Collapse of single-walled carbon nanotubes

Single-walled carbon nanotubes with a circular cross section can collapse into ribbons under the influence of self-van der Waals interactions. We present closed-form results for the energetics of this self-collapse using continuum analysis verified by molecular simulations. Two critical tube radii are predicted by the continuum analysis: Rmin, below which there is no collapse; and Rmax, above which the collapsed configuration is energetically favored. We present simple and accurate analytical results for Rmin and Rmax as functions of two length scales, d0 and D∕Wflat, where d0 is the equilibrium distance between two flat parallel graphite sheets, Wflat is the work per unit area needed to separate the two sheets, and D is the effective bending stiffness of the tube.