Flory-Huggins swelling behavior

For more strongly sorbing penetrants, such as C02 and C2 and C hydrocarbons, BET 111 isotherms indicative of Flory-Huggins swelling behavior ate common. The Floiy-Huggins model, shown below, relates the penetrant activity (at) to the sorbed volume fraction v or the component. Typically, (he ectivily is replaced by the ratio of the penetrant partial pressure p and the component vapor pressure p0 . 

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. 

The behavior is predicted in the Flory-Huggins treatment of swelling, which leads to a relation between the degree of swelling Q for a particular solvent and the shear modulus G of the unswollen rubber... 

The binary interactirMi generally refers to the interactions between polymer-polymer and polymer-solvent The nature of solvent-polymer interaction plays an important role in the miscibility of blends. Many thermodynamic properties of polymer solutions such as solubility, swelling behavior, etc., depend on the polymer-solvent interaction parameter (y). The quantity was introduced by Flory and Huggins. Discussions of polymer miscibility usually start with Flory-Huggins equation for free energy of mixing of a blend (refer to Chap. 2, Thermodynamics of Polymer Blends ). 

The swelling of vulcanized crosslinked rubber by solvents has long been observed. This behavior was first modeled in the 1940s by Flory and Refiner [47]. They combine the Meyer-Flory-Huggins statistical thermodynamic theory of polymer solutions (Section 3.3) with the molecular theory of crosslinked rubber elasticity [48]. The molecular weight between crosslinks of the vulcanizates was predicted from the swelling to be... 

The swelling in liquid water could be a nonrelevant value to describe the membrane behavior in fuel cells. As an example, the sulfonated polyether ketones suffer from an excessive water uptake when immersed in hquid water at elevated temperatures [110], while a high-temperature fuel eeU test over 1400 h has been performed with fully hydrated gases [2]. Therefore, the swelling in hquid water at elevated temperature is of limited value. Most of the authors prefer nowadays to determine the water uptake under defined temperature and RH conditions. Water sorption isotherms have been measured and analyzed [40,104,119]. These results confirmed the previous data since the sorption isotherms are superimposable when expressed in 2 values for different ion contents and chemical structures [40,48,49,56]. The sorption isotherms were classically analyzed as the superposition of different phenomena (Henry, clustering, dual-mode, Flory-Huggins, and BET II processes) [119]. The water sorption isotherms exhibit a distinct sorption-desorption hysteresis, which was attributed to the very low desorption process [40]. 

Fig. 18 Composition of the phases coexisting for the system water/cellulose at 80° C as a function of the number of segments N of the polymer determined in swelling experiments [57]. Symbols indicate experimental data the solid line was calculated by means of (26) as described in the text the two phase area is hatched. The dashed line (nmmal behavior) was calculated by means of the original Flory Huggins theory, setting the interaction parameira equal to 0.54...

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