Transport properties of nonhomogeneous segregated composites

TL;DR

This paper investigates how segregation in conductor-insulator composites enhances electrical conductivity by reducing interparticle distances, extending tunneling network models to nonhomogeneous systems, and providing a scaling relation applicable to experimental data.

Contribution

It extends the tunneling network model to segregated composites, deriving a scaling relation for conductivity based on interparticle distances.

Findings

Segregation enhances composite conductivity even at low filler concentrations.

A scaling relation links segregated and homogeneous system conductivities.

The model accurately fits experimental data on RuO2-cermet composites.

Abstract

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.