Defects in carbon nanotubes: Implications for mechanical properties

The mechanical properties of graphene-based systems such as carbon nanotubes are remarkable. Carbon nanotubes are stiff in tension and torsion, and there are indications of plastic deformation: observations of strain stiffening in nanotube torsional shafts as well as direct observations of kink motion to assist with elongation. These observations suggest the importance of defects to the mechanical properties of carbon nanotubes. Understanding defects, both their formation and their dynamics, will be important to further exploiting the unique properties of these systems.; Remarkably, defect formation energies are not well-understood. Stone-Wales defects are dislocation-like defects that are present in graphene-derived systems. Reported values of the defect formation energies vary by ≈3 eV, depending on the environment. Further, no real attempt has been made to compute the total energies of dissociated Stone-Wales defects.; To address these issues, a continuum theory of defect formation in graphene and carbon nanotubes is developed. This theory is based on the simple idea that the distortion field associated with the presence of a distribution of defects is that which minimizes the total elastic and curvature energies but is consistent with the topological constraints imposed by the defects. It makes no a priori assumptions about the analytical form of the defect strain fields, accounts for defect-defect interactions, and accommodates changes to the curvature and out-of-plane buckling.; Then, formation energies of Stone-Wales defects in a wide variety of configurations in graphene and carbon nanotubes are computed using total energy electronic structure methods and compared with the results of the continuum theory. The agreement between the two descriptions is excellent, with the continuum theory reproducing the trends in defect formation energies exhibited in the atomistic description, irrespective of defect arrangement. The result is an accurate and transferable continuum description of defect formation energies for any geometry and defect arrangement.