A recasting of the effective parameters of composite mixtures into the language of artificial dielectrics

Abstract

Effective medium theories (EMTs) along with percolation theory allow the characterization of the electromagnetic properties of binary composite mixtures at a frequency when the scale of a particle size allows the quasi-static limit approximation. These theories formulate an effective permittivity and permeability ( ε^ eff and μ^ eff) to predict the expected electromagnetic response of binary composite mixtures of a scale size L much larger than the average homogeneous size ξ within the mixture (the correlation length of percolation theory). It can be shown that any physically realizable material's permittivity (i.e. a complex permittivity which is causal and analytic in the upper-half complex frequency plane) can be represented as a sum of series LRC circuits. From the effective permittivity described by EMTs (away from the percolation threshold) or percolation theory (near the percolation threshold), the corresponding distributed circuit models are formulated to recast the expected composite material electric response into a more familiar form. This corresponding circuit model describes the dominant contributions to the composites material response at any frequency in terms of the individual LRC circuit elements of the permittivity dispersion's model. We are demonstrating an equivalent deterministic representation (which can be recast as a distribution of particle sizes and shapes within an ordered medium) in the LRC circuit model for the effective permittivity of composites. Future considerations will include extending this permittivity model to an analogous model of the permeability dispersion. Also, incorporating within the model a description of composite mixtures at higher frequencies (for the non-quasistatic case) when effects like the skin effect in high conducting particles must be accounted for.