Armchair-type carbon nanotube

Figure 1.12 Three types of carbon nanotubes (a) armchair, (b) zigzag, and (c) chiral. The definition of nanotube types is according to the orientation perpendicular to the nanotube axis. (Figure from Ref. [82].)

Figure 23 Three types of carbon nanotube zigzag (left), chiral or twisted (centre), and armchair (right).

Lukovits and Janezic182 generated the number of Kekule structures of (1,1) armchair-type carbon nanotubes using the following recurrence equation 184 

Just as cycloparaphenylenes and cyclophenacenes represent the unit cycles of armchair carbon nanotubes of the type (n,n), cyclacenes are the shortest possible members of the zigzag nanotube family of (n,0) (Fig. 44). 

Figure 5.1 The three types of CNT structures (a) armchair, (b) zigzag, (c) chiral. (Reprinted with permission from International Materials Review, Carbon Nanotube Composites by P. J. F. Harris, 49, 1, 31 3. Copyright (2004) Maney Publishing www.maney.co.uk/journals/lmr)

From Table 5, one can see that the Kekule structures in polyphenanthrenes, (1,1)B armchair-type carbon nanotubes and in extended (1,1) nanotubes are related by the following equalities  

Fig. 5.3 a Schematic diagram showing how a blade or hexagonal graphene sheet is rolled to form a nanotube [38]. b types of carbon nanotubes based on its chirality (Zig-zag, chiral and armchair nanotubes)[39] 

In that nomenclature system, the center of a hexagon is chosen as the origin (0,0) and then it is superimposed with the center m,n) of another hexagon to form the nanotube. There are three types of carbon nanotubes. If the graphene sheet is rolled in the direction of the axis, it will produce either an armchair nanotube m = ) or a zig-zag nanotube m = 0). On the other hand, if the graphene sheet is rolled in any other m,n) direction it will produce a chiral nanotube and the chirality will depend on whether the sheet is rolled upwards or backwards. 

In the framework of semi-empirical method PM3 (worked out by Stewart [2,3] especially for calculation of electronic structure of carbon-contained organic molecules) the calculations of equilibrium configurations, full energy, heat of formation and electronic structure of different types of T-junctions of carbon zigzag and armchair nanotubes were done. 

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