Explicit solutions for a SWCNT collapse

Self-collapse of carbon nanotubes may prominently affect their electrical properties and holds promise for important applications in the emerging nano-mechanical or electronic systems. Based upon the potential energy functional, we derived the governing equation and transversality boundary condition for a collapsed single-walled carbon nanotube (SWCNT). Considering the inextensible condition of the elastica, some closed-form solutions for the collapsed configuration were obtained in terms of elliptical integrals. These analytical solutions include the critical length of the flat contact segment, critical radii for collapsed and circular shapes of the cross-section, deflections and potential energies of the SWCNTs. Finally, the energy states and the collapsed morphologies of the SWCNTs were presented. These explicit solutions are beneficial for the design of nano-structured materials, and cast a light on enhancing their mechanical, chemical, optical and electronic properties.