  The permeability of certain polymer membranes with impenetrable
nanoinclusions increases with the particle volume fraction (Merkel et al.,
Science, 296, 2002). This intriguing observation contradicts even qualitative
expectations based on Maxwell's classical theory of conduction/diffusion in
composites with homogeneous phases. This letter presents a simple theoretical
interpretation based on classical models of diffusion and polymer physics. An
essential feature of the theory is a polymer-segment depletion layer at the
inclusion-polymer interface. The accompanying increase in free volume leads to
a significant increase in the local penetrant diffusivity, which, in turn,
increases the bulk permeability while exhibiting reverse selectivity. This
model captures the observed dependence of the bulk permeability on the
inclusion size and volume fraction, providing a straightforward connection
between membrane microstructure and performance.
