Applying complex network theory to the understanding of high-aspect-ratio carbon-filled composites

This work demonstrates that the theoretical framework of complex networks typically used to study systems such as social networks or the World Wide Web can be also applied to material science, allowing deeper understanding of fundamental physical relationships. In particular, through the application of the network theory to carbon nanotubes or vapour-grown carbon nanofiber composites, by mapping fillers to vertices and edges to the gap between fillers, the percolation threshold has been predicted and a formula that relates the composite conductance to the network disorder has been obtained. The theoretical arguments are validated by experimental results from the literature.

Effect of cylindrical filler aggregation on the electrical conductivity of composites

This work reports on the effect of carbon nanotube aggregation on the electrical conductivity and other network properties of polymer/carbon nanotube composites by modeling the carbon nanotubes as hard-core cylinders. It is shown that the conductivity decreases for increasing filler aggregation, and that this effect is more significant for higher cylinder volume fractions. It is also demonstrated, for volume fractions at which the giant component is present, that increasing the fraction of cylinders within clusters leads to a break of the giant component and the formation of a set of finite clusters. The decrease of the giant component with the increase of the fraction of cylinders within the cluster can be related to a decrease of the spanning probability due to a decrease of the number of cylinders between the clusters. Finally, it is demonstrated that the effect of aggregation can be understood by employing the network theory.