Effective conductivity of two-phase materials consisting of long parallel cylinders

The effective conductivity σe of a dispersion of long, parallel cylinders (or two-dimensional systems), distributed in a second continuous matrix phase, is determined as a function of its microscopic structure. We obtained an expression for the effective conductivity of two-dimensional systems (based on an approximate scheme) that includes the one-body and two-body terms in the cluster expansion for σe. The effective conductivities of two-dimensional hard disks and square-well particles are computed. It is found that this expression yields excellent estimates for the effective conductivity over a wide range of cylinder volume fractions, and for cases in which the cylinder to matrix phase conductivity ratios are high.