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Information on Carbon Nanotubes

Carbon fullerenes are large, closed caged carbon structures in a spherical shape. Fullerenes, discovered in 1985, are stable in gas form and exhibit many interesting properties that have not been found in other compounds before. Figure 1 is a representation of a C60 Fullerene molecule. A fullerene is a spherical structure composed of both pentagonal and hexagonal carbon rings. Fullerenes are considered zero dimensional quantum structures which exhibit interesting quantum properties. Once fullerenes were proven to exist, research for other fullerene like structures led to the discovery of Carbon nanotubes in 1991.
Figure 1: Representation of a Fullerene Molecule

Nanotubes are the 1 dimensional wire form of a fullerene; the diameter is typically 1 to 5 nanometers (nm), while the length can be in the range of microns. Single Walled Nanotubes (SWNT) can be considered as a flat graphene sheet (Figure 2) cylindrically rolled into a tube. The tubes consist of two regions: the sidewall of the tube, and the end region of the tube.

A significant physical property of CNT is the tube tip. Tube tips may be open ended or close capped. Closed tips are "capped" with a structure that is similar to one half of a C60 fullerene molecule. The sidewalls of CNT consist of only hexagonal carbon rings, whereas the end caps are made of pentagons and hexagons in order for curvature to exist. Due to the symmetry of the cylindrical tube, CNT have a discreet number of directions that can form a closed cylinder (Figure 2).

Figure 2: Graphene Sheet illustrating chiral arrangements

Two atoms in the sheet are selected as the origin, and when the sheet is rolled, the two atoms coincide with one another. The vector OA is known as the "rollup" vector, whose length is equal to that of the circumference of the nanotube. The tube is created so that point O touches point A, and B touches B´. The tube axis is perpendicular to the rollup vector. The chiral vector of the nanotube, OA, can be defined by
OA = nâ1 + mâ2

where â1 and â2 are unit vectors in the two-dimensional hexagonal lattice, and n and m are integers.

Another important parameter is the chiral angle, ?, which is the angle between Ch and â1. All nanotubes can be described as having:
0°<= ? <30°

Carbon atoms in SWNT can be assigned to a coordinate system (n,m), with m <= n at all times. As chiral vectors change, nanotube properties change from metallic to semi-conducting (Figure 3). The (n, 0) direction is known as zigzag structure, while the n=m s denoted as armchair structure (Figure 4). Although Figure 3 shows all co-ordinations of (n, m), not all of these chiralities have been observed in CNT.

Figure 3: Possible Structures Based on Chiral Vectors for CNT

Figure 4: Armchair, Zigzag and Chiral Nanotubes

It should be noted that all armchair chiralities of CNT display metallic properties (green circles in Fig. 3). In addition, chiral vectors with:
n - m = 3i

where i is an integer value, yield metallic properties. All other arrangements of (n, m) in CNT display semi-conductor properties (Blue circles in Fig. 3). Chirality affects the electrical properties of nanotubes, as well as optical activity, mechanical strength, and various other properties. Deformations and defects in CNT can also have a profound impact on intrinsic properties. Junctions or bends in nanotubes can be introduced by the replacement of a hexagonal carbon ring with a pentagonal or heptagonal ring. Bends, which may be inward or outward, can severely affect the electrical conductivity of nanotubes.

Many experiments have resulted in bundled SWNT. These are regular SWNT in very close proximity to one another, but the tubes do not share a wall. Multi Walled Nanotubes (MWNT) are another common type of fullerene structure. MWNT are concentric rings SWNT with different diameters centered around a common point. Figure 5 shows TEM images of isolated SWNT, bundled SWNT, and MWNT. Since the nested tubes in a MWNT structure are independent of one another, each tube has its own chiral vector, and therefore chiralities of individual tubes in a MWNT structure may be different . Furthermore, since CNT are simply rolled graphene sheets, the spacing between individual tubes in MWNT can be considered equal to the spacing of adjacent graphene layers in graphite, or approximately .34nm .

Bonding in CNT is exactly as bonding of graphene sheets in graphite. Each carbon atom within the graphene sheet holds a covalent bond with three neighbor carbon atoms. The bonds are due to the interaction of the each carbon atom's three sp2 orbitals interacting with the sp2 orbitals of neighboring carbon atoms. As a result, s bonds are formed, and one 2p orbital is left un-hybridized. Individual tubes in MWNT experience only van der Waals forces between adjacent tube layers.

Figure 5: TEM Images of (A) SWNT, (B) Bundled SWNT, and (C) MWNT

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