Computation of static effective permittivity for a multiphase lattice of cylinders

A methodology is described to calculate the static effective permittivity f or a two-dimensional multiphase lattice composed of dielectric and/or condu cting circular cylinders. This methodology uses an accurate T-matrix method to determine the dipole moments of the cylinders immersed in a uniform ele ctric field, and then computes the effective permittivity by relating the l attice to a macroscopic model. Wit this methodology, the multiple scatterin g solution for the infinite lattice is presented in a succinct matrix-vecto r notation and is valid for any lattice type. The static effective permitti vity 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 met allic inclusions. These results are compared with the Maxwell Garnett formu la 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 situa tions deviates from the Maxwell Garnett result at high-volume fractions, as expected. This deviation is the most obvious for the cluster lattice becau se of the significant mutual coupling between the cylinders, even at relati vely low-volume fraction.