Homogenization of time-dependent dielectric composites containing space charges, with applications to polymer nanoparticulate composites

This paper presents the derivation of the homogenized equations for the macroscopic response of time-dependent dielectric composites that contain space charges varying spatially at the length scale of the microstructure and that are subjected to alternating electric fields. The focus is on dielectrics with periodic microstructures and two fairly general classes of space charges: passive (or fixed) and active (or locally mobile). With help of a standard change of variables, in spite of the presence of space charges, the derivation amounts to transcribing a previous two-scale-expansion result introduced in Lefèvre and Lopez-Pamies (2017a) for perfect dielectrics to the realm of complex frequency-dependent dielectrics. With the objectives of illustrating their use and of showcasing their ability to describe and explain the macroscopic response of emerging materials featuring extreme dielectric behaviors, the derived homogenization results are deployed to examine dielectric spectroscopy experiments on various polymer nanoparticulate composites. It is found that so long as space charges are accounted for, the proposed theoretical results are able to describe and explain all the experimental results. By the same token, more generally, these representative comparisons with experiments point to the manipulation of space charges at small length scales as a promising strategy for the design of materials with exceptional macroscopic properties.