Spontaneous polygonization of multi-walled carbon nanotubes: perturbation analysis

Spontaneous polygonization for a multi-walled carbon nanotubes (MWCNTs) have been observed for about two decades. In present manuscript, this phenomenon is understood by the competition between cohesion energy (with lattice mismatching effect) and curvature elastic energy of tubes inside the MWCNTs. Based on a continuum elastic model and perturbation analysis, the crucial conditions for spontaneous polygonization of MWCNT is expressed by fundamental parameters of MWCNTs, which are in reasonable agreement with all relevant experiments and computer simulations reported in literatures. Present approach can be used in further studies of crossectional geometry-dependent properties of MWCNTs.