Phase separation Flory-Huggins theory

Remember that the hump which causes the instability with respect to phase separation arises from an unfavorable AH considerations of configurational entropy alone favor mixing. Since AS is multiplied by T in the evaluation of AGj, we anticipate that as the temperature increases, curves like that shown in Fig. 8.2b will gradually smooth out and eventually pass over to the form shown in Fig. 8.2a. The temperature at which the wiggles in the curve finally vanish will be a critical temperature for this particular phase separation. We shall presently turn to the Flory-Huggins theory for some mathematical descriptions of this critical point. The following example reminds us of a similar problem encountered elsewhere in physical chemistry. 

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. 

The tendency of differing blocks to microseparate from each other is quantified by Flory s chi parameter /, introduced in Chapter 2. An increasing, positive value of x implies an increasing tendency for the two chemically dissimilar species to segregate from each other. As discussed in Section 2.3.1.2, for a blend of two different homopolymers (A and B) of equal degree of polymerization Na — Ag at a 50/50 composition, the Flory-Huggins theory predicts that phase separation should occur at a critical value of Xc = For block... 

Although the Flory-Huggins theory is sound in principle, several experimental results cannot be accounted for. For example, it was found that the x parameter depends on the polymer concentration in solution. Most serious is the fact that many polymer solutions (e.g., PEO) show phase separation on heating, when theory predicts that this should occur only on coohng. Another complication arises from specific interactions with the solvent, for example hydrogen bonding between the polymer and solvent molecules (e.g. with PEO and PVA in water). Aggregation in solution (a lack of complete dissolution) may also present another problem. 

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. 

Make suitable derivations from the Flory-Huggins theory to show that when phase separation takes place in a polymer solution, the proportion of a -mer in the poljmier-rich phase increases as x increases. 

Phase separation in initially miscible blends of thermoplastic (TP) and epoxy-diamine occurs during the reaction because the increase in the molecular weight of epoxy-amine copolymers diminishes the entropy of the blend. We can consider our systems as pseudobinary blends of TP and copolymer epoxy-amine for ease of understanding. The Flory-Huggins theory can be used in this case (I, 2). The miscibility during the reaction is controlled by the... 

This interpretation shows that the viscoelastic measurements can characterize the phase-separation mechanism in TP-modified epoxy systems. If we apply the Flory-Huggins theory to this pseudobinary blend (20), the calculated phase diagrams are in very good agreement with the morphologies encoun-... 

FIGURE 6.17 Solubility of a homopolymer according to the Flory-Huggins theory. Variables are the excluded volume parameter ft (or the polymer-solvent interaction parameter y), the net volume fraction of polymer q>, and the polymer-to-solvent molecular volume ratio q. Solid lines denote binodal, the broken line spinodal decomposition. Critical points for decomposition (phase separation) are denoted by . See text. 

The Flory-Huggins theory of polymer solubility suggests that if a polymer is growing in a poor solvent, when it reaches a critical molecular weight, a phase separation will occur in which a polymer-rich or gel phase... 

The terms within the brackets of Equation 7 can be used to estimate the scale of phase separation (6). Flory-Huggins theory (15) gives ... 

If a polymer solution undergoes phase separation into two liquid phases then the solution cannot be too far removed from the 0-point. It follows that the Flory-Huggins theory, which was derived for moderately concentrated solutions, can be applied to both of the polymer solution phases, one of which is dilute and the other concentrated. The chemical potentials of both the polymer and the solvent must be equal in the two co-existing phases ... 

The latter prediction appears to be well substantiated by experiment. On the other hand, it appears, as first shown by Freeman and Rowlinson (1960), that most, if not all, polymer solutions phase separate not only on cooling but also on heating. This constitutes a serious contravention of the predictions of the Flory-Huggins theory. In what follows, it will become apparent that the Flory-Huggins theory correctly identifies the driving force behind the mixing of polymer and solvent but overlooks a major factor that disfavours mixing. 

The free volume dissimilarity provides one of the important conceptual features that is missing from the Flory-Huggins theory. It rationalizes (i) the observed phase separation on heating (ii) the strong entropic contribution to X that opposes mixing and (iii) the observed increase in x with volume fraction of polymer in certain systems. Qualitatively, we can write for the mixing of polymer and solvent at room temperature ... 

Most of the shortcomings of the Flory-Huggins theory have been overcome by the use of the free volume theory (1). The entropic contribution to xi was attributed to the difference in free volume between the solvent and the polymer. The increase in the value of Xi with concentration was explained on the basis of the ordering of the solvent molecules on increasing the segment concentration. The phase separation near the critical temperature of the solvent was attributed to the decrease in entropy on mixing the solvent and polymer under such conditions. 

Several experimental results cannot be accounted for by the Flory-Huggins theory, such as the dependence of the X parameter on polymer concentration and phase separation of many polymer solutions on heating, e.g. PEO. 

The assumption of unperturbed chain statistics. Implicit in Flory-Huggins theory is the assumption that the long-range chain statistics of polymer chains are ideal random walks. This is not to be expected a polymer chain in a solvent collapses as conditions are changed to bring about phase separation between the polymer and the solvent (Grosberg and Khokhlov 1994). One would expect a polymer chain in a mixture to do the same as the conditions for phase separation were approached (Sariban and Binder 1987). 

Preparation of vertical stratified blend films relies upon an understating and control of the phase separation process. The Flory-Huggins theory expresses a... 

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