Comparison of dielectric properties determined from a computational approach and experiment for anisotropic and periodic heterostructures

The physics of heterostructures is among the forefront problems in materials science. Composite materials also are attractive from the point of view of technological applications such as current-limiting thermistors, radar absorbers, and electromagnetic shields, because they exhibit a variety of interesting mechanical, electric and magnetic properties with the advantage of much reduced cost and weight. To quantify the dielectric response of anisotropic and periodic heterostructures, consisting of two-component composites arranged in a regular simple cubic lattice, in the quasistatic approximation we use an exact numerical technique which is based on a boundary integral equations solution of the Laplace equation which is solved by using the field calculation package PHI3D. 'Exact' means that the correct properties are computed for the given microstructure and choice of individual component properties because all internal electric multipole interactions contributing to the polarization of the material medium are taken into account. The main goal of this work was to confront these numerical calculations with experimental data. Measurements of the effective complex permittivity were carried out in samples composed of identical aligned inclusions, in the form of circular cylinders, embedded in a polymer matrix and filled either by de-ionized water or air. We test our numerical data for two specific examples, i.e. the parallel and perpendicular orientation of the electric field vector with respect to the principal axis of the circular cylinders. Of particular importance is that our numerical simulation captures reasonably well the observed trend in the experimental data over a wide range of volume fraction of inclusions. The experimental results roughly indicate a significant decrease in the permittivity in the x-y plane over that of the z axis, for inclusions containing de-ionized water, while no anisotropy effect is found for inclusions With air. However, there are quantitative differences between the experiment and calculations. These differences were tentatively ascribed to limitations in the experimental model, i.e. finite size, and air bubbles due to ill-controlled filling of the cylindrical inclusions.