Effective Electrodynamic Parameters of Nano-Composite Media and the Theory of Homogenisation

Abstract

When creating new lighting and optoelectronic devices, great attention in recent years is paid to use nano-composite materials, i.e. the media containing impregnations of nanometre size, such as nano-particles of metals, quantum points, carbon nanotubes, graphenes, etc. This allows obtaining media with new, formerly unattainable characteristics. An initial point when describing properties of such medias is usually evaluation of their effective parameters (dielectric permeability, conductivity, heat conduction and of other similar transport coefficients) in the model of macroscopically heterogeneous media, in other words, media containing macroscopic impregnations with known or determined from experiments characteristics. Main approaches used in such cases are known Maxwell Garnett and Bruggeman approximations. In this review, methodical questions connected with various approaches to obtain these approximations and of their generalisations are discussed. Also some new results are given, which connected with evaluations of percolation thresholds within generalised Bruggeman approximations in the event of multi-component media.