Elastic properties of carbon nanotubes: An atomistic approach

Energetically the single sheet of graphite (graphene) is more stable than the nanotube. The energy difference between the two systems can be directly related to the strain energy involved in rolling up the graphene sheet to form the nanotube. We have carried out first-principle electronic structure calculations and evaluated the strain energy as a function of the nanotube radius. The dependence of the strain energy on the diameter of the nanotube has been found by several groups to be well-described by a continuum elasticity model. We attempt to examine why this is the case and show where atomistics enter the description.