Helical Wrapping of Carbon Nanotubes by Wormlike Chain Polymers

The helical wrapping of single walled carbon nanotubes (SWNTs) by long polymers is an interesting process, owing to the ability of some polymers to effectively solvate and separate individual nanotubes in solution without affecting their useful underlying electronic properties. Yet polymer behaviour at the nanotube surface remains poorly understood from a theoretical perspective. Although Monte-Carlo and molecular dynamics simulations have been carried out for individual polymer-nanotube combinations, and some approximate analysis has been done, there has not been a full theoretical study completed using a fundamental model over a large range of nanotube and polymer types. Here, we present an analysis of polymer statistics at the surface of the polymer-SWNT system using the standard wormlike chain (WLC) model. We calculate the expected helix pitch for a polymer wrapped SWNT over the full parameter space and compare to pitch measurements from 10 different studies in the literature. Good agreement is seen between our solution and the data over the full parameter range. Associated distribution functions are discussed. We conclude by calculating the exact scaling behaviour for small nanotubes, which we find agrees with expected behaviour for a tightly confined WLC system.