon atom at the liquid-gas transition of argon, and the Flory-Huggins approximation is not valid. 

Phase Equilibrium (PE) Binary mixtures of a polymer in a single solvent phase-separate at various temperatures, Tsep, depending on the volmne fi-action (/12 of the polymer. The maximmn of the 7 sep=/(< 2) fiuiction is called the critical solution temperature Test-The experiment is repeated for a series of dilute solutions of polymers of the same constitution and configmation but of different molar mass. The relation between the eritieal solution temperature and the molar mass of the polymer is based on the Flory-Huggins lattice theory which predicts that... 

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