Effective dielectric properties of composite materials in the surface layer

Abstract

In the framework of the mean-field picture, an expression for the effective dielectric permittivity of an inhomogeneous medium near a flat interface with another dielectric is derived as a function of the distance from the boundary. The obtained formula should be considered as a counterpart of the standard Maxwell-Garnett one, but in the vicinity of a flat boundary. Possibilities of a more precise derivation using already established methods for bulk systems are briefly discussed as well.

Ultrathin optical switch based on a liquid crystal/silver nanoparticles mixture as a tunable indefinite medium

“…However, for nanoparticles close to the sample interface the above polarizability evaluation is wrong since it does not take into account the additional field existing within the nanoparticle which is due to surface polarization charges (i.e. to the discontinuity of the electromagnetic material properties at the interface) [31]. Since the corrections to the permittivity scales as (r/z) 3 (z being the distance from the interface) the nanoparticles responsible for the edge effect are those whose distance from the interface is smaller than 40 or 50 nm (four or five times its radius r = 10 nm), so that we conclude that roughly a fourth of the considered slab volume can not be described through the Maxwell Garnett approach.…”

Dielectric function of a colloidal solution near an interface with pure solvent

“…In the ⑀ m ⑀ m Ј case, ␣ J ͑1͒ is the first nontrivial z-dependent term and is caused by the interaction between the particle and its electrostatic image. 18 However, for the situation addressed here, where a solution is in equilibrium with a pure solvent, ⑀ m ϵ ⑀ m Ј , and therefore no electrostatic images are present. Let us consider spherical particles with continuously distributed radii (i , j =1, ... ,N are used further on to number the particles).…”

“…In theoretical works the interaction between inclusions and their images has been claimed to be responsible for the spatial dependence of ⑀ J. In the simplest approximation, spherical particles interacting with their own interface images were considered, 6,18 leading to the expression…”

“…As has been shown in Ref. 18, the components of ⑀ J can be determined via the polarizability tensor A J ͑z͒ (A J is defined 20 as the proportionality coefficient between the dielectric polarization vector P ជ and the external field E ជ 0 :…”

“…6 from Ref. 18. In turn, the polarizability tensor A J of the colloidal system is related 21 to the set of irreducible polarizabilities ␣ ជ ͑k͒ of groups of k particles…”