Electrodynamic calculation of the complex effective permeability of nanocomposites based on the arrays of carbon nanotubes in the microwave frequency range

Background. The nanostructured materials, based on carbon nanotubes (CNTs), have attracted a special interest due applications thereof in the fields of microwave absorption and shielding. The goal of the present work is the theoretical research of interaction of electromagnetic waves with arrays of CNTs and the calculation of the effective permeability for the anisotropic CNT nanocomposites in the microwave frequency range using mathematical modeling at the electrodynamic level of rigor. Materials and methods. Using the numerical method of autonomous blocks with Floquet channels (FABs) the authors carried out mathematical modeling of propagation of electromagnetic waves in the 3D- periodic arrays of CNTs at microwaves. The computational algorithm for determining the conductivity matrix of FAB in the form of a rectangular parallelepipeds, containing CNT, was developed to solve 3D-diffraction boundary problem using the Galerkin's projection method. The methodology of calculation of the effective permeability of nanocomposites based on the arrays of CNTs was developed based on the effective medium theory. Results. The authors obtained the results of electrodynamic calculation of the frequency dependencies of the complex effective permeability for the CNT nanocomposites, at different orientation of the rf electric field of the wave with respect to CNT axis depending on the CNT filling factor of materials at microwave frequencies of 2-5 GHz. Conclusions. It is shown that the dielectric losses and the absorption in arrays of CNTs increase due to the conductivity of CNTs, the CNT filling factor of materials, change depending on the orientation of the rf electric field of wave with respect to CNT axis and increase with parallel orientation in comparison with the orthogonal one.