No abstract

The electrical and electromagnetic interference shielding effectiveness (EMI SE) properties of composites with a polycarbonate matrix and varying amounts of three different types of carbon fillers (carbon black, carbon nanotubes, and graphene nanoplatelets) are analyzed experimentally and theoretically over the 8.5–12 GHz frequency range. A finite element model is also used to study the EMI shielding mechanisms. The theoretical study predicts that the carbon fillers' concentration, sample thickness, incident angle, polarization type, and frequency are the main parameters that have effect on shielding effectiveness of a sample that is confirmed by the experimental and simulation results. Permittivity and related alternating current (AC) conductivity measurements in the above mentioned frequency range are presented for these three types of composites, providing an appropriate way to design a shield. Experimental, theoretical and simulation results indicate that both permittivity and conductivity have significant effects on the SE. It is found that the electrical conductivity, which itself needs a percolating (connected) path, is not the only criterion for shielding and that the connectivity of fillers (and, hence, higher conductivity) does not necessarily lead to a higher SE.

Using a mixture of different types of fillers has been experimentally shown to improve the electrical conductivity of polymer nanocomposites beyond the weighted average due to synergistic effects. In this study, we develop a critical path analysis-based tunneling-percolation model for multicomponent systems of nanocomposites with ellipsoidal fillers. The nature of the interaction between different filler components is controlled by a key modeling parameter capturing the tunneling interactions between fillers. This generalization allows us to examine scenarios where the nature of a given type of filler can be varied continuously from an insulating-type to a conductive-type. The percolation behavior of two-component systems with a combination of prolate, oblate, and spherical fillers is investigated using Monte Carlo simulations for different relative volume fractions and nature of interactions while keeping the total volume fraction fixed. The simulation results are shown to be in semi-quantitative agreement with predictions made by the second-virial-approximation-based theories. Our results suggest that for multicomponent systems with well-dispersed fillers, the synergistic effects are linked directly with the nature of interactions between different filler types. Moreover, addition of prolate fillers to oblate or spherical fillers should generally improve the electrical conductivity of multicomponent nanocomposites.

Scale dependence of electrostatic and magnetostatic properties is investigated in the setting of spatially random linear lossless materials with statistically homogeneous and spatially ergodic random microstructures. First, from the Hill-Mandel homogenization conditions adapted to electric and magnetic fields, uniform boundary conditions are formulated for a statistical volume element (SVE). From these conditions, there follow upper and lower mesoscale bounds on the macroscale (effective) electrical permittivity and magnetic permeability. Using computational electromagnetism methods, these bounds are obtained through numerical simulations for composites of two types: (i) 2D random checkerboard (two-phase) microstructures and (ii) analogous 3D random (three-phase) media. The simulation results demonstrate a scale-dependent trend of these bounds towards the properties of a representative volume element (RVE). This transition from SVE to RVE is described using a scaling function dependent on the mesoscale δ, the volume fraction v f , and the property contrast k between two phases. The scaling function is calibrated through fitting the data obtained from extensive simulations (∼10,000) conducted over the aforementioned parameter space. The RVE size of a given microstructure can be estimated down to within any desired accuracy using this scaling function as parametrized by the contrast and the volume fraction of two phases.

No abstract