Fractal characterization of polyester based standard and single walled carbon nanotube modified composites

Abstract

Abstract The electrical properties of composite materials over a wide frequency range are of great interest, not only for experimental applications, but also for theoretical studies such as fractal analysis. This study presents comparative analysis of alternating current (ac) conductivity and fractal structure characteristics in standard and single walled carbon nanotube (SWCNT) reinforced polymer composites based unsaturated polyester resin (UPR). The electrical characteristics of polymer matrices at 320 K have been analyzed as a function of frequency by impedance analysis method. It was found that the conductivity of the nanotube doped material in the dc conductivity region, which is the low frequency region, is independent of the frequency and takes a constant value. It was proved that conductivity obeys Jonscher’s power law toward the high frequency region. The standard sample showed an insulating behavior that exhibits continuous increase with increasing frequency. The images of the samples were obtained by scanning electron microscope (SEM) to reveal the relationship between the conductivity of the materials and their fractal properties. All samples were converted to binary format for calculations. Cellular particle density for each sample was determined according to scaling theory. Then, the surface coverage ratio, fractal dimensions, cluster densities, average cluster sizes and critical interface exponent values of the samples were calculated and compared with different samples in the literature. It was determined that the coverage ratio and fractal dimension increased when carbon nanotubes were added. In addition, it was observed that the interface critical exponent decreased when the carbon nanotube was doped.