Determination of dielectric performance and surface heteromorphology in single-walled carbon nanotube/vinylester polymer composites by fractal approaches

Abstract This study aims to establish a relationship between the dielectric characteristics and fractal parameters of single walled carbon nanotube reinforced vinylester based nanocomposites manufactured by sheet molding compound process. The complex dielectric permittivity was analyzed and interpreted using electric modulus formalism. The topography of both unfilled and single-walled carbon nanotube reinforced nanocomposites has been investigated using scanning electron microscopy (SEM) to provide correlation between experimental dielectric data and fractal theory. The self-similar microstructure was observed in micro photos for both materials. The superficial particle and cluster coverage ratio were calculated with the application of the scaling theory. Additionally, critical exponent and the fractal dimensions that determine the environment-area relationship have been determined by Slit Island Method (SIM) which is used to process 2-dimensional digital microscopic images. Fractal dimensions estimated with SIM were compared with the fractal dimensions computed obtained by box counting method for reliable results. It has been revealed that the surface of the composite consists of amorphous clusters with different sizes independent of each other and the structure is self-affine. In addition, the superficial area and cluster size have been shown to have a significant effect on the fractal dimension. As a result, the relationship between the dielectric permittivity of the material, determined by the electrical module formalism, and the morphological surface formation defined by the fractal analysis method and the SIM method, were determined and the results were compared with similar studies in the literature in this article.