Transition states and minimum energy pathways for the collapse of carbon nanotubes

Carbon nanotubes (CNTs) can undergo collapse from their customary cylindrical configurations to ribbons. The energy minima corresponding to these two states are identified using either atomistic molecular mechanics or the theory of finite crystal elasticity with reduced dimensionality. The minimum energy path between these two minima is found using the nudged elastic band reaction-pathway sampling scheme. The energetics of CNT collapse is explored for both single- and multi-walled CNTs as well as small bundles. The process has a strong diameter dependence, with collapse being more favorable for the larger diameter tubes, but is nearly independent of chirality. The saddle point always lies close to the collapsed state, and the absolute barrier energies-even for fairly short tube lengths-are sufficiently high, even when the reaction is highly exothermic, that thermal activation cannot initiate collapse via this pathway. The hydrostatic pressure required to buckle and collapse CNTs of various diameters is discussed.