Self-consistency conditions for the effective-medium approximation in composite materials

Abstract

Two different self-consistency conditions are used in the literature to derive the effective-mediumapproximation equations. They are (a) that the net polarization of the medium should be zero, and (b) that the effective electric field should be the same as the average of the electric field in every grain.These two approaches lead to different predictions, as we show, for conducting spheroidal particles in an insulating background. It is found that the self-consistency condition of the zero net polarization field should be used to explain the transport properties of randomly inhomogeneous media.

Optical response of single‐wall carbon nanotube sheets in the far‐infrared spectral range from 1 THz to 40 THz

“…Consequently, it contains contributions from all NT sorts, orientations, and the interspaces. Applying effective-medium theory [19], one obtains the simple relationship eff F ε ε ≈ [20] where ( ) ε ω is the dielectric function of the NTs parallel to the tube axis averaged over all NT types and orientations. = THz.…”

Mechanism of the Far-Infrared Absorption of Carbon-Nanotube Films

“…2(a) and 2(b) is the conductivity of an effective and homogeneous medium since our NT film is uniform on the $10 m scale of the probe wavelength. More explicitly, effective-medium theory in Maxwell-Garnett approximation yields [22] "…”

Effective medium approximation for optical bistability in nonlinear metal-dielectric composites

“…For realistic composites, the individual grains are not perfectly aligned and ever randomly oriented. In this connection, we should adopt effective medium approximation based on whether a self-consistent condition on the net polarization is invoked [23].…”