Important information should be included in this paper
1. First time in situ observation of fullerene shrinkage under Joule heating condition
(similar process for carbon onion has been observed under electron irradiation).
2. The linear sublimation rate implies that carbon atoms are departed from pentagons
only.
3. Such a process is very close to the ‘shrink and wrap’ process of fullerenes observed
by Smalley in laser heated experiments but under very different condition. The
‘shrink and wrap’ occurs at very high temperature and the sublimation time scale is
very short (e.g., ms). This experiment occurs at relatively low temperature and whole
process occurs in a very long time (~ 1 hour).
4. As a reverse process of fullerene nucleation, the experiment provides some useful
information about the fullerene growth mechanism (a strong proof to recent ‘hot
giant’ mechanism)
5. Theory reveal that carbon atom removal from the pentagon cost lower energy than
from other places but create extra defects, a 5|7 pair. Annealing the extra defect can
be done by gliding or climbing the 5|7 to another pentagon.
Organization of the paper:
1. Introduction part should include short history of fullerene; update understanding
of fullerene growth; shrink and wrap experiments; different from onion
shrinkage observed under electron irradiation.
2. Experimental part includes experimental condition, formation of giant fullerene
(in supporting materials); sublimation process of the giant fullerene; linear
sublimation rate; little discussion about the ‘hot giant’ mechanism.
3. Theoretical part includes C2 removal from different places in a fullerene surface;
explanation of linear sublimation rate; mechanism of defects annealing in the
fullerene surface.
4. Summary of the paper: First in situ observation of giant fullerene sublimation
under thermal condition; linear sublimation rate been understood by the
energetic preferred C2 removal from pentagons.; Annealing of defects by the
collaboration of pentagons.
Suggestions
1. Maybe add a Figure about ‘Rice Mechanism’ to the supporting material (Figure S1)
2. Adding the fullerene formation figure as supporting material (Figure S2)
3. Change C1270 to C1300 since 1270 is too precise and actually there no way to measure
the exact mass of a large fullerene up to that level.
In-situ shrinkage of giant fullerenes: direct evidence to
the “shrink-wrap” fullerene formation mechanism
Jianyu Huang*
Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque
87123, USA
Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA
Fend Ding, Kun Jiao, Boris Yakobson
ME&MS Department, Rice University, Houston, TX 77005, USA
We report the first in-situ atomic-scale evidence on the shrinking process of giant
fullerenes under thermal condition. Giant fullerenes are formed in-situ inside a joul
heated multi-walled carbon nanotube at high temperatures. Prolonged annealing of
the giant fullerenes leads them to shrinking all the way down to its bitter end. The
mechanism of the shrinkage was studied by theoretical calculation and simulation,
which showed that C2 pairs were removed predominantly from the pentagon sites,
and the pentagons acted as both sources and sinks of pentagon-heptagon (5|7)
defects. The glide and climb of a 5|7, which were attributed to the C-C bond flipping
and Carbon atom removal respectively, were responsible for the continuous
shrinkage and healing of defects during the shrinkage of the fullerenes.
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 nanotechnology. 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. As an alternative method the reverse process, fullerene sublimation
was used to study its growth and attract many attentions.(ref. paper about C60 subliamtion
experiments) Very recently, Marukuma et al., propose a ‘hot giant’ mechanism about C60
nucleation: at very high temperature,(ref. hot giant papers) the initial nucleated large
fullerenes may release the carbon atoms until the size of C60. But no direct evidence to
support such a growth route.
In 199x, R. Curl, S. O’Brien and R. Smalley et. al. proposed a ‘Rice mechanism’
when they studied the “shrink-wrap” of C60. (S. C. OBrien, J. R. Heath, R. F. Curl, R. E.
Smalley, J. Chem. Phys. 1988, 88, 220-230.)1 The ‘Rice Mechanism’ basically requires a
pre-bond rotation (or Stone-Wales/SW)) step to create an adjacent pentagon pair (5|5)
(which is similar as an ad-dimmer in graphene or carbon nanotube (CNT) surface) as the
first step. (See supporting materials Figure S1) Eliminating C2 molecular from the
adjacent of 5|5 is the most energetically favored path due to creating no extra defects 5.
