In-situ shrinkage of giant fullerenes: direct evidence to
the “shrink-wrap” fullerene formation mechanism
Jian-Yu Huang*,+
Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque
87123, USA
Feng Ding, Kun Jiao, Boris Yakobson
ME&MS Department, Rice University, Houston, TX 77005, USA
*Corresponding author, email: jhuang@sandia.gov; + On leave from Boston College
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Abstract
We report the first in-situ atomic-scale evidence on the “shrink-wrap” formation
mechanism of fullerenes. Giant fullerenes are formed in-situ on the carbon nanotube
surfaces at high temperatures inside a high resolution transmission electron
microscope. Prolonged annealing of the giant fullerenes leads them to shrinking all
the way down to its bitter end. The dynamics of the shrinkage process was revealed
by molecular dynamic simulation, which showed that C2 pairs were removed
predominantly from the pentagon sites, and the pentagons acted as both sources and
drains of pentagon-heptagon (5|7) defects. The glide and climb of a 5|7, which were
attributed to the Stone-Wales transformation and vacancy/interstitial generation,
respectively, were responsible for the continuous shrinkage of the fullerenes.
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Introduction
The discovery of carbon cage structure Buckminsterfullerene (C60)1 has led to an
explosion in research in the physical and chemical properties of carbon nanostructures2-21.
The research in the fullerenes and carbon nanotubes has become the forefront of the
current nanoscience and nanotechnologies. Despite the enormous scientific endeavors in
the carbon nanostructure research in the last twenty years, we found surprisingly that the
formation mechanisms of C60 and its family members of large hollow-cage fullerenes
remain unknown. This is mainly duo to the fact that fullerenes are produced at extremely
crucial experimental conditions, such as very high temperatures, which makes it
impossible to direct observe the fullerene nucleation and growth process by in-situ
electron microscopy.
Nevertheless, a number of fullerene nucleation and growth mechanisms have been put
forward2-18. Among the most significant ones are the “pentagon road” 5-8, the “fullerene
road” 5-8, the “shrink-wrap” mechanism4,5, and the very recent “hot-giant” mechanism9-11.
In the pentagon road5-8. it is assumed that small graphite sheets are formed when the
carbon cluster size passes about 30 atoms, and the pentagons are added to the edges of
the hexagons in the graphite sheets to reduce the dangling bonds. The incorporation of
pentagons causes the sheet to curl up until a cage of C60 is formed. In the fullerene road58
, it is proposed that fullerenes form at cluster size of about C30 (how C30 is formed is
unknown) and grow to C60 by the addition of C2. The “shrink-wrap” mechanism4,5
suggests that giant fullerenes are formed initially from the hot carbon vapor at high
temperatures, and they then shrink continuously by ejecting a C2 upon further annealing
until the formation of a C60. As the fullerene cage shrinks, the bond strain increases until,
at C32, it bursts. The “hot giant” mechanism9-11 is essentially similar to the “shrink-wrap”
mechanism4,5, and it involves the formation of giant fullerenes directly from the hot
carbon vapor first, and then the giant fullerenes shrink to form smaller fullerenes by
losing C2 upon further prolonged annealing. Although the “shrink-wrap” theoretical
model reconciles various experimental results, direct experimental evidence of such a
route is not available.
In this paper, we report a first in-situ atomic scale observations on the fullerene shrinkage
process. Our results agree surprisingly with the “shrink-wrap” theoretical model. We
found that giant fullerenes are formed first at high temperatures, and then the giant
fullerenes shrink continuously all the way down to its bitter end upon prolonged
annealing. Atomic simulation reveals that the shrinkage of the giant fullerenes occurs via
a different channel from the ‘shrink-wrap’ mechanism.
Experimental Results
Our experiments were conducted inside a JEOL 2010F high resolution transmission
electron microscopy (HRTEM) equipped with a Nanofactory transmission electron
microscopy-scanning tunneling microscopy (TEM-STM) system. The detailed
experimental procedure has been described previously22-26. In brief, individual multiwall
carbon nanotubes (MWCNTs) were Joule heated to high temperatures (~2000 C) , after
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which large fullerenes were frequently observed inside the cavity or on the outer surface
of the MWCNTs.
