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Nanomaterials Fabrication 79

The next stable homologue is C 70 (Figure 3.34b), which has D 5h sym-
metry with a shape similar to a rugby ball or American football. This
is followed by C , C , C , and so on, in which an additional six mem-
78
76
74
bered rings are added. Mathematically and chemically, to make a
stable fullerene, one has to follow two principles: Euler’s theorem and
the isolated pentagon rule (IPR). Euler’s theorem states that for the
closure of each spherical network, n (n
2) hexagons and 12 pen-
tagons are required, while the IPR says no two pentagons may be con-
nected directly with each other, as destabilization is caused by two
adjacent pentagons.
2
Fullerenes are composed of sp carbons in a similar manner to
graphite, but unlike graphite’s extended solid structure, fullerenes are
spherical and soluble in various common organic solvents. Due to
their hydrophobic nature, fullerenes are most soluble in CS (C 60
2
1 1
7.9 mg mL ) and toluene (C 60 2.8 mg mL ), an important
requirement for chemical transformation. Although fullerenes have a
conjugated system, their spherical aromacity is distinctive from ben-
zene due to the closed shell structure. In contrast to benzene, which
has all C-C bonds in equal length, fullerenes such as C have two dis-
60
tinct classes of bonds. As determined experimentally, the shorter
bonds at the junctions of two hexagons ([6, 6] bonds) and the longer
bonds at the junctions of a hexagon and a pentagon ([5,6] bonds); see
Figure 3.35. The alternation in bond length shows that the double
bonds are located at the junction of hexagons, while there is almost
no double bond character in the pentagon rings in the lowest energy
state. As expected from the I symmetry of C , there is by symmetry
h
60
13
only one carbon type, which can be confirmed by C NMR spec-
13
symmetry, C has five C signals
troscopy. In agreement with its D 5h 70
in the ratio of 1:2:1:2:1.
Fullerenes represent a unique category of cage molecules with a wide
range of sizes, shapes, and molecular weights. Most of the effort thus
far has gone into the study of C fullerenes, which can now be prepared
60
to a purity of parts per thousand. Because of the unique icosahedral

Figure 3.35 Bond lengths of [5,6]
and [6,6] bonds of C 60 .