Carbon nanotube knots

Kyle Rego,Vincent Meunier

doi:10.1063/1.5088145

Abstract

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.

Highlights

Knots have been used throughout history for innumerable purposes, playing an immensely important role in everyday life since prehistoric times
It is common in molecular dynamics to define which pairs or groups of atoms will interact and for these pairs to remain the same throughout the simulation
The results reported here for each knot correspond to a single simulation each, as the identification of the plastic limit is a tedious process

Summary

Introduction

Knots have been used throughout history for innumerable purposes, playing an immensely important role in everyday life since prehistoric times. There is evidence that ropes and knots were used long before the invention of the wheel. It is even speculated, based on the behavior of modern apes, that knotting began before the evolution of Homo sapiens.. That knots have been such a reliable technology in our everyday world raises the possibility that in the future nanoscopic knots tied using tiny ropes could be a desirable and useful nanotechnology. Applications could be as simple as attaching one polymer to another or as sophisticated as using nanoscopic ropes to perform nanosurgery with knotting techniques reminiscent of the way surgeons use sutures to close wounds. Perhaps the tightening of a knot could even be used as the trigger for activating a machine

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