Radial deformation of single-walled carbon nanotubes adhered to solid substrates and variations of energy: Atomistic simulations and continuum analysis

Radial deformation of carbon nanotubes (CNTs) adhered to substrates can strongly influence their physical properties and the performance of CNT-based nanodevices. Here we explore the radial deformation and related energy variations of single-walled carbon nanotubes (SWCNTs) attached to solid substrates by adopting the classical molecular dynamics (MD) simulations and continuum analysis. The radial deformation of a SWCNT can be divided into three stages: the drop-shaped stage, the half-hourglass-shaped stage and the half-dumbbell-shaped stage. Three continuum models are established to mimic the radially deformed configurations. Minimization of the total free energy provides the equilibrium profiles of the SWCNT during the radial deformation. There is a good agreement between the theoretical predictions and the results of MD simulations. By analyzing the variations of free energy, we find that the favorable configuration of a substrate-supported SWCNT can be characterized by two threshold diameters. For SWCNTs with diameter below the first threshold diameter, the circular state is stable. For SWCNTs with diameter exceeding the second threshold diameter, the collapsed half-dumbbell-shaped state is energetically most favorable. The energy barrier, for obtaining a fully collapsed SWCNT, decreases with the increasing diameter, which approximately keeps a negative exponential relationship. The adhesion work is demonstrated to play an important role in the radial deformation and morphology stability of substrate-supported SWCNTs.