Computation of Static Effective Permittivity for a Multiphase Lattice of Cylinders

Abstract

A methodology is described to calculate the static effective permittivity for a two-dimensional multiphase lattice composed of dielectric and/or conducting circular cylinders. This methodology uses an accurate T-matrix method to determine the dipole moments of the cylinders immersed in a uniform electric field, and then computes the effective permittivity by relating the lattice to a macroscopic model. With this methodology, the multiple scattering solution for the infinite lattice is presented in a succinct matrix-vector notation and is valid for any lattice type. The static effective permittivity equation described in this work allows us to account for the effect of all mutual interactions between the cylinders. This methodology is used to calculate the static effective permittivity for a two-phase lattice of metallic inclusions. These results are compared with the Maxwell Garnett formula and another formula presented by Kharadly and Jackson. Three additional examples are presented including two-phase dielectric lattices, multiphase lattices, and clusters. The static effective permittivity in all three situations deviates from the Maxwell Garnett result at high-volume fractions, as expected. This deviation is the most obvious for the cluster lattice because of the significant mutual coupling between the cylinders, even at relatively low-volume fraction.