Statistical Mechanical Theory of Penetrant Diffusion in Polymer Melts and Glasses

We generalize our force-level, self-consistent nonlinear Langevin equation theory of activated diffusion of a dilute spherical penetrant in hard sphere fluids [1] to predict the long-time diffusivity of molecular penetrants in supercooled polymer liquids and non-aging glasses. Chemical complexity is treated using an a priori mapping to a temperature-dependent hard sphere mixture model where polymers are disconnected into effective spheres based on the Kuhn length as the relevant coarse graining scale. A key parameter for mobility is the penetrant to polymer segment diameter ratio, R. Our calculations agree well with experimental measurements for a wide range of temperatures, penetrant sizes (from gas molecules with R$\sim $0.3 to aromatic molecules with R$\sim $1) and diverse amorphous polymers, over 10 decades variation of penetrant diffusivity. Structural parameter transferability is good. We have also formulated a theory at finite penetrant loading for the coupled penetrant-polymer dynamics in chemically (nearly) matched mixtures (e.g., toluene-polystyrene) which captures well the increase of penetrant diffusivity and decrease of polymer matrix vitrification temperature with increasing loading. [1] R. Zhang and K. S. Schweizer, J. Chem. Phys., 143, 144906 (2015).