  We analyze diffusion of small particles in a solid polymeric medium taking
into account a short range particle-polymer interaction. The system is modeled
by a particle diffusion on a ternary lattice where the sites occupied by
polymer segments are blocked, the ones forming the hull of the chains
correspond to the places at which the interaction takes place, and the rest are
voids, in which the diffusion is free. In the absence of interaction the
diffusion coefficient shows only a weak dependence on the polymer chain length
and its behavior strongly resembles usual site percolation. In presence of
interactions the diffusion coefficient (and especially its temperature
dependence) shows a non-trivial behavior depending on the sign of interaction
and on whether the voids and the hulls of the chains percolate or not. The
temperature dependence may be Arrhenius-like or strongly non-Arrhenius,
depending on parameters. The analytical results obtained within the effective
medium approximation are in qualitative agreement with those of Monte Carlo
simulations.
