Zero-dimensional fullerene molecule

A characteristic of the DOS of a metallic element is its large magnitude in the vicinity of the Fermi level. This feature, above and below the Fermi level, is associated with the highly delocalized character of the metallic bonding. However, most solid-state compounds are not metallic. Hence, we consider now the examples of graphite and diamond, two allotropic forms of elemental C. The chemically bonded network of the former is two-dimensional and that of the latter is three-dimensional. In Section 6.2.4 we presented the band stmcture of a hypothetical one-dimensional allotropic form of C. Zero-dimensional (molecular) forms do exist also these are the fullerenes such as C6o which was mentioned in Chapter 2 and will again be discussed in Chapter 7. C nanotubes are intermediate between molecules and macroscopic solids and also will be considered further in Chapter 7. 

Ideal point free nanoelements are fullerenes C o or C70 (Figure 1.11) [4] such structures could be defined as zero-dimensional continua. These elements are symmetric and nearly independent of all external influences. Some nanostmctures in liquids, due to their forms and electrical charges, are also close to ideal point nanoelements. Clusters of water molecules or atoms of metals, are nonideal point nanoelements. 

Figure 1 presents the typical geometries of the nanodimensional fillers which are commonly used to modify the elastomeric matrix [5], Nanoparticles possess many shapes and sizes (Fig. 1), but primarily they have three simple geometric forms sphere, cylinder and plate type. Three-dimensional nanofillers (3D) are relatively equiaxed particles, smaller than 100 nm (often below 50 nm [6]), e.g. nano SiOa, Ti02. These nanoparticles are described in the Sects. 2.2-2.4. Sometimes in the literature, the term 3D nanofillers (spherical) is described as a zero-dimensional (OD) system, but actually OD nanofillers are represented by POSS molecules, fullerenes, crystals or quantum dots [6]. What s more, very often the term physical form of these nanoparticles is referred to as agglomerates . The dispersion of particles from agglomerates to nanoparticles seems to be a big challenge to all... 

As fibers, CNTs can be considered one-dimensional molecules. Their radius virtually reduces to zero, whereas their lengths are typically on the order of micrometers. A useful simplification describes CNTs as hybrids of two other low-dimensional molecules graphene sheets (2D) are rolled up into tubes and capped at either end with fullerene (OD) hemispheres. It is worth considering some of the properties of these materials in detail to better understand certain properties of CNTs. 

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