Optimum diameter of single-walled carbon nanotubes in carbon nanotube ropes

In this paper, the optimum diameter of stable single-walled carbon nanotubes (SWNT’s) in a rope is calculated theoretically using its conformation energy, which consists of curvature elastic energy and intertube van der Waals energy. An equlibrium shape equation for single layer fullerenes is derived by means of variation of the conformation energy. For straight SWNT’s in an SWNT rope, the solution to the equlibrium shape equation gives the optimum diameter to be $1.36\mathrm{nm}$ for stable SWNT’s. This agrees well with the experimental observation [Nature 388, 756 (1997); Science 273, 483 (1998)].

Figure 1

The cross section of an SWNT rope. The least possible distance between two neighboring tubes is $b=3.2\mathrm{\AA }$. A single tube’s radius is represented by $r$ and $L=2r+b$ is the distance between the centers of two adjacent tubes.

Figure 2

The variation energy is dependent on the SWNT’s tube radius $r$ of SWNT’s when $b=3.2\mathrm{\AA }$.

Figure 3

The conformation energy is a function of the tube radius $r$ and intertube distance $b$.

Figure 4

The energies, $F_b$, $F_V$, and $F$, as functions of the tube radius $r$ for the intertube distance $b=3.2\mathrm{\AA }$.