Glass transition temperatures solute diffusion

The basic transport mechanism through a polymeric membrane is the solution diffusion as explained in Section 4.2.1. As noted, there is a fundamental difference in the sorption process of a rubbery polymer and a glassy polymer. Whereas sorption in a mbbery polymer follows Henry s law and is similar to penetrant sorption in low molecular weight liquids, the sorption in glassy polymers may be described by complex sorption isotherms related to unrelaxed volume locked into these materials when they are quenched below the glass transition temperature, Tg. The various sorption isotherms are illustrated in Figure 4.6 [47]. 

Hansen (57) pointed out that evaporation of a solvent from a polymer solution faced two barriers when cast on an impermeable substrate resistance to solvent loss at the air-liquid interface and diffusion from within the film to the air interface. Evaporation of neat solvents as well as moderately dilute solutions is limited by resistance at the air interface, but as solvent concentration becomes low (5-10-15%), the rate-controlling step is diffusion through the film. Hansen pointed out that at the point when solvent loss changes to a diffusion-limited process, the concentration of solvent is sufficient to reduce the glass transition temperature, Tg, of the polymer to the film temperature. 

The relationship is, however, only strictly valid in those systems where either molecular diffusion or migration of electronic energy is possible. The former has been shown to occur in the triplet-state quenching of the poly(ethylene)-cyclooctadiene system at 80°C (26), and where energy transfer was equally efficient in either solution or the solid due to ready diffusion of small molecules through the polymer matrix at temperatures above the glass-transition temperature. 

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