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There has been much recent interest in how morphological descriptors may affect the electromagnetic wave transport in particulate composite mediums. In this work, we present results of finite-element simulations that model the permittivity of two-dimensional (or cross sections of infinite three-dimensional parallel, infinitely long, identical, circular cylinders, where the properties and characteristics are invariant along the perpendicular cross-sectional plane) three-phase heterostructures made of a multilayered discoidal particle. While strictly valid only in a direct current situation, our analysis can be extended to treat electric fields that oscillate with time provided that the wavelengths and attenuation lengths associated with the fields are much larger than the microstructure dimension in order that the homogeneous (effective medium) representation of the composite structure makes sense. From simulations over a range of parameters, our analysis evaluates the effect of the surface fraction of inclusion, the conductivity, and thickness (relative to the particle radius) of the particle conductive coating on the effective complex permittivity of isotropic heterostructures in which the filler particles have a core-shell structure. Four main effects are found. First, the importance of the surface fraction of inclusion on the effective complex permittivity at high frequencies (from microwave to infrared) is illustrated over a broad range of coating thicknesses and conductivities. Second, the encapsulation phase (metallic coating) conductivity is identified as the key property controlling the dielectric relaxation due to interfacial polarization. Third, a simple parametrization of the high-frequency effective permittivity spectrum allowed us to obtain a reliable modelization of the Debye-type relaxation processes. From the least-squares fit of the effective complex permittivity data, we extract information on these relaxation processes, i.e., relaxation frequencie- s, relaxation strengths, and the limiting high-frequency permittivity. A salient point is that for core-shell structures there is a transition between a single peak and a two-peak relaxation spectrum which is under the dependence of the coating thickness. Fourth, we show how the features of permittivity spectra depend on the local dielectric environment (matrix and inclusion core) and shell conductivity. These results may have experimental consequences in the recent experiments on the dielectric relaxation in nanocoated particles.