Remarkably, we found that when the giant fullerenes are subjected to prolonged high
temperature annealing, they shrink continuously all the way down to its end. Figure 1 is
consecutive HRTEM images showing the continuous shrinkage of a giant fullerene (see
also Movie M1). Initially two giant fullerenes (Fig. 1a, C1100 for the upper one, C1270 for
the lower one) present in the cavity of the MWCNT. The C1100 is rectangular, while the
C1270 is polyhedral. The C1270 was trapped in the cap of the innermost wall and adapt the
same shape as the innermost wall. The C1100 attached intimately to the lower fullerene
and the sidewall of the innermost wall. Both fullerenes change their shape and reduce
their size continuously at high temperatures (Movie M1). The upper fullerene jumps up
and down frequently. In Fig. 1d, the upper fullerene has already moved out of the field of
view, and in Fig. 1e, it moves back to the field of view and gets in touch with the lower
fullerene at the same location as before. In Fig. 1f, the upper fullerene moves out of the
field of view again and never comes back to its original position. The reason for such
movement is unclear, but it could be due to a static charge in the fullerenes. The C 1270
continues to shrink and maintains its polyhedral shape until the formation of C 330 (Fig.
1j). In between C330 and C60 (Fig. 1n), the fullerenes maintain almost a spherical shape.
The cage structure appears to be opened and disintegrated when its size is less than that
of a C60. Once the cage structure is opened, it bursts instantaneously.
During the fullerene shrinkage process, the number of atoms in the fullerenes decreased
linearly with the time (Fig. 1q), indicating a constant sublimation rate. This contradicts
the normal 2-dimensional (2D) liquid sublimation process, in which the sublimation rate
is proportional to the surface area or the total number of atoms, i.e. dN/dt = -N, where
dN/dt is the sublimation rate, is a constant, and N is the total number of atoms in the
fullerene, and N decreases exponentially with the time (N=N0e-t, where N0 is the initial
number of atoms, and t is time). ref ? The reason for this contradiction is explained later.
The fullerene shrinkage process agrees remarkably with the “shrink-wrap” mechanism,
which suggests that giant fullerenes shrink to smaller ones by ejecting C2 consecutively.
Theoretical modeling
Our molecular dynamic simulation supports our experimental results, and reveals that the
shrinkage of a giant fullerene occurs by removing a C2 predominantly from the pentagon
sites, and then by annealing of the 5|7 defects.
A semi-empirical PM3 method is used to calculate the reaction energy of losing a C1 and
a C2 from a C320, in which the distance between two neighboring pentagons is 0.95 nm,
and the results are showed in Fig 2. The energy cost for removing a C2 from a ring of a
pentagon is about 3.0 eV lower than that from a hexagonal lattice because the latter
creates a di-vacancy (5|8|5), but the former only creates a pentagon-heptagon pair (5|7).
Our simulation also indicates that, regardless of the sites, removing a C2 always costs a
lower energy than removing a C1, which agrees well with the previous experimental
results and theoretical models27.
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From a thermal dynamics point of view, a 3.0 eV energy difference causes a huge
thermal probability differences, i.e. e-/kT~10-6, at the experimental temperature T~2000
C. With such a huge thermal probability difference, the constant sublimation rate can be
easily understood in the following way. For a large fullerene contains a few thousands
carbon atoms, the thermal ratio of carbon atoms departure from a hexagon is ~10-4 of that
from a pentagon. During the sublimation process, almost all the carbon atoms are
eliminated from the 12 pentagons in the fullerene surface. If all the defects generated
during the C2 sublimation process can be healed efficiently, the number of pentagons in
the fullerene will keep a constant. Thus the sublimation rate remains steady, because the
number of sublimation channels, the 12 pentagons, is independent of the fullerene size.
So the experimental observed constant sublimation rate also implies that the fullerene is
in a high quality during the sublimation process.
Interestingly, a pentagon can not only emit but also absorb a 5|7, and it can be considered
as both a source and a drain of a 5|7. The 5|7 is an edge dislocation on 2D hexagonal
lattice. It can glide and climb on a fullerene surface by rotating a C-C bond and removing
C atoms28. At the sublimation temperature, the twelve pentagons in a fullerene surface
can anneal possible high mobility 5|7 efficiently.
Figure 3ab shows the defect formation after removing a C2 from a pentagon. A 5|7|5
topological defect was created after removing a C2. The 5|7|5 can be viewed as a
pentagon plus a 5|7 pair, i.e. 5+5|7, which means that an extra topological defect, a 5|7
pair, was created after removing a C2. Removing a C2 from an isolated pentagon is less
clean than that from the ‘Rice mechanism’ proposed for ‘shrink and wrap’ of a fullerene5.
The topological 5|7 defect created after removing a C2 is a well-known 2D edge
dislocation in a hexagonal lattice. As a 2D edge dislocation, it can glide on the hexagonal
lattice by rotating one of the shoulder bonds of the heptagon. Under the sublimation
condition, it has another possible way of motion: emitting a C2 from the pentagon leading
to the 5|7 climbing up one step28. Once a 5|7 meet another pentagon it may be annealed
by a C2 removal or a Stone-Wales (SW) bond rotation. Generally, there are two principle
ways to anneal topological defects in a fullerene: two adjacent pentagons with one
heptagon can be annealed to one pentagon by removing a C2 (Fig. 3cd), and two
separated pentagons and a heptagon can be annealed to a pentagon by rotating a C-C
bond (Fig. 3ef). The above analysis shows that a pentagon can be taken as both a
source and a drain of a topological defect (e.g, 5|7) in a fullerene surface.
