Van der Waals' Elastica

Experimental investigations of carbon nanotubes have revealed that they can collapse into nanoribbons that have a dumbbell shape cross-section. Due to the extreme e xibility of single-atom thick graphene sheets, if the tube is large enough self-induced Van der Waals forces acting on the at surfaces of the ribbon will be large enough to hold the nanorube in the collapsed (ribbon) con guration. Energetically, the additional strain (bending) energy stored in the collapsed state is offset by the decrease in energy of the Van der Waals interactions. Because Van der Waals forces are short ranged, one nds that tubes of great enough diameter are bistable. Here we investigate the natural of this bistability by investigating how the energy stored in the tube changes as it is compressed by at rigid indenters of various widths. The nanorube is assumed to deform uniformly along its length and the cross-section is modeled using inextensible, non-linear beam theory (Euler's Elastica). We nd that the in ated (tube) con guration is always stable but that the energy barrier against decreases with increasing tube radius. Additionally, the energy difference between the in ated and collapsed states decreases nearly linear with increasing radius and for tubes with radius greater than 26 A the collapsed state is energetically favored.