15
The Fullerene Molecules
1.0 GENERAL CONSIDERATIONS
1.l State of the Art
The |
recent |
discovery |
of a family |
of large, |
solid carbon |
molecules |
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with |
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great stability, |
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the |
so-called |
‘fullerenes”, |
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has |
considerably |
extended |
the |
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scope |
and variety |
of carbon |
molecules |
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known |
to exist |
and |
is opening |
an |
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entirely |
new |
chapter |
on the |
physics |
and |
chemistry |
of |
carbon, |
with |
many |
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potential |
applications. |
The fullerenes |
can |
be considered |
as another |
major |
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allotrope |
of carbon |
and its first stable, |
finite, discrete |
molecular |
form. |
They |
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are different, |
in that |
respect, |
from |
the |
other two |
allotropes, |
graphite |
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and |
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diamond, |
which |
are |
not |
molecular |
but |
infinite-network |
solids. |
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The |
other |
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known |
carbon |
molecules, |
C, to C,,, |
are unstable |
and found only |
in thevapor |
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phase |
at high |
temperature |
(see Ch. 2, Sec. 5.0). |
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The |
fullerenes |
are |
generally |
arranged |
in |
the |
form |
of |
a |
geodesic |
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spheroid |
and thus |
were named |
after the inventor |
of the geodesic |
dome, |
the |
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renowned |
architect |
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Buckminster |
Fuller. |
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They |
were |
originally |
(and still |
are |
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occasionally) |
called |
“buckminster-fullerenes”, |
a name |
fortunately |
short- |
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ened to fullerenes. |
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They |
are |
also |
known |
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as ‘buckyballs”. |
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1.2Historical Perspective
The fullerenes were discovered |
in 1985 |
by Smalley |
and |
Kroto who, |
while performing mass-spectroscopy |
analysis |
of carbon |
vapor, |
observed |
356
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The Fullerene |
Molecules |
357 |
the presence |
of even-numbered clusters of carbon atoms in the molecular |
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range |
of C, |
- C,,, as illustrated in Fig. 15.1 .tlj-M The |
experiment |
was |
canied |
out in the apparatus shown schematically in Fig. 15.2, consisting of |
a pulsed laser beam directed onto the surface of a rotating-translating
graphite disk. Clusters of fullerenes |
were generated spontaneously |
in the |
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condensing |
carbon vapor when the hot plasma was quenched by a stream |
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of helium. |
This research |
provided the clue that led to the elucidation |
of the |
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fullerene |
structure. |
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The practical synthesis of fullerenes |
as solid aggregates was demon- |
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strated by Kratschmer and Huffman |
in 1990, by the simple evaporation of |
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a graphite electrode as will be described |
in Sec. 5.0.t4] |
Fullerenes are now |
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readily available in increasing quantities |
for study and evaluation. |
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These |
discoveries |
generated |
considerable interest in the scientific |
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community |
and in the general public, as demonstrated |
by the number of |
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publications |
on the subject, estimated to total nearly one thousand in 1993, |
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only eight years after the fullerenes |
were first observed. |
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'00 |
'11 I |
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60' |
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80
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h A |
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20 |
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40 |
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60 |
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80 |
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100 |
120 |
Cluster Size
Figure 15.1. Time-of-flight mass spectrum of carbon clusters produced by laser vaporization of graphite.[*]
358 Carbon, Graphite, Diamond, and Fullerenes
ton Detector
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Pulsed |
Cluster |
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Vaporization |
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High Pressure |
Growth |
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Laser |
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Helium (10 atm) |
Zone |
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t |
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Time-of-Flight |
Lias |
Beam |
Mass |
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Rotating |
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Spectrometer |
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JPPet |
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Translating |
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‘alve |
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disk |
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Seal |
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Figure 15.2. Carbon-cluster beam source with |
pulsed |
laser.121[3] |
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2.0 STRUCTURE |
OF THE FULLERENE |
MOLECULES |
2.1Molecular Structure of the Fuiierenes
Geodesic |
Structure. |
Unlike graphite or diamond, |
the fuiierenes are |
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not a single material, but a family of molecular, geodesic |
structures |
in the |
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form of cage-like |
spheroids, |
consisting of a network of five-membered |
rings |
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(pentagons) and six-membered rings (hexagons). In order to close |
into a |
spheroid, these geodesic structures must have exactly twelve pentagons,
but can have a variable number of hexagons (m), with the general composition: C20+2m. Such an even-numbered distribution is unique to the
element carbon.
