Effect of the distribution of sorption sites on transport diffusivities: A contribution to the transport of medium-weight-molecules in polymeric materials

The detailed transports of both small and large molecules in heterogeneous media including either random disorder or periodic obstacles are known to decrease the value of macroscopic diffusion coefficients. This work proposes to analyze the successive displacements of medium-sized molecules in polymer materials according to the dispersion and topology of sorption sites from a modified application of the transition state theory. In absence of available information on the dispersion of rate constants between sorption macrosites for such molecules, their transport mechanisms at molecular scale is related to their sorption properties, which are more likely to be available. Simulations by kinetic Monte Carlo (KMC) techniques are presented for different distributions of occupancy values randomly allocated in space or distributed in self-similar clusters. Network structures are generated from the equilibrium occupancy on the basis of transition-state theory formulation on 2D lattice approximations. Different reconstruction strategies on 2D hexagonal lattices are examined regarding maximum likelihood principles including maximization of obstruction effects and minimization of either local or global variance of conductances between sorption sites. Effects of short time scales are assessed by comparing results obtained with networks verifying reversible and non-reversible random walks.