Page 175 - Carbon Nanotubes

166 D. UGARTE
ions with a very small inner empty space, which con- 5 hexagons (non-planar structure with a bowl shape)
trasts with the polyhedral particles prepared by heat is a very floppy structure. This molecule is the basic
treatment of fullerene black[l3]. unit of C60, and also the atomic arrangement present
at the corners of faceted giant fullerenes. It has been
observed by NMR that, at room temperature, it spon-
4. ENERGETICS
taneously presents a bowl inversion transition, with an
The elimination of the energetic dangling bonds energy barrier of only 440 meV[321. Then, we may use
present at the edges of a tiny graphite sheet is supposed this value to get a bare estimation of the energy nec-
to be the driving force to induce curvature and closure essary to crash the 12 corners of a polyhedral graphitic
in fullerenes; this phenomenon is also associated with cage (containing the corannulene configuration) into
the formation of larger systems, such as nanotubes a spherical one, and it turns out to be of the same
and graphitic particles. order of magnitude that the gain in van der Waals
The remarkable stability of onion-like particles[l5] energy mentioned previously (=5 eV). This fact in-
suggests that single-shell graphitic molecules (giant ful- dicates that a global evaluation of multi-shell struc-
lerenes) containing thousands of atoms are unstable tures should be performed to answer the question of
and would collapse to form multi-layer particles; in the minimal energy structure of onion-like graphitic
this way the system is stabilized by the energy gain particles.
from the van der Waals interaction between shells From a different point of view, the sphericity of the
[ 15,26,27]. irradiation generated onion-like particles have also
Graphite is the most stable form of carbon at am- been attributed to imperfect shells with a large num-
bient conditions, and it is formed by the stacking of ber of defects[33].
planar layers. The extreme robustness of the concen- Concerning the possible arrangement of concentric
tric arrangement of spherical fullerenes led to the hy- defect-free graphitic cages, a polyhedral graphitic par-
pothesis that the quasi-spherical onion-like graphitic ticle has all the shells in the same orientation, so that
particles are the most stable form of carbon parti- all the comers (pentagons) are perfectly superimposed
cles[l5]. This controversy between planar configura- (see Fig. 4a). If the pentagons of the concentric shells
tion of the sp2 bonding in macroscopic graphite and are not aligned, the final shape of graphitic particles
the apparent spherical shape in nanometric system, has should be much closer to a sphere. In the spherical
attracted a great deal of interest[28]. Calculations of particles, an interesting issue is the fact that the shells
the structure of giant fullerenes are not able to give a may be rotating relative to each other[l5]. This behav-
definitive answer: (a) models based on elastic or em- ior has been predicted for C60 in C240[30] and for
pirical potentials predict that the minimal energy struc- multi-shell tubes[34].
ture is a slightly relaxed icosahedron with planar
facets, the curvature being concentrated at the corner
of the polyhedron (pentagons)[26,29,30]]; (b) ab ini- 5. SUMMARY AND PERSPECTIVES
tio calculations predict two local energy minima for The multi-shell fullerenes constitute the transition
C240. One represents a faceted icosahedron, and the from fullerenes to macroscopic graphite. They present
second, a nearly spherical structure distributing the both the closed graphitic surface of fullerenes and the
strain over all atoms, is slightly more stable (binding stacked layers interacting by van der Waals forces, as
energy per atom -7.00 and -7.07 eV for polyhedral in graphite.
and spherical fullerenes)[3 11. One of the main scientific issues of the discovery
When using these theoretical results to analyze of the bucky-onions is the unresolved question of min-
onion-like particles, we must take into account that imal energy configuration of carbon clusters (onion-
calculations are performed for single graphitic shells,
which are subsequently arranged concentrically and,
then, conclusions are obtained about the minimal en-
ergy configuration. This fact arises from the limited
number of atoms that may be included in a calcula-
tion due to present computational capabilities (the
smallest onion-like particles are formed by Cso in a
C240 and this system represents 300 atoms).
The inter-layer interaction (EvdW, van der Waals
energy) is usually added at the end, and then it does
not participate in the energy minimization. Evaluating
inter-shell interaction by a simple Lennard-Jones pair
potential shows that concentrical spherical shells are P S
more stable than icosahedral ones (EvdW between C240
and C540 is -17.7 and -12.3 eV for spherical and
icosahedral shells, respectively). An interesting com- Fig. 4. Onion-like graphitic particles formed by three con-
centric layers (C,,,, Cm, &,):
polyhedral (marked P) and
parison may be performed by considering that coran- spherical (marked S) structures. For clarity, only a half part
nulene CzoHlo, which is a pentagon surrounded by of each shell is shown.