Rolling vector, single walled

A single-walled carbon nanotube is often described as the result of seamless wrapping of a graphene sheet into a cylinder along the ( , m) roll-up vector,... 

One way to define the structure of single-walled CNT is to think of each CNT as a result of rolling a graphene sheet specifying the direction of rolling and the circumference cross-section (Figure la). The unit vectors of the planar... 

Many of the structural and physical properties of single-walled nanotubes can easily be understood based on a the picture of a strip of a two-dimensional graphite sheet rolled into a cylindrical form. Adapted to this symmetry, we will use the real space unit vectors ai, 2 of a hexagonal lattice in x,y coordinates ... 

Figure 10.1 Armchair (n,m = 5,5) (top) zigzag (9,0) (middle) and chiral (10,5) single-wall nanotubes. All armchair tubes are metallic, whereas only 1/3 of the chiral tubes have metallic character. (n,m), the roll-up vectors are proportional to the tube diameter. The dangling bonds at the tube ends are saturated by hemispherical fullerene caps.

Figure 18.1. AU single-walled carbon nanotubes can be described by the numbers (n, m) corresponding to a chiral vector (rollup vector) indicating the direction in which a graphene sheet is rolled and fused to yield a carbon nanotube.

Carbon nanotubes are classified as single-walled nanotubes (SWNTs) and multiwalled nanotubes (MWNTs). A SWNT can be visualized as a grapheme sheet that has been rolled into a hollow cylinder with ends caps. So the atomic structure of SWNT can be described by the chiral vector and the chiral angle 6 (see Fig. 23.5) given by Refs. [70-77] ... 

---