Equilibrium shape equation and possible shapes of carbon nanotubes

Behavior of the van der Waals force between a plate and a single-walled carbon nanotube under uniform hydrostatic pressure: a theoretical study

We study the behaviour of the non-retarded van der Waals force between a planar substrate and a single-walled carbon nanotube, assuming that the system is immersed in a liquid medium which exerts hydrostatic pressure on the tube's surface, thereby altering its cross section profile. The shape of the latter is described as a continual structure characterized by its symmetry indexn. Two principle mutual positions of the tube with respect to the substrate are studied: when one keeps constant the minimal separation between the surfaces of the interacting objects; when the distance from the tube's axis to the substrates bounding surface is fixed. Within these conditions, using the technique of the surface integration approach, we derive in integral form the expressions which give the dependance of the commented force on the applied pressure.