  The effective transport properties of heterogeneous nanoscale materials and
structures are affected by several geometrical and physical factors. Among them
the presence of imperfect interfaces plays a central role being often at the
origin of the scale effects. To describe real contacts between different phases
some classical schemes have been introduced in literature, namely the low and
the high conducting interface models. Here, we introduce a generalized
formalism, which is able to take into account the properties of both previous
schemes and, at the same time, it implements more complex behaviors, already
observed in recent investigations. We apply our models to the calculation of
the effective conductivity in a paradigmatic structure composed of a dispersion
of particles. In particular we describe the conductivity dependence upon the
size of the inclusions finding an unusual non-monotone scale effect with a
pronounced peak at a given particle size. We introduce some intrinsic length
scales governing the universal scaling laws.
