Continuum percolation of carbon nanotubes in polymeric and colloidal media.

We apply continuum connectedness percolation theory to realistic carbon nanotube systems and predict how bending flexibility, length polydispersity, and attractive interactions between them influence the percolation threshold, demonstrating that it can be used as a predictive tool for designing nanotube-based composite materials. We argue that the host matrix in which the nanotubes are dispersed controls this threshold through the interactions it induces between them during processing and through the degree of connectedness that must be set by the tunneling distance of electrons, at least in the context of conductivity percolation. This provides routes to manipulate the percolation threshold and the level of conductivity in the final product. We find that the percolation threshold of carbon nanotubes is very sensitive to the degree of connectedness, to the presence of small quantities of longer rods, and to very weak attractive interactions between them. Bending flexibility or tortuosity, on the other hand, has only a fairly weak impact on the percolation threshold.