Backbone of conductivity in two-dimensional metal-insulator composites

Abstract

In percolation theory, the backbone is defined by chopping off dangling ends from the percolating cluster. For structures with high degree of spatial correlation, as they are typical for porous thin films, trimming of the full structure to reveal the part determining the electrical conductivity is more subtle than the classic definition of the backbone. To expand the applicability of the concept, we present a purely geometric definition for the backbone of a two-dimensional percolating cluster. It is based on a sequence of image analysis operations defining the backbone in terms of an image filter. The change of both area fraction and effective conductivity induced by applying the backbone filter to various binary images and a two-parameter family of sets is assessed by numerical means. It is found that the backbone filter simplifies the geometry of complex microstructures significantly and at the same time preserves their electrical DC behavior. We conclude that the backbone will be useful as a first ingredient for a geometric estimator of the effective conductivity of metal-insulator composites.