Applications of the graph theory to the prediction of electrical and dielectric properties of nano-filled polymers

Abstract

The addition of carbon nanofibers to a polymeric matrix is known to affect its mechanical and electrical properties, although the mechanisms responsible for the changes are not sufficiently understood. Particularly, there are currently no adequate predictive methods that allow the creation of knowledge-based structures tailored for specific electrical response. We have developed a method for predicting the electric and dielectric properties of nanofiber-reinforced polymer matrices based on the application of the graph theory and circuit laws. We consider the individual properties of the polymeric matrix and the complex nanofiber network (including fiber orientation, concentration, and size), under an applied external electric field, and from the analysis we obtain information such as perlocative pathways, breakdown voltage, and impedance of the overall system. Simulations for two-phase systems consisting of a dielectric matrix and randomly oriented nanofibers have shown that the concentration and the length of the fibers affect the properties. Increased concentrations or longer fibers both result in networks for which it is easier to establish conducting paths through breakdown mechanisms.