The Effective Dielectric Constant of a Composite with Conductive Nanoparticles
A model of a composite consisting of a dielectric base with a small admixture of semiconductor nanoparticles shaped as identical ellipsoids of revolution is considered. A uniform spatial distribution of the impurity and a uniform distribution of the directivity of the axes of revolution are assumed.
It is shown that the formulas obtained for the effective dielectric constant of the composite correspond to a superposition of two Debye processes with different relaxation times. The dielectric constant strongly nonlinearly depends on the ratio of semi-axes of the ellipsoids of revolution. This feature allows one to obtain good agreement with experimental data under the assumption that the aggregation of nanoparticles is possible even at low concentrations.
The model implies that, in the absence of an increase in the aggregation of conducting nanoparticles with an increase in the concentration, the dielectric constant of the composite linearly depends on the impurity concentration. For a composite with growing aggregation of nanoparticles, this dependence exhibits a nonlinear growth.