Fractal Approach to Alternating Current Impedance Spectroscopy Studies of Carbon Nanotubes/Epoxy Polymer Composites

Since the documented discovery of carbon nanotubes (CNT), many researchers have sought to manufacture advanced composite CNT materials that exhibit one or more of their unique physical (mechanical, thermal, and electrical) properties (Ali & Mousa, 2016; Han & Fina, 2011; Sahoo et al., 2010). Polymer based composites have been considered the most suitable for further reinforcement with CNT (Cooper et al., 2002). Progress in reinforcing polymers with CNT has recently been reported for rubbery epoxy matrices (CNT/ epoxy) (Allaoui et al., 2002; Lau et al., 2002). Epoxy resins have excellent heat resistance, high strength, good stiffness, chemical resistance; therefore, they are applied in the field of coatings, casting, composites, laminates and encapsulation of semiconductor devices (El-Tantawy & Deghaidy, 2000; Kang et al., 2001; Park et al., 2000). The fractal geometry is a mathematical concept that describes objects of irregular shape. It has been used to analyze different objects in various scientific and technological branches since their description by Mandelbrot (Mandelbrot et al., 1984). Application of the fractal concept for the prediction of the physical properties of composites has demonstrated that the fractal dimension is related to the dielectric relaxation process (Hopkins et al., 2011; Lira-Olivares et al., 2000). The correlation of the insulator-conductor transition of composite materials with the fractal dimension of the aggregates has been studied in some works (Boukheir et al., 2016; Salome & Carmona, 1991). Fractal dimension of a certain surface can, in principle, be inferred from different ways. These include, but are not limited to: surface image analysis, small angle neutron scattering (SANS) and impedance spectroscopy (IS). The latter two methods are especially widespread and used in different areas of research (Hattenhauer et al., 2015; Tagmouti et al., 2015; Tapasztó et al., 2014). The aggregated fillers in IS have constant phase element (CPE) behavior, i.e. they show