A discussion on the effective permittivity of multi-component medium derived by Maxwell–Garnett, strong fluctuation and quasicrystalline-CP modeling

Abstract

To evaluate the average dielectric property, the effective permittivity (EP) of multi-component media in low frequency region is the first issue. The most classical formula is the Maxwell–Garnett (MG) model. However, it needs guidelines to restrict the applicability of MG model. Later on, the strong fluctuation theory (SF model) and QCA-CP model (quasi-crystalline approximation with coherent potential) have been studied. Similarities and difference between these models need to be clarified. In this paper, all these models are derived in a consistent way. Numerical examples show the difference between the EPs of these models. It is found that when the dielectric perturbation is not large (dielectric particle is not quite different from background) and especially, the fractional volume of inclusions is not large (e.g. less than 0.15), all these models are good enough to evaluate EP. But, if these pre-conditions are not well met, the MG model becomes unsuitable. Thus the SF and QCA-CP models are better than MG in either cases of strongly or weakly fluctuating cases. If the discrete spherical particles are well defined, e.g. size, complex dielectric constant, the QCA-CP would be a rigorous model for the calculation of EP and extinction coefficient.