Polymer nanocomposites (PNC) have been shown to exhibit extraordinary properties that are counter intuitive. A prime example would be with PNC barrier properties: it has been shown that upon addition of spherical nanofillers to a polymer matrix the membrane's permeability (and diffusivity) is increased. One hypothesis that has been made suggests that the interfacial matrix layer around the nanoparticle has properties that vary significantly from the bulk properties, and that the volume fraction of these layers is high enough to allow its properties to manifest at the macroscopic level. We have developed a multiscale approach that allows us to quantify the influence of the interfacial properties on the macroscopic barrier properties. We present results which illustrate the effects of particle size, interfacial layer thickness, and polymer stiffness on a penetrant's diffusivity.