Study on the semi-empirical model for the complex permittivity of carbon nanocomposite laminates in microwave frequency band

A semi-empirical model is proposed for the complex permittivity of composites containing electrical conductive carbon nanomaterials such as carbon black (CB), carbon nanofiber (CNF) and multi-walled carbon nanotube (CNT). The composites were fabricated with E-glass fabric/epoxy prepregs. The model is based on the percolation theory. The model is available for the composite of filler content over the percolation threshold and applicable within the high frequency band in which AC electrical conductivity of the composite is continuously proportional to the frequency. The proposed model is composed of the numerical equations of the scaling law in percolation theory and constants obtained from experiments to quantify the model. The model describes the complex permittivity as a function of frequency and filler content. The model was verified when compared with the measurements. The measurements for the complex permittivities of the composites were performed at the frequency band between 0.5 and 18.0 GHz using a vector network analyzer with a 7 mm coaxial air line.