Diffusion in glassy polymers: A model using a homogenization method and the effective medium theory

Glassy polymers are considered as inhomogeneous with regions in which the gas sorption follows Henry's law and others where it follows Langmuir's law. It is assumed that the linear dimensions of these regions are small compared with the macroscopic length of interest but large compared with the mean free path of the penetrant gas molecules. Applying an homogenization method it is shown that the average flux is directly proportional to the concentration gradient in the polymer. This relationship can be expressed in terms of an effective diffusion coefficient D_eff, which depends on the details of the microstructure. D_eff is evaluated in the framework of the effective medium theory and compared with experimental data for diffusion of five vapors in ethylcellulose.