Carbon nanotube Armchair

Fig. 17. Schematic models for a single-wall carbon nanotubes with the nanotube axis normal to (a) the 6 = 30° direction (an armchair (n, n) nanotube), (b) the 0 = 0°...

Early transport measurements on individual multi-wall nanotubes [187] were carried out on nanotubes with too large an outer diameter to be sensitive to ID quantum effects. Furthermore, contributions from the inner constituent shells which may not make electrical contact with the current source complicate the interpretation of the transport results, and in some cases the measurements were not made at low enough temperatures to be sensitive to 1D effects. Early transport measurements on multiple ropes (arrays) of single-wall armchair carbon nanotubes [188], addressed general issues such as the temperature dependence of the resistivity of nanotube bundles, each containing many single-wall nanotubes with a distribution of diameters d/ and chiral angles 6. Their results confirmed the theoretical prediction that many of the individual nanotubes are metallic. 

Fig. 24. The armchair index n vs mode frequency for the Raman-active modes of single-wall armchair (n,n) carbon nanotubes [195]. From Eq. (2), the nanotube diameter is given by d = Ttac-cnj-K.

Fig. 3. The 2D graphene sheet is shown along with the vector which specifies the chiral nanotube. The pairs of integers ( , ) in the figure specify chiral vectors Cy, (see Table I) for carbon nanotubes, including zigzag, armchair, and chiral tubules. Below each pair of integers (n,m) is listed the number of distinct caps that can be joined continuously to the cylindrical carbon tubule denoted by (n,wi)[6]. The circled dots denote metallic tubules and the small dots are for semiconducting tubules.

The symmetry groups for carbon nanotubes can be either symmorphic [such as armchair (a ,/ ) and zigzag... 

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 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... 

Carbon nanotubes with armchair shape present a special interest because it is possible to see that the metal catalyst is not always located at the top of nanotube. Therefore it is evident that the growth of graphene layers may occur not only from a surface of a metal nanoparticle, as it is usually understood. Among the products... 

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...

Fig. 14.9 The variation of H-chemisorption energies at the B3LYP/6-31G(d) level for the chemisorption of one and two hydrogen atoms on the external surface of (3, 3), (4, 4), (5, 5) and (6, 6) armchair single-walled carbon nanotubes (SWNTs) of 9 and 15 carbon layers...

T.C. Dinadayalane et al., Chemisorption of hydrogen atoms on the sidewalls of armchair single-walled carbon nanotubes. J. Phys. Chem. C 111, 7376 (2007)... 

Fig. 1.1 Idealized representation of different structures of defect-free and opened carbon nanotubes (a) concentric MWCNT (b) metallic armchair [10,10] SWCNT (c) helical...

Since the [10]cyclophenacene comprises a unit structure of the [5, 5] armchair carbon nanotubes, the present data provided the basis analysis for the chemical reactivities of carbon nanotubes [27b]. The data on the various experimental and theoretical parameters of 7, 8 and A thus gave us useful information on the structures and properties of finite length carbon nanotubes, C50H20, Cf>0H20, C70H20, QoH2o, etc., and also on their chemical reactivities [51]. 

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