Chiral nano tubes

The ID electronic energy bands for carbon nanotubes [170,171, 172, 173, 174] are related to bands calculated for the 2D graphene honeycomb sheet used to form the nanotube. These calculations show that about 1/3 of the nano tubes are metallic and 2/3 are semiconducting, depending on the nanotube diameter di and chiral angle 6. It can be shown that metallic conduction in a (ra, m) carbon nanotube is achieved when... 

Figure 16 Schematic representation of (a) armchair, (b) zigzag and (c) chiral single-walled nano tubes. (Reprinted with permission from Ref 91. 2002 American Chemical Society)...

Fig. 3 Schematic model for single-wall CNTs with the nano tube axis normal to the chiral vector, which, in turn, is along (A) the Q = 30° direction [an armchair n, n) nanotube], (B) the 0 = 0° direction [a zigzag n, 0) nanotube], and (C) a general 6 direction, such as OB (see Fig. 2), with 0 < 0 < 30° [a chiral n,m) nanotube]. The actual nanotubes shown here correspond to (n, m) values of (A) (5, 5), (B) (9, 0), and (C) (10, 5). The nanotube axis for the (5, 5) nanotube has fivefold rotation symmetry, while that for the (9, 0) nanotube has threefold rotation symmetry. (View this art in color at www.dekker.com.)...

Dominicis and Fantoni present a method for the computation of the electronic first hyperpolarizability of chiral carbon nano-tubes (CNTs). The CNT eigenstates are computed by an algorithm reported by Damnjanovic et al. They discuss the symmetry properties of CNTs and selection rules for electronic transitions and demonstrate that the use of symmetry reveals the state-to-state transitions, which contribute to the first hyperpolarizability of CNTs. The latter is related to particular state-to-state transitions. The principles for predicting the magnitude of the first hyperpolarizability and its relation to the topology of CNTs are also discussed. 

Carbon nanotubes are one of the most important classes of new carbon materials. Distinctions are made between single- and multiwalled as well as between zig-zag, armchair, and chiral nanotubes. The structure is characterized by the descriptors n and m. These structural parameters allow for a prediction of the electric conductivity. Only armchair nano tubes n,n) and such species with m-n = iq are electric conductors. Any other nanotube is semiconducting. These statements have been established from symmetry considerations and from determining the band structure by way of the zone-folding method. There are different approaches to the production of single- and multiwalled nanotubes. Important methods of preparation are ... 

Fig. 14 Triangular zigazag, chiral and armchair boron nano tubes. ...

P20.36 Single-walled carbon nanolubes (SWNT) may be either conductors or semiconductors depending upon the tube diameter and the chiral angle of the fused benzene rings with respect to the lube axis. Van der Waals forces cause SWNT to slick together in clumps, which are normally mixtures of conductors and semiconductors. SWNT stick to many surfaces and they bend, or drape, around nano-sized features that are upon a surface. 

Amphiphilic compounds can form chiral tubes and nano-structures. These systems are rather crystalline than liquid crystalline and will not be discussed here. 

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