where a and az are unit vectors in a two-dimensional graphite sheet and(n,m) are called chirality numbers.Both n and m are integers and they define the way the graphite sheet is rolled to form a nanotube. Nanotubes with n0,m 0 are called the zigzag tubes(Figure 8.6a)and nanotubes with n=m0 are called armchair tubes(Figure 8.6b).In zigzag tubes,two opposite C-C bonds of each hexagon are parallel to the tube's axis, whereas in the armchair tubes,the C-C bonds of each hexagon are perpen- dicular to the tube's axis.If the C-C bonds are at an angle with the tube's axis, the tube is called a chiral tube(Figure 8.6c).The chiral angle 0 is defined as the angle between the zigzag direction and the chiral vector,and is given by [3/2m1 =tan (8.2) 2n+m a (b) (c) FIGURE 8.6 (a)Zigzag,(b)armchair,and (c)chiral nanotubes.(From Rakov,E.G., Nanomaterials Handbook,Y.Gogotsi,ed.,CRC Press,Boca Raton,USA,2006.With permission.) 2007 by Taylor Francis Group,LLC.where a1 and a2 are unit vectors in a two-dimensional graphite sheet and (n, m) are called chirality numbers. Both n and m are integers and they define the way the graphite sheet is rolled to form a nanotube. Nanotubes with n 6¼ 0, m ¼ 0 are called the zigzag tubes (Figure 8.6a) and nanotubes with n ¼ m 6¼ 0 are called armchair tubes (Figure 8.6b). In zigzag tubes, two opposite C–C bonds of each hexagon are parallel to the tube’s axis, whereas in the armchair tubes, the C–C bonds of each hexagon are perpen￾dicular to the tube’s axis. If the C–C bonds are at an angle with the tube’s axis, the tube is called a chiral tube (Figure 8.6c). The chiral angle u is defined as the angle between the zigzag direction and the chiral vector, and is given by u ¼ tan1 31=2m 2n þ m
(8:2) (a) (b) (c) FIGURE 8.6 (a) Zigzag, (b) armchair, and (c) chiral nanotubes. (From Rakov, E.G., Nanomaterials Handbook, Y. Gogotsi, ed., CRC Press, Boca Raton, USA, 2006. With permission.)
2007 by Taylor & Francis Group, LLC.