Conductivity of structurally anisotropic 2D composites

The character of electric conduction in a two-dimensional structurally anisotropic composite containing elliptic inclusions with a large ratio of the semiaxis. Dielectric and ideally conducting inclusions were considered. It was demonstrated that the approximation linear in concentration of inclusions fails beginning from rather small concentrations. The region of intermediate concentrations was studied using approximate methods based on the analogy between electric conductivity and the diffusion of a single particle in a nonuniform medium. The conductivity of the model system under study was analyzed over a wide concentration range with the use of the effective medium theory; the results are in close agreement with those obtained by qualitative methods. The behavior of conductivity near the percolation threshold (metal-to-dielectric phase transition) was examined using the similarity. The conductivity of thin composite films with inclusions in the form of carbon nanotubes was examined, as an example.