Carbon nanotubes armchair tubes

The electronic properties of single-walled carbon nanotubes have been studied theoretically using different methods[4-12. It is found that if n — wr is a multiple of 3, the nanotube will be metallic otherwise, it wiU exhibit a semiconducting behavior. Calculations on a 2D array of identical armchair nanotubes with parallel tube axes within the local density approximation framework indicate that a crystal with a hexagonal packing of the tubes is most stable, and that intertubule interactions render the system semiconducting with a zero energy gap[35]. 

The conductive properties of SWCNTs were predicted to depend on the helicity and the diameter of the nanotube [112, 145]. Nanotubes can behave either as metals or semiconductors depending upon how the tube is rolled up. The armchair nanotubes are metallic whereas the rest of them are semiconductive. The conductance through carbon nanotube junctions is highly dependent on the CNT/metal contact [146]. The first measurement of conductance on CNTs was made on a metallic nanotube connected between two Pt electrodes on top of a Si/Si02 substrate and it was observed that individual metallic SWCNTs behave as quantum wires [147]. A third electrode placed nearby was used as a gate electrode, but the conductance had a minor dependence on the gate voltage for metallic nanotubes at room temperature. The conductance of metallic nanotubes surpasses the best known metals because the... 

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. 

For single-walled carbon nanotubes, it is also possible to predict the stracture of their infrared spectra. It turns out that depending on the structure of the tube under consideration, a different number of bands should be IR-active. Zig-zag nanotubes possess IR-active A2 - and two Eiu-modes for armchair tubes there are three Eia-modes, and chiral species exhibit one A2- and five Ej-modes. The signals can be expected to lie chiefly in one of two spectral regions about 870 and 1590 cm" . The first of these is always Raman-inactive, whereas for the latter this is only true... 

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 ... 

Let us fix the parameter 2A = 0.34 nm which is equal to the graphite inter-layer separation. The chirality and the radius of single-wall carbon nanotube are uniquely specified by the chiral vector C/, = iai +112 2 - ( i. 2)> where ni,ri2 are integers and ai, a2 are the unit cell basis vectors of graphite [1]. The chiral vector C is a circumferential lattice vector defined on nanotube surface, and C is perpendicular to the tube axis. For armchair nanotubes n =ri2 = n, and the tube radius r is defined by r = C/, /2ti = a f3n/2n, where a = 0.249 nm is the lattice constant for graphite. These values of r are used in our calculations. 

Vm Fig. 28.22 (a) Vectors on a graphene sheet that define achiral zigzag and armchair carbon nanotubes. The angle 0 is defined as being 0° for the zigzag structure. The bold lines define the shape of the open ends of the tube, (b) An example of an armchair carbon nanotube, (c) An example of a zigzag carbon nanotube. 

Examples of capping units that covalently bond to open carbon nanotubes to yield closed tubes. The examples shown are portions of a C o molecule and are compatible with (a) an armchair and (b) a zigzag carbon nanotube. 

A Figure 12.48 Atomic models of carbon nanotubes. Left Armchair nanotube, which shows metallic behavior. Right Zigzag nanotube, which can be either semiconducting or metallic, depending on tube diameter. 

Most theoretical studies of inorganic and carbon nanotubes deal with achiral structures, i.e. zigzag and armchair nanotubes. In terms of their integer denominators these are (n,n) and (w,0) nanotubes. There is, however, a plethora of other tubular structures with denominators (n,m) (and n m) that are chiral. Using periodic-boundary conditions, the calculational unit cells of chiral nanotubes contain a lot more atoms than those of the achiral tubes. Thus, calculations of chiral tubes with the generally used techniques are computationally demanding. 

In a batch of newly synthesized carbcai nanotubes, a significant proportion of carbon nanotubes are capped, i.e. the open ends of the tubes shown in Fig. 28.34 are capped by hemispherical units, formally derived from fuUerenes. By removing atoms from Cgo (Fig. 14.5), end-capping units compatible with an armchair SWNT (Fig. 28.35a) or zigzag SWNT (Fig. 28.35b) can be generated. As noted earlier, arc discharge methods of synthesis tend to favour the formation of MWNTs. These consist of concentric tubes, packed one inside another. 

---