Cage curvature

The resonance destabilization that results from the adjacent pentagons (8tt electrons which do not satisfy the Hiickel rule) and reduction of the r-orbital overlap due to the cage curvature explain the lower stability of those so-called non-IPR fullerenes [9-11]. 

A second doping method is the substitution of an impurity atom with a different valence state for a carbon atom on the surface of a fullerene molecule. Because of the small carbon-carbon distance in fullerenes (1.44A), the only species that can be expected to substitute for a carbon atom in the cage is boron. There has also been some discussion of the possibility of nitrogen doping, which might be facilitated by the curvature of the fullerene shell. However, substitutional doping has not been widely used in practice [21]. 

All fullerenes (C ) are composed of sp2 hybridized carbon atoms forming a 3-D network of fused (n - 20)/2 six-membered and 12 five-mem-bered rings. As enshrined in the Isolated Pentagon Rule (IPR), so far, none of the structures isolated have two pentagons fused together. The curvature of the cage results in some strain, and the three angles around a carbon atom sum to 348° instead of the ideal value of 360° for . The [6,6] fusions have most double-bond character and are invariably where complexation occurs. For there are 30 such equiva-... 

Stability within the IPR fiillerene family is dependent on a balance of electronic and molecular strain factors. The carbon atoms in the fullerenes are approximately sp hybridized (although curvature of the cage causes a small admixture of sp ), with the remaining p-orbitals (mixed with... 

Higher fuUerenes are by far less abound than the archetypical compound 50. The formation of these cage-like compounds is kineticaUy controUed among the fuUerenes, is by no means the molecule with the least enthalpy per carbon atom. Normally the larger, thermodynamically more stable homologs (refer to Section 2.4) should be more abundant than 50 with its higher curvature-induced... 

Figure 2.9 The formation of a flillerene cage. The tendency toward minimizing the number of unsaturated bonding sites causes the generation of five-membered rings and thus an increasing curvature and final closure of the stmcture to be a cage-like molecule.

PolycycUc aromatic hydrocarbons (PAH) are suitable for the preparation of fullerenes because they aheady contain shuctural elements of the fullerene cage. In particular, such hydrocarbons consisting of five- and six-membered rings should rather easily transform into fullerenes upon thermal treatment as a part of the curvature is preformed already. 

The carbon nanotubes also have a lot of structural features in common with the carbon cages described in Chapter 2. Contrasting some fidlerene species, however, they do not occur naturally in any form, neither on earth nor in space, so they are a completely artificial form of carbon indeed. The question of whether nanotubes are a real modification will be discussed further below. In any case they exhibit bent graphene layers, but while the whole three spatial directions are affected in the fuUerenes, the curvature is limited to two dimensions here. Hence, the incorporation of five-membered rings-indispensable to achieve closure of the bowl in fullerenes-is unnecessary for the construction of nanotubes. It suffices to bend the graphene sheet from its plane and make it a cylinder. Compared to fuUerenes... 

It has already been mentioned in Section 2.3.5 that a rational synthesis of even the simplest fuUerene makes high demands on the preparation of a suitable precursor, which has to be closed to the carbon cage in a subsequent pyrolytic reaction. This problem becomes all the more salient in attempts on designing a strategy for the rational synthesis of multishell fullerenes it is not only the curvature of the carbon skeleton that must be considered here, but also the supramolecular pattern of concentric fullerenes of suitable sizes. Hence, for the time being, a directed synthesis of these multilayered species has not yet succeeded. 

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