Introduction Description of Molecular Nanotubes

In 1991, nanotubes of carbon were discovered by Sumio Iijima in carbon deposits on an arc-deposition system similar to that used for the production of C60 (termed Buckminster-fullerene) [3]. From a structural perspective, a single-walled carbon nanotube (SWNT) can be visualized as consisting of a single (graphene) sheet rolled into a tube. To maintain the periodic structure of the 2-D honeycomb lattice formed by the carbon atoms within the sheet, there is a discrete relationship between the tube diameter and the chi-rality of the tube [83, 84]. This relationship is summarized in Figure 16, and utilizes a simple 2-D lattice notation. The diameter and chirality of a given SWNT are defined by an integer pair (n, m) which denotes a point on the edge of a graphene sheet that is mapped onto the origin (0, 0) as the sheet is rolled. Rolled (n, 0) graphene sheets are referred to as zigzag tubes as C atoms on an open end form such a pattern. Rolled (n, n) graphene sheets are referred to as armchair tubes as the C atoms on an open end form undulating hexagonal tiles (see Fig. 16). Rolled (n, m) sheets, where n = m, are typically referred to as chiral, although the use of this taxonomy varies throughout the literature.

Figure 15. HFM phase maps (10 /m x 10 /m scans) for tip and sample vibrations below (left) and above (right) threshold amplitude, respectively, for polymer/Al test structure. The dark regions are polymeric plugs in an Al field. The structure was fabricated using IC processing. The reduced contrast for the polymeric regions correspond to an increase in the viscoelasticity compared to the Al.

Figure 15. HFM phase maps (10 /m x 10 /m scans) for tip and sample vibrations below (left) and above (right) threshold amplitude, respectively, for polymer/Al test structure. The dark regions are polymeric plugs in an Al field. The structure was fabricated using IC processing. The reduced contrast for the polymeric regions correspond to an increase in the viscoelasticity compared to the Al.

Figure 16. Schematic diagram outlining how a 2-D graphite sheet is "rolled" to form a nanotube. The diagonal dotted lines denote graphene sheet edges that, if joined, would form a (3, 2) nanotube.

Multiwall carbon nanotubes (MWNTs) consist of multiple nested (graphitic) sheets rolled into a tube. The spacing of these sheets has been experimentally measured at 0.34 nm, only slightly larger (3-5%) than the c spacing of conventional graphite [84]. SWNTs typically possess diameters in the 1-5 nm range, and lengths ranging to many microns. Depending upon the method of synthesis and purification, SWNTs entangle to form nanoropes [85-86]. The cross section of these ropes consists of individual SWNTs on a triangular lattice. For example, the SWNT ropes investigated by Yu et al. consisted of 1.35 diameter SWNTs on a triangular lattice with a center-to-center distance of 1.7 nm [87]. As expected, MWNT diameters are significantly larger, ranging from 7 to over 200 nm. Multiwall NTs also form fibrous ropes, the mechanical properties of which will be discussed next.

From a mechanics perspective, two fundamental properties of NTs are of interest. First, the planar sp2 bonding of the carbon atoms in the graphene sheets provides for an enormous mechanical modulus, that is, a very low strain is seen for a given in-plane applied stress [88]. And, in stark contrast to fourfold coordinated sp3 bonding of carbon in diamond or diamond-like materials, the quantum-mechanical electron energy levels of an sp2-bonded graphene sheet may permit electron conduction [89-90]. Second, the energetics of NT growth are often suitable for the production of crystal defect-free SWNTs or MWNTs [91]. This is a truly remarkable mechanical feature in that the presence of crystalline defects dramatically impacts mechanical properties.

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