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 having the shape of 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 obtained formulas for the effective dielectric constant of the composite correspond to a superposition of two Debye processes with different relaxation times. The dielectric constant has a strong nonlinear dependence on the ratio of the semi-axes of the ellipsoids of revolution. This feature allows one to obtain good agreement with experimental data, suggesting the possibility of aggregation of nanoparticles even at low concentrations.It follows from the model that in the absence of an increase in the aggregation of conducting nanoparticles with an increase in concentration, a linear dependence of the dielectric constant of the composite on the impurity concentration takes place. For a composite with growing aggregation of nanoparticles, this dependence exhibits nonlinear growth.