On extended homogenization formalisms for nanocomposites

In a long wavelength regime, the effective properties of particulate composites, including nanocomposites, may be estimated using one of various homogenization formalisms, such as the Bruggeman and Maxwell Garnett formalisms, and the approach of the strong--property--fluctuation theory (SPFT). In the conventional implementations of these formalisms, the constituent particles are treated as point--like scattering centres. However, extended formalisms have been established--which involve integral formulations--that take account of the spatial extent of the constituent particles. In particular, the extended second--order SPFT takes account of both the size of the constituent particles and their statistical distributions. We derive explicit representations of the extended second--order SPFT appropriate to isotropic chiral and uniaxial dielectric homogenized composite mediums. These results may also be employed in extended versions of the Bruggeman and Maxwell Garnett formalisms.