Atomic Bonding. in order to account for the bonding of the carbon
atoms of a fuiierene |
molecule, the hybridization must be a modification of |
the sp3 hybridization |
of diamond and sp2 hybridization of graphite (see Ch. |
2, Sets. 3.0 and 4.0). |
It is such that the sigma (a) orbitais no longer contain |
ail of the s-orbital character and the pi (z) orbitals are no longer of the purely p-orbital character, as they are in graphite.
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The Fullerene |
Molecules |
359 |
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Unlike |
the |
sp3 or sp2 hybridizations, |
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the |
fullerene |
hybridization |
is not |
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fixed |
but has |
variable |
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characteristics |
depending |
on the |
number |
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of carbon |
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atoms |
in the |
molecule. |
This number varies from twenty |
for |
the |
smallest |
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geometrically |
(but |
not |
thermodynamically) |
feasible |
fullerene, |
the |
C20. to |
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infinity |
for graphite |
(which |
could |
be considered |
as the |
extreme |
case of all |
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the |
possible |
fullerene |
structures). |
It determines |
the |
size |
of the molecule |
as |
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well |
as the angle |
0 |
of the basic pyramid |
of the structure |
(the common |
angle |
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to the |
three |
u-bonds). |
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The number |
of |
carbon |
atoms, |
the pyramidization |
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angle |
(0 - |
903, |
and |
the |
nature |
of |
the |
hybridization |
are |
related |
and |
this |
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relationship |
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(in |
this |
case |
the s |
character |
in |
the n-orbital) |
is |
given |
in |
Fig. |
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15.3.[51 |
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The bond lengths |
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of the fullerenes |
are reported |
as 0.145 |
+/-0.0015 |
nm |
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for the bonds |
between |
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fiveand six-membered |
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rings, and |
0.140 |
+/- 0.0015 |
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nm for the |
bond |
between |
the six-membered |
rings.f6) |
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5 |
10 |
15 |
Pyramidalization Angle (8,,-90)”
Figure 15.3. Hybridization of fullerene molecules as a function of pyramidization angle (&XT - 907. @an is the common angle of the three CTbonds.[5]
360 Carbon, Graphite, Diamond, and Fullerenes
2.2 Characteristics of the Fuilerene Molecules
General Characteristics. The fullerene structure is unique in the sense that the molecules are edgeless, chargeless, and have no boundaries, no dangling bonds, and no unpaired electron. These characteristics
set the fullerenes apart from other crystalline structures such as graphite or diamond which have edges with dangling bonds and electrical charges.p)
Such features allow these molecules, and particularly the C, which is the most symmetrical, to spin with essentially no restraint at a very high rate.R
The Fullerene Family. Many fullerene structures are theoretically possible, some with hundreds of atoms. Five have been unambiguously identified and structurally characterized so far: the C,, &, &, C,s, and c,.m
. At one end of the fullerene family is the CZO,the simplest structure, which is composed of twelve pentagons with no hexagon and with a pyramidization angle of 18”. All its atoms would have the sp3 configuration but it is thermodynamically unstable.fe)
•The first stable fullerene and the first to be discovered is the C,. It is the dominant molecule with sixty carbon atoms arranged so that they form twenty hexagons, in addition to the necessary twelve pentagons, giving it the appearance of a soccer ball (known as a football outside the U.S.A. and U.K.). Each hexagon is connected to alternating pentagon and hexagon, and each carbon atom is shared by one pentagon and two hexagons. Its hybridization is partially sp3 and partially sp2, with a
pyramidization angle of 11.6”. It is shown schematically
in Fig. 15.4. |
The C, |
has a calculated diameter |
of 0.710 |
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t/- 0.007 nm. It is intensely |
purple in apolar solvents.fr)f6) |
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. The higher |
fullerenes |
are |
shown schematically |
in Fig. |
15.5.p) The Cr, is the second most prominent fullerene. It has a rugby-ball appearance and is has a deep orange-
red color in solution. The CT6 is chid with a structure
consisting of a spiraling arrangement of pentagons and hexagons.t9) It has a bright yellow-green color in solution
The Fullerene Molecules 361
and in the crystal. The Cr, is chestnut brown or goldenyellow and the C,, is olive-green. The electronic absorption spectra for these fullerenes is shown in Fig. I 5.6.t61
. As the number ofcarbon atoms increases, the s-character in the x-orbital becomes less and less pronounced to become zero in the case of the ideal graphite crystal, when the pyramidization angle is zero and the number of atoms is infinite.
