Statistical mechanics of nanotubes*

We investigate the effect of thermal fluctuations on the mechanical properties of nanotubes by employing tools from statistical physics. For 2D sheets it was previously shown that thermal fluctuations effectively renormalize elastic constants beyond a characteristic temperature-dependent thermal length scale (a few nanometers for graphene at room temperature), where the bending rigidity increases, while the in-plane elastic constants reduce in a scale-dependent fashion with universal power law exponents. However, the curvature of nanotubes produces new phenomena. In nanotubes, competition between stretching and bending costs associated with radial fluctuations introduces a characteristic elastic length scale, which is proportional to the geometric mean of the radius and effective thickness. Beyond elastic length scale, we find that the in-plane elastic constants stop renormalizing in the axial direction, while they continue to renormalize in the circumferential direction beyond the elastic length scale albeit with different universal exponents. The bending rigidity, however, stops renormalizing in the circumferential direction at the elastic length scale. These results were verified using molecular dynamics simulations.