Electrical Conductivity of a Two-Dimensional Model for a Structurally Anisotropic Composite

摘要

The electrical conductivity of a two-dimensional structurally anisotropic model for a composite is considered. The model represents an isotropic matrix with a system of nonconducting inclusions in the form of infinitely thin straight line segments (scratches). The scratches make an angle theta or -theta with a preferred axis (for definiteness, axis y) at the same probability, and their centers are chaotically distributed. An approximate effective medium method is used to obtain a general expression for the effective conductivity tensor (sigma) over cap (e) of this model that is valid over a wide concentration range. In this approximation, both components of tensor (sigma) over cap (e) are shown to vanish at the same percolation threshold, which is expressed explicitly. The conductivity of the model in a critical region is considered in terms of the similarity hypothesis.