Introductory remarks

Among all the elements of the Periodic Table, carbon has the astounding property of being able to form stable chains and rings of any magnitude. Only three other elements have this property to a degree: boron, silicon and sulfur. Boron [65] is the only one that can form n-bonds with significant strength similarly to carbon, and the existence of borazine, borazaro and boroxaro compounds is proof for this similarity. However, its electron deficit relatively to carbon makes boron a unique element in its propensity of forming two-electron-three-center bonds leading to various types of clusters and to the interesting boranes and carboranes. Silicon, although tetravalent like carbon, lacks its ability of forming stable n -bonds and this fact makes CO2 and SiO2 so different. Elemental silicon is isostructural with diamond (and does not form any graphite analog), but silanes are very different from alkanes because they ignite spontaneously in air and are rapidly hydrolyzed by aqueous bases, although they are stable to acids and water [66]. Divalent sulfur can yield various allotropes (but no other compound), and so can silicon, which in addition does give rise to many chemical compounds, but because its sp2-hybridized state has distinctly lower bond energy, it does not rival carbon with its many aromatic derivatives that make organic chemistry much richer than any other class of compounds. The "vegetal and animal kingdoms," i. e. the constituents of all living organisms, represent but a tiny fraction of these carbon containing compounds.

In addition to the infinite possibilities of organic chemistry, based on carbon as a single chain-forming element, one may conceive two-element alternative chemistries. One of these is based on silicon and oxygen; indeed silicates offer also an infinite number of possible compounds, and constitute the major "mineral kingdom". Another two-element pair is formed by boron and nitrogen, and indeed boron nitride (BN) also gives rise to two allotropes with similar structures with diamond and graphite [65]. The hexagonal BN (a white non-conducting solid) forms planar sheets that are not staggered like graphite, but have alternating B/N atoms in eclipsed positions of successive layers; the cubic BN analog of diamond is almost as hard, and may replace it in tools. More information on aromatic hetero-cycles involving B, Si, S and other elements can be found in a recently published review [67].

The traditional allotropes of carbon are the two 3-dimensional diamond lattices with sp3-hybridization (cubic diamond, the hardest solid, with ABAB layers, and hexagonal diamond, lonsdaleite, having ABCABC layers with some eclipsed bonds), and the two forms of planar graphite with sp2-hybridization (hexagonal graphite with ABAB layers and rhombohe-dral graphite with ABCABC layers). The first investigation of alternative possibilities of infinite lattices in addition to the above forms was published in 1968 [68]. Later, various other alternatives were investigated [69-71] and the possibility of a regular combination of sp2- and sp3-hybridized carbon atoms was also considered [72]. The known thermally-favored transition between diamond and the thermodynamically favored graphite at normal pressure must involve gradual interconversion of the two nets, and some theoretical possibilities were examined for this transition, as well as for the reverse process (diamond synthesis at high pressure and temperature). Both these processes must also involve combinations of sp2- and sp3-hybridized carbon atoms, but without any regularity [73-75].

On rolling a graphene sheet one may convert it into "buckycones" (predicted [76] before their experimental detection [77], and briefly discussed later) or carbon nanotubes. Before discussing nanotubes, however, one has to emphasize that like all synthetic polymers and many natural macromolecules such as polysaccharides (starch, glycogen, and cellulose), nanotubes are not substances, strictly speaking. Indeed, their molecules are similar (but not identical), and differ in the polymerization degree and molecular weight; their resulting polydispersity may be broad or narrow. Only two classes of natural polymers are monodisperse: proteins and polynucleotides. So far, it has not yet become possible to obtain monodisperse carbon nanotubes.

It is well known since Euler's time that in order to obtain a polyhedral molecule formed from hexagons and pentagons, there must be exactly twelve pentagons. The presence of odd-membered rings explains why BN analogues of fullerenes are not stable. By contrast BN analogues of bucky-cones and carbon nanotubes are possible, but they are not yet known, therefore in the following when we will discuss nanotubes it will be understood that they are carbon nanotubes.

In an interesting survey of the number of publications since the discovery of fullerenes [78] (with their large-scale synthesis five years later [79]) and carbon nanotubes [80, 81], it was found that the number of publications about fullerenes has reached a plateau, whereas those about nanotubes continue to increase exponentially [82].

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