  In conductor-insulator composites in which the conducting particles are
dispersed in an insulating continuous matrix the electrical connectedness is
established by interparticle quantum tunneling. A recent formulation of the
transport problem in this kind of composites treats each conducting particle as
electrically connected to all others via tunneling conductances to form a
global tunneling network. Here, we extend this approach to nonhomogeneous
composites with a segregated distribution of the conducting phase. We consider
a model of segregation in which large random insulating spherical inclusions
forbid small conducting particles to occupy homogeneously the volume of the
composite, and allow tunneling between all pairs of the conducting objects. By
solving numerically the corresponding tunneling resistor network, we show that
the composite conductivity is enhanced by segregation and that it may remain
relatively large also for very small values of the conducting filler
concentration. We interpret this behavior by a segregation-induced reduction of
the interparticle distances, which is confirmed by a critical path
approximation applied to the segregated network. Furthermore, we identify an
approximate but accurate scaling relation permitting to express the
conductivity of a segregated systems in terms of the interparticle distances of
a corresponding homogeneous system, and which provides an explicit formula for
the conductivity which we apply to experimental data on segregated RuO2-cermet
composites.
