Nanotube armchair

The band structure of four concentric armchair tubules with 10, 20, 30, and 40 carbon atoms around their circumferences (external diameter 27.12 A) was calculated, where the tubules were positioned to minimize the energj for all bilayered pairs 17). In this case, the four-layered tubule remains metallic, similar to the behavior of two double-layered armchair nanotubes, except that tiny band splittings form. 

Inspired by experimental observations on bundles of carbon nanotubes, calculations of the electronic structure have also been carried out on arrays of (6,6) armchair nanotubes to determine the crystalline structure of the arrays, the relative orientation of adjacent nanotubes, and the optimal spacing between them. Figure 5 shows one tetragonal and two hexagonal arrays that were considered, with space group symmetries P42/mmc P6/mmni Dh,), and P6/mcc... 

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]. 

Fig. 22. Phonon dispersion relations for a (5,5) carbon nanotube. This armchair nanotube would be capped with a Cr,o hemisphere [194],...

In the low frequency region, the calculations predict nanotube-specific E g and E2g modes around 116 cm-1 and 377 cm-1, respectively, for (10,10) armchair nanotubes, but their intensities are expected to be lower than that for the A-[g mode. However, these E a and E2g modes are important, since they also show a diameter dependence of their mode frequencies. In the very low frequency region below 30 cm-1, a strong low frequency Raman-active E2g mode is expected. However, it is difficult to observe Raman lines in the very low frequency region, where the background Rayleigh scattered is very strong. 

If m = 0, the nanotubes are called zigzag nanotubes, if n = m, the nanotubes are defined as armchair nanotubes, and all other orientations are called chiral . The deviation of Cn from a is expressed by the inclination angle 0 and ranges from 0° ( armchair ) to 30° ( zigzag ) [17]. 

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 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. 

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... 

Figure 2. From the left Bge cluster segments in form of two 48-rings (Fig. 2a), three 32-rings (Fig. 2b), four 24-rings (Fig. 2c) and six 16-rings (Fig. 2d) with the structures of (24, 24), (16,16), (12,12) and (8,8) armchair nanotubes, respectively.

Figure 14.9 shows that the chemisorption reactions of one and two hydrogen atoms on the surface of the armchair nanotubes are highly exothermic. The... 

Generation of the chiral (8,4) carbon nanotube by rolling a graphite sheet along the vector C = naj + ma2, and definition of the chiral angle 9. The reference unit vectors aj and a2 are shown, and the broken lines indicate the directions for generating achiral zigzag and armchair nanotubes. 

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. 

The attempt of systematic theoretical investigation of the influence of defects on geometrical configuration and electronic structure of carbon zigzag and armchair nanotubes is undertaken. 

The SWNT systems chosen in the present studies include 3 armchair nanotubes and 3 zigzag nanotubes with diameters ranging from 4 A to 12 A, and 1 chiral nanotube with a diameter of 8.28 A. The nanotubes were carefully chosen to address the fundamental issues of curvature and chirality and the effect of each on the adsorption capacity. First, to understand the curvature effect on hydrogen uptake, we selected nanotubes with diameters varying from about 4 A to 12 A. Next, to investigate the effect of nanotube chirality, we intentionally chose the nanotubes of different chiral architectures with similar diameters. Finally, to study the capacity of a given nanotube, we included three different H2 loadings at 0.4 wt. %, 3.0 wt. % and 6.5 wt. %, respectively, in our MD simulations. 

We studied the cohesive energy of the BCN-NT and found that zigzag nanotubes are more stable than armchair nanotubes. Moreover, we found that tubes of type-5 and type-6 have lowest energy so they should be synthesized by methods described above. 

These factors, in turn, are dependent on the diameter and helicity. It has been found that metallicity occurs whenever (2n + m) or (2 + 2m) is an integer multiple of three. Hence, the armchair nanotube is metallic. Metallicity can only be exactly reached in the armchair nanotube. The zigzag nanombes can be semimetallic or semiconducting with a narrow band gap that is approximately inversely proportional to the tube radius, typically between 0.5 -1.0 eV. As the diameter of the nanombe increases, the band gap tends to zero, as in graphene. It should be pointed out that, theoretically, if sufficiently short nanotubes electrons are predicted to be confined to a discrete set of energy levels along all three orthogonal directions. Such nanotubes could be classified as zero-dimensional quantum dots. 

Figure 4 (A) Atomically resolved scanning tunneling microscopy (STM) of a SWNT in the surface of a rope revealing chiral-twist. (Reprinted with permission from Ref 15. 1998 Macmillan Magazines Ltd (www.nature.com).) (B) STM images of SWNTs produced by arc-discharge method (a) chiral nanotube with angle 7°, (b) zigzag nanotube, and (c) armchair nanotube. The tube axis is shown with dashed arrows. (Reprinted with permission Ref. 16. 1998 Macmillan Magazines Ltd)...

Nanoscale Building Blocks and Applications Armchair nanotube (5,5)... 

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