Effective conductivity in two-dimensional two-component structures: macroscopic isotropy

Abstract

In this paper we use the mathematical methods of the homogenization theory to model the electrical conductivity of a two component nanostructure. We consider here a nanocomposite material in the form of a thin plate of negligible thickness compared to the diameter. Hence we assume that our problem is two-dimensional. As an example of such material we choose a carbon-palladium nanocomposite. We use the homogenization theory to study our problem, because of a complex microgeometry of the nanostructures. We show that the effective coefficient, under some assumptions, may be equal to a geometric mean of the coefficients of both components.