A modification of the well-known Maxwell-Garnett equation for the mobility (effective diffusion coefficient) in 2-phase media (a matrix with inclusions) was suggested which permitted the description of a wide range of experimental situations. The novel approach correctly treated the partial trapping of a diffusing particle by an inclusion as well as the consequences of an energy barrier for particle penetration into an inclusion. Computer simulations showed that the presented mean-field theory reproduced surprisingly well the results for square inclusions without concentration limitation. For inclusions with other shapes (e.g. spherical) the theory worked well up to concentrations at which mobile particles became trapped in pockets between inclusions.

Calculations of the Effective Diffusion Coefficient for Inhomogeneous Media. J.R.Kalnin, E.A.Kotomin, J.Maier: Journal of Physics and Chemistry of Solids, 2002, 63[3], 449-56