Carbon Nanotubes

      Since 1991, when multi-walled nanotubes (MWNTs) were accidentally synthesized using the arc process,[1] much progress has been made in learning more about them and how they are formed. For example, in 1993, nanotubes with only one wall or shell were synthesized in the arc in the presence of Fe[2] or Co[3] catalysts, and called single-walled nanotubes (SWNTs). However, in 1992 before SWNTs had been synthesized, the metallic conductivity of SWNTs was predicted using a first-principles local density-functional band structure approach and tight-binding model.[4] The electronic properties of SWNTs were found to depend on their atomic structures, which are described by their chiral angle and diameter, which are specified by the lattice indices (m,n).[5, 6] Atomically resolved scanning tunneling microscope (STM) images have subsequently been used to experimentally probe the structures of SWNTs and are also interpreted using these lattice indices.[7, 8]
Figure 1. Flat hexagon lattices of a graphene sheet.

      Fig. 1 shows the origin of these indices on the flat hexagonal lattice of a graphene sheet. The structure of a SWNT can be thought of as this graphene sheet rolled into a pipe or tube. A chiral vector Ch in an unrolled graphene sheet is defined as na1 + ma2, where n and m are integers (0 ≤ |m| ≤ n), a1 and a2 are real space unit vectors of a hexagonal lattice as shown in Fig. 1. The structure of a SWNT can be represented by Ch, which corresponds to the section of the nanotube perpendicular to the nanotube axis. Therefore, Ch = (n,m) defines the diameter and chiral angle of a SWNT. The chiral angle is defined to be the angle between Ch and the unit vector a1. According to the chiral angles and chiral vectors, SWNTs are classified as zigzag (Fig. 2A), armchair (Fig. 2B), and chiral (Fig. 2C) types. The chiral angle and Ch of zigzag nanotubes is 0º and (n,0). The chiral angle is 30º and Ch is (n,n) for armchair nanotubes. Chiral SWNTs have Ch = (n,m) where n is not equal to m, and a chiral angle which is greater than 0º and less than 30º. The electronic properties of nanotubes depend greatly on their structure. For example, it is known that (n,m) nanotubes are metallic if (2n + m) is a multiple of 3 and that other nanotube structures are semiconducting.[9]
A B C

Figure 2. Side views of various nanotubes. A) Zigzag (10,0) nanotube. B) Armchair (6,6) nanotube. C) Chiral (7,4) nanotube.

      Nanotubes are a special type of nanoporous material that may produce unique behavior in fluids confined to the nanotube interiors relative to fluids confined to the interiors of zeolites and other molecular sieves.[10] This is because nanotubes have continuous, smooth structures of uniform composition, whereas zeolites have non-uniformly distributed diameters along the length of the pore, and are composed of multiple elements, such as Al, Si, and O. In addition, variations in the helical alignment of the carbon atoms along the nanotube axis may influence molecular motion. The following section reviews computational and experimental studies that have examined molecular transport and flow through opened carbon nanotubes and zeolites. In order to fill a normally capped nanotube, the nanotube must be first treated with carbon dioxide,[11] oxygen,[12] or acids (e.g., HNO3),[13] which open the ends through chemical reactions that include oxidation and esterification.

References
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[2] Iijima, S. and T. Ichihashi, Single-shell carbon nanotubes of 1-nm diameter. Nature, 1993. 363: p. 603-605.
[3] Bethune, D.S., et al., Cobalt-catalyzed growth of carbon nanotubes with single-atomic-layer walls. Nature, 1993. 363: p. 605.
[4] Mintmire, J.W., B.I. Dunlap, and C.T. White, Are fullerene tubules metallic? Physical Review Letters, 1992. 68(5): p. 631-634.
[5] Saito, R., et al., Electronic-Structure of Chiral Graphene Tubules. Applied Physics Letters, 1992. 60(18): p. 2204-2206.
[6] Wildoer, J.W.G., et al., Electronic structure of atomically resolved carbon nanotubes. Nature, 1998. 391(6662): p. 59-62.
[7] Odom, T.W., et al., Scanning tunneling microscopy and spectroscopy studies of single wall carbon nanotubes. Journal of Materials Research, 1998. 13(9): p. 2380-2388.
[8] Venema, L.C., et al., Atomic structure of carbon nanotubes from scanning tunneling microscopy. Physical Review B, 2000. 61(4): p. 2991-2996.
[9] Dresselhaus, M.S., G. Dresselhaus, and P.C. Eklund, Science of fullerenes and carbon nanotubes. 1996, San Diego: Academic Press.
[10] Bhide, S.Y. and S. Yashonath, n-pentane and isopentane in one-dimensional channels. Journal of the American Chemical Society, 2003. 125(24): p. 7425-7434.
[11] Tsang, S.C., P.J.F. Harris, and M.L.H. Green, Thinning and Opening of Carbon Nanotubes by Oxidation Using Carbon-Dioxide. Nature, 1993. 362(6420): p. 520-522.
[12] Ajayan, P.M., et al., Opening Carbon Nanotubes with Oxygen and Implications for Filling. Nature, 1993. 362(6420): p. 522-525.
[13] Ravindran, S., et al., Covalent coupling of quantum dots to multiwalled carbon nanotubes for electronic device applications. Nano Letters, 2003. 3(4): p. 447-453.