Rubbery polymers free-volume theories

The diffusion coefficient appearing in Eq. (20.4-3) b a true measure of the molecular mobiitty of the penetrant in question. Intuitively, the free-volume theory proponents argue that a penetram can execute a diffitsive jump when a free-volume element greater than or equal to a critical size presorts itself to a penetrant. The native poiymer, totally devoid of penetrant, still possesses a certain amount of free-volume packets of distributed size which wander spontaneously and randomly through the rubbery matrix. In fact, when a packet of sufficient size presents itself to a polymer segment, the polymer may execute a self-diffiisive motion, and this is the action that causes slow interdiffusion of polymer chains. 

Therefore, although rather cumbersome, the free-volume theory permits one to prepare theoretical plots of permeability as a function of temperature, penetrant pressure, and amorphous volume fraction in the rubbery polymer. 

FREE-VOLUME THEORY OF DIFFUSION IN RUBBERY POLYMERS... 

For diffusion of liquid through rubbery polymer composites, Fickian and non-Fickian diffusion theories are frequently used to describe the mechanism of transport, but for gas or vapour, other models have been developed to fit experimental data of diffusion profiles. The models of gas transport include Maxwell s model," free volume increase mechanism," solubility increase mechanism," nanogap hypothesis," Nielsen model, " " Bharadwaj model, ° Cussler model " " and Gusev and Lusti model, " etc. 

According to the glass transition theory, lipids are dispersed in the free volume of the food matrix composed of carbohydrates and protein polymers. In the rubbery state, the lipids react readily with oxygen and become oxidized. In the glassy state, however, the lipids are stable to oxidation because they are encapsulated and there is no free volume. The glass transition temperature, which determines when the food matrix changes from one state to the other, increases with a decrease in moisture and water activity. In many foods the... 

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