The molecular transport of small molecules through polymer films has been the subject of active research over almost three decades [1–8]. The main thrust in this area is either to accumulate a large body of experimental data to assess the stability of polymer films for extreme serviceability or to develop new theories which describe the phenomenology of transport processes, the latter often being studied in terms of three important parameters: permeation, diffusion, and solubility, in adition to the swelling phenomenon.