It is interesting to note that a 5|7 can’t be eliminated by the same pentagon where it was
created because the whole structure just restored to its original one. The only way to
eliminate an extra 5|7 topological defect is by its approaching and interacting with
another pentagon in the fullerene surface. There are 12 pentagons in fullerene surface, so
the temporary 5|7 pair can be efficiently annealed.
We now turn to the dynamics of the sublimation process of giant fullerenes. A modified
Monte-Carlo dynamic simulation was used to study the carbon removal channel and the
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sublimation process of the large fullerenes. The initial fullerene is an icosahedral C 720. In
each step, a C2 was removed from the most energetic preferred site in the fullerene after a
full scan of all possible C2 removals. Following the C2 removal, the most energetic
preferred bond rotation was performed to anneal the topological defect until the energy
can’t be further reduced by any possible SW transformation. The simulation was
performed with the Tesorff-Brenner potential. Ref?
Figure 4ad shows a dynamic annihilation process of a 5|7 defect observed in the
simulation. This process starts with two separated pentagons in the fullerene surface (Fig.
4a). The created 5|7 climbs up one step by another C2 removal (Fig. 4bc), and then it
was annihilated by one SW step.
With efficient annealing, a large fullerene can avoid big hole formation and maintain its
high quality close-cage structure during the sublimation process. The snapshots in Fig. 4
(lower panel) show clearly that the large fullerenes have polyhedron structure as observed
experimentally (Fig. 1).
Discussion
It is noted that the beautiful Buckminsterfullerene C60 molecule has dominated
researcher’s attention since its discovery, and the giant fullerenes has since been largely
overlooked. This may partly be attributed to the fact that the earlier mass spectrometers
were unable to resolve large fullerenes5. However, the original mass spectra from the
Rice group as well as that from the Exxon29 indicated clearly that larger fullerenes
beyond C60 is abundant. Moreover, Robert Curl and Sean O’Brien found that larger
fullerenes could shrink to smaller ones by loss of C2, which prompted the Rice group to
propose the “shrink-wrap” mechanism4. Remarkably, our in-situ observations and
molecular simulations proves that such a “shrink-wrap” mechanism indeed operates
during the fullerene formation process. Our results also agree excellently with the recent
proposed “hot-giant” mechanism9-11, which suggests that giant fullerenes are actually the
energetic favored structures at temperatures close to 2000 K, and these giant fullerenes
then shrink continuously by losing C2 upon annealing until its disappearance. In fact,
Smalley attributed the Rice group’s failure to produce large quantity of C60 in their earlier
experiments to the fact that their experimental setup cools too fast to allow for the large
fullerenes to anneal, so that the majority of the product is giant fullerenes5.
Our results provide, to the best of our knowledge, the first experimental evidence of the
vast amount fullerene formation mechanisms that have appeared in recent years. The
important “shrink-wrap” theoretical model has been verified.
Acknowledgement: Sandia is a multiprogram laboratory operated by Sandia Corporation,
a Lockheed Martin Company, for the United States Department of Energy’s National
Nuclear Security Administration under contract DE-AC04-94AL85000. The project at
Sandia is supported by BES, and at Rice University is supported by , which are greatly
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acknowledged. JYH would like to thank Dr. S. Chen for making the STM probe, and Drs
S.H. Jo and Z.F. Ren for providing the nanotube samples.
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Figure Captions
Fig. 1 (a-p) Continuous shrinkage of a giant fullerene (C1270) trapped inside the cavity of
a MWCNT at high temperatures. The bias voltage in the MWCNT is 2.26 V and
the current is reduced from 140 A to 110 A during the fullerene shrinkage
process. (q) The number of carbon atoms in the fullerenes decreased linearly with
time during the sublimation process.
Fig. 2 Energy cost of removing a C2 and a C1 from different sites in the fullerene C320.
Fig. 3 A pentagon acts as both a source and a drain of 5|7. (ab) Removal of a C2 from
a pentagon creates a 5+5|7 defect; (cd) when a 5|7 approaches to a pentagon,
removal of a C2 annihilates the 5|7 defect; (ef) a bond rotation step annihilates a
5|7 in the vicinity of a pentagon, and the inverse process creates an additional 5|7.
Fig. 4 Typical C2 removal process and the annihilation of 5|7 defects in the large
fullerene surface (abcd, upper panel), and snapshots of the shrinking of
fullerenes during the simulation process (lower panel).
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