Fractal medium model for diffusion in dense polymer membranes

The mechanism of penetrant's diffusion in polymer membrane is described on the basis of free volume theory and the concept of diffusion path is presented. The statistical character of diffusion path is then related with the size of penetrant molecules, the temperature, and the freevolume of merrbranes based on percolation theory. The membrane structure can be divided into two regimes, i. e., the fractal regime and the homogeneous regi me. The geometrical and the topological structures of diffusion path in the fractal regime can be described by the fractal dimension d
f
and the graph dimension d
1
. On these basis, the transport behavior of penetrant in diffusion path is studied. In the fractal regime, the diffusion is nomalous and can not be described by the Fick' s law. With the change of the size of penetrant molecules, the temperature and the thickness of membrane, the transport behavior of penetrant can transform from normal diffusion to anomalous diffusion.