Figure 15.4. Schematic of a C,, fullerene molecule.
362 Carbon, Graphite, Diamond, and Fullerenes
c70
c76
c78
Figure 15.5. Schematic of GO, C,,, and C,, fullerene rnolecules.~]
The Fullerene Molecules 363
x20
tL c70
C78
200 300 400 500 600 700 800 900
Wavelength (nm)
Figure 15.6. Electronic-absorption spectra of fullerenes in solution (C,, and GO in hexane, G, and C,, in dichloromethane).v]
364 Carbon, Graphite, Diamond, and Fuiierenes
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Related Structures. |
it appears |
that |
the spheroid |
fuiierenes |
such |
as |
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C, |
are not the |
only type of large curved |
carbon |
molecules. |
Geometrically, |
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many |
such |
structures |
are feasible.tlOl |
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iijima and |
coworkers |
have actually |
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detected |
carbon molecular |
structures |
by transmission |
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electron |
microscopy |
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that |
are |
in |
the |
form |
of |
cylindrical |
tubes, |
closed |
by |
polyhedral |
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caps |
and |
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known |
as “buckytubes”. |
These structures |
have |
the |
hexagons |
arranged |
in |
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a helix |
around |
the tube axis and some |
have a negative |
curvature.[ll] |
The |
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defect |
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in |
the |
hexagonal |
network |
that |
triggers |
the |
formation |
of |
such |
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structures |
is believed |
to be a single |
heptagonal |
ring. |
Some |
of these tubes |
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are |
whisker-like |
and |
may |
reach micron |
size. |
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2.3Mechanism of Formation
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As described |
by |
Smalley, |
the |
formation |
of a |
fuiierene |
follows |
an |
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“efficient mechanism |
of self-assembly |
of an architecturally |
useful |
structure |
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on a nanometer |
scale.“f2t |
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The isolated Pentagon Rule. A model |
of the |
growth |
mechanism |
of |
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thefullerenes |
is based |
on the isolated |
Pentagon |
Rulewhichstates |
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that such |
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geometrical |
structure |
must |
meet |
the |
following |
three |
criteria: (a) it must |
be |
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made |
only |
of hexagons |
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and pentagons, |
(b) it must |
have |
twelve |
pentagons, |
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and (c) it must |
not include |
adjacent |
pentagons.[2tmt12j |
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This |
last criterion |
is also requiredfrom |
the thermodynamicsstandpoint |
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since |
the |
fusion |
of |
two |
pentagons |
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is |
not |
favorable |
energetically |
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due |
to |
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increased |
ring |
strain, |
and |
carbon |
structures |
with |
adjacent |
pentagons |
are |
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unstabie.p] |
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The C, |
is the |
first fullerene |
that |
avoids abutting |
pentagons. |
it |
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is the |
most |
stable |
and |
symmetrical |
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of |
all |
the |
stable |
fullerene |
molecules. |
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Smallergeodesicstructures, |
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such |
asthe |
C,, |
mentioned |
above, |
cannot form |
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or be stable |
since |
they |
would |
incorporate |
abutting |
pentagons. |
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Formation. It had been |
originally |
suggested |
that the molecule |
begins |
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as a graphitic |
network |
that |
adds carbon |
atoms |
as pentagons |
(in addition |
to |
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the graphitic |
hexagons) |
causing |
the |
sheet |
to |
curl |
and |
eventually |
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close |
to |
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form |
a |
geodesic |
sphere. |
A |
more |
likely |
mechanism |
is formation |
by |
the |
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aggregation |
of |
small |
carbon |
radicals.f21 |
This occurs |
when |
graphite |
is |
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vaporized |
at very |
high |
temperature. |
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The condensing |
free-flowing |
graphitic |
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sheets |
in the vapor |
have |
no atoms |
to form |
dangling |
bonds and the |
physical |
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tendency |
to reach |
the |
lowest |
energy |
level |
induces |
them |
to curl |
and |
anneal |
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into the |
fullerene |
structure.t3tf13] |
A hypothetical |
growth |
sequence |
is shown |
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in Fig. |
15.7.R |
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The Fullerene Molecules 365
Figure 15.7. Hypothetical growth sequence of a C,, molecule.[31