Carbon nanotube knots

The structural and mechanical properties of carbon nanotube knots are investigated using molecular dynamics simulations. Using parametric representations of mathematical (harmonic) knots, a method is provided for calculating the initial atomic coordinates of carbon nanotubes in the shape of arbitrary knots for use in molecular dynamics simulations. A computational stress-strain testing scheme is implemented and applied to (5, 5) knotted carbon nanotubes to determine their tensile strength, plastic limit, and relative knot strength. Stress-strain curves are given for (5, 5) carbon nanotube stopper knots. It is determined that a carbon nanotube’s tensile strength is reduced to at most 1/3 of its original strength when tied into a knot. It is also shown that it is possible to form tight and stable carbon nanotube knots by subjecting the knots to stress beyond the plastic limit. In contrast, loose knots stabilized by noncovalent interactions are not dynamically stable and spontaneously untie. To help understand the stability of loose carbon nanotube knots, the relationship between bending strain energy and curvature is studied using carbon tori. Our study demonstrates the possibility to tie carbon nanotubes into various stable knots and provides a general framework for the study of other macromolecular knots relevant to potentially useful nanotechnology.