Free-Volume Theory of Diffusion in Rubbery Polymers

6 FREE-VOLUME THEORY OF DIFFUSION IN RUBBERY POLYMERS 

As mentioned in Section 13.3.2, the diffusion coefficient of simple gases in polymers above the glass transition temperature is independent of concentration 

On increasing the temperature above 0 K, the volume increases by homogeneous expansion and by the formation of holes, which are distributed discontinuously throughout the material at any instant. The former kind of change is called the interstitial free volume, whereas the latter is called the hole free volume. Thus, we have 

By appealing to the similarity in the behavior of the diffusion coefficient and the reciprocal of the viscosity [see Eq. (13.4.3)] and by assuming that the statistical redistribution of the free volume opens up voids large enough for 

E = molar energy needed to overcome attractive forces 

---