Mixing Rules

Abstract

This chapter provides a theoretical background for the prediction of macroscopic dielectric properties of materials. Dielectric mixing rules are algebraic formulas with which the effective permittivity of the mixture can be calculated as a function of the constituent permittivities, their fractional volumes, and possibly some other parameters characterizing the microstructure of the mixture. The mixture can be discrete, which means that homogeneous inclusions are embedded in another homogeneous medium; otherwise the permittivity function can be continuous. The concept of effective, or macroscopic, permittivity implies that the mixture responds to electromagnetic excitation as if it were homogeneous. It may, however, be proper to remember that the dielectric constant of a material is seldom constant with respect to temperature, frequency, or any material property. However, in the domain of negative-permittivity inclusions, the plasmonic resonances cause particular complications in estimating the effective permittivity.