An armchair nanotube ([n.sub.1] = [n.sub.2]) subjected to a longitudinal tensile load [F.sub.T] is studied first.
For the armchair nanotube, the geometry relationships satisfy
The total axial force [F.sub.T] acting on the armchair nanotube can be related to bond force f as [F.sub.T] = 2[n.sub.1]f, so the force density over tube circumference can be defined as
The axial strain [[epsilon].sub.x] and circumferential strain [[epsilon].sub.[theta]] of armchair nanotube can be calculated as
The load-strain relationship for a zigzag tube can be calculated in a similar manner to the armchair nanotube described earlier.
We consider various armchair nanotubes
as models of (n,n) SWCNTs, n = 3-8.
But in the nanotubes, it had been predicted that the formation energies for divacancies in armchair nanotubes
are higher than in zigzag nanotubes.
White, "First-principles band structures of armchair nanotubes
," Applied Physics A, vol.
Among the topics are synthesizing bowl-shaped and basket-shaped fullerene fragments with benzannulated enyne-allenes, experimental and calculated properties of fullerene and nanotube fragments, hemispherical geodesic polyarenes as attractive templates for the chemical synthesis of uniform-diameter armchair nanotubes
, conjugated molecular belts based on three-dimensional benzannulene systems, and toward fully unsaturated double-stranded cycles.
Thus the vectors (0,n) and (m,0) denote zig-zag nanotubes, the vectors (m,m) or (n,n) denote armchair nanotubes
and all other vectors correspond to chiral nanotubes.
They finally concluded that in the case of zigzag CNTs, the axial modes appeared to be decoupled whereas the armchair nanotubes show coupling between such modes.
Since higher natural frequencies may be important in some applications such as mass sensing at nanoscale , we exemplarily evaluated the second and third natural frequency and the corresponding mode shapes for the case of three armchair nanotubes, see Figure 9.