Armchair-type carbon nanotube

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

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 ... 

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. 

Three examples of particular structures of SWCNTs, depending on the orientation of the hexagons related to the tube axis, (a) armchair-type tube (0 = 30°), (b) zigzag type tube (0 - 0°), and chiral tube (0 < 0 < 30°). Reprint from Carbon, vol. 33, No. 7, Dresselhaus M.S., Dresselhaus G., Saito R., Physics of carbon nanotubes, pages 883-891, Copyright (1995) with permission from Elsevier. 

Fig. 14.3 Representative structures of (a) armchair, (b) zigzag, and (c) chiral type single-walled carbon nanotubes...

Stability of, for example, (10,10)-nanotxibes, but kinetic reasons contribute as well to the effect. In achiral nanotubes, and especially in those of the armchair type, the replacement of metal atoms by carbon is much easier due to the orientation of the lattice structure (see below). What is more, several SWNTs at a time wiU emerge from very reactive sites. With the prevaiUng temperature being constant for all tubes nucleating in these zones, their respective diameters wiU also be more or less the same. Consequently, they may form a symmetric packing, which is why the most stable bundles are observed in these cases. 

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)...

An SWNT s rolling vector, or chirality, has the most profound effect on its electronic properties. Figure 1 shows the three possible types of carbon nanotubes as defined by chirality. If a carbon nanotube is formed by connecting one carbon atom in the graphene lattice to another carbon atom that is located directly along one of the imit vectors of the surface, the result is what is known as an armchair carbon nanotube. If an SWNT is formed in such a way that one atom cormects and atom which is 30° from the zigzag direction, the result is an... 

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. Different types of carbon nanotubes (a) armchair (5,5)-SWCNTs, (b) zigzag (10,0)-SWCNTs,...

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]... 

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

There are three general types of CNT structure (Figure 12.10). The zigzag nanotubes correspond to ( ,0) or (0,m) and have a chiral angle of 0°. The carbon-carbon position is parallel to the tube axis. Armchair nanotubes have (n,n) with a chiral angle of 30°. The carbon-carbon positions are perpendicular to the tube axis. Chiral nanotubes have general (n,m) values and a chiral angle of between 0° and 30°, and as the name implies, they are chiral. 

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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