Modelling the relative permittivity of anisotropic insulating composites

Three models have been developed for predicting the dielectric permittivity of insulating composites with inclusions of different lengths (from nm and larger) and different shapes. Firstly, for approximately periodic materials, a finite element model based on a smallest repeating box method was used in order to mimic frameworks with fibres, crystals, clay platelets, foams and lamellar layers. The introduction of parameters for relative aspect ratio, overlap, rotation and packing density made the model very flexible while maintaining its simplicity. Secondly, a finite element composite model with oriented, randomly positioned particles of different shapes was constructed. Thirdly, an analytical relationship to approximate the effective permittivity of two- or three-phase insulators with brick-shaped inclusions was derived. For a wide range of volume fractions, permittivity ratios and packing conditions, this model gave solutions very close to corresponding finite element simulation data for lamellae, much closer than all the other analytical relationships found in the literature. Results obtained by simulation were in agreement with experimental data from the literature for composites of micrometre-sized hollow glass spheres in epoxy and nanocomposites of mica platelets in polyimide, provided that a third (interfacial) component was introduced.