Experimental observation shows that, via such a clean mechanism, a fullerene can reduce
its size down to ~C32 in sphere shape in spite of its initial size. For fullerenes smaller or
little larger than C60 (e.g., C62, C64, C66 and C68), the SW transformation isn’t a necessary
step because the violation of isolated pentagon rule (IPR) ensures the existence of
adjacent pentagons in these fullerene. For fullerenes little larger than C60 (e.g., C70), one
or two pre-SW steps are enough to create a 5|5 structure and thus the ‘Rice’ mechanism is
applicable as well. However, if the fullerene is so large that pentagons are far from each
other (e.g., two neighboring pentagons are separated by 5 hexagons in the surface of
icosahedral C_720), many high barrier SW steps are required to create a 5|5 formation
and thus such a clean mechanism is not applicable. Early experiments suggested that the
large fullerenes have fragmented by successive losses of C2 and higher even-numbered
units when it is heated by laser. (Samlley)
Carbon onion composes two or more concentric fullerenes and its shrinkage under
electron irradiation was well studied for a long time. (Banhart and Ajayan’s work)
Although the geometry behavior during onion size reduction is very close to that of
fullerene sublimation, they are different in many aspects. For example, under irradiation,
carbon onion often has a spherical shape but the ground structure of a large fullerene is a
polyhedron with 12 vortexes; the layer-layer interaction is very important and the high
pressure accumulated inside the onion can even induce a phase transition from graphene
layers to nanodiamond; the shrinkage of the inner layers must emitting some carbon
atoms that needs to diffuse away from inside to the surface; Furthermore, high
concentration electron irradiation obvious will create a lots of defects in each layer.
In this letter, we report a first time in-situ high-resolution transmission electron
microscopy (HRTEM) observations and a theoretical model of the continuous shrinkage
of large fullerene until total disappearance by Joel heating. During the shrinkage process,
the fullerene maintained a perfect closed cage structures and polyhedral shapes until C330,
and then they becomes almost spherical until C60, after which the cage structure is opened
and then disappeared rapidly. The results provide the first electron microcopy evidence
for the ‘hot giant’ fullerene growth mechanism. Atomic simulation supports our
experimental results reveal that sublimation of large fullerene is via a different channel
from the ‘Rice’ mechanism.
Experiment
Our experiments were conducted inside a JEOL 2010F HRTEM equipped with a
Nanofactory TEM-STM system. The experimental procedure has been described
previously6. In brief, individual MWCNTs were subjected to electric breakdown, after
which large fullerenes were frequently observed inside the cavity or on the outer surface
of the MWCNTs. The formation of these large fullerenes is a solid-solid diffusion
process, and no gas phase was involved, which is different from the arc discharge
procedure. (See supporting materials Figure S2) These larger fullerenes were then
annealed at high temperatures induced by high bias voltage Joule heating.
Our previous experiments proved that the MWCNTs were heated to temperatures
higher than 2000 C at high bias voltages 6. At such high temperatures and inside the high
vacuum (<10-5 Pa), we found the continuous shrinkage of large fullerenes due to the
sublimation of carbon atoms.
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 Supporting Movie M1). Initially two giant fullerenes (Fig. 1a, ~C1100 for the upper
one, ~C1300 for the lower one) present in the cavity of the MWCNT. The C1100 is
rectangular, while the C1300 is polyhedral. The C1300 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 C1300 continues to shrink and maintains its polyhedral shape until
the formation of ~C330 (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)
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=N 0e-t, where N0
is the initial number of atoms, and t is time). The reason for this contradiction is
explained later.
Fig1. (a). (a-p) Continuous shrinkage of a giant fullerene (C1300) 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.
Theoretical Analysis
Semi-empirical PM332 method is used to calculate the reaction energy of losing C1
and C2 from fullerene C320, in which the distance between two neighboring pentagons is
0.95 nm. The reaction energies of removing C1 and C2 from different sites are showed in
Fig 2.
Figure 2. Energy cost of removing C2 and C1 from different places in the fullerene C320.
The energy cost for removing a C2 from a ring of pentagon is about 3.0 eV lower than
that from the hexagonal lattice because the former create a di-vacancy (5|8|5) but the later
only create a pentagon-heptagon pair (5|7). Calculation also indicates that, without
respect of the removal site, removing C2 always costs lower energy than C1, which is in
agreement with the well know experimental fact that carbon sublimation from fullerene is
in the unit of C2.7
From thermal dynamics point of view, 3.0 eV energy differences cause a huge
thermal probability differences, e-E/kT~10-6, at the experimental temperature, T~2000 oC.
With so huge thermal probability difference, the constant sublimation rate can be easily
understood. For a large fullerene contains a few thousands carbon atoms, the thermal
ratio of carbon departure from hexagonal lattice is ~10-4 of that from pentagon ring. So
during the sublimation process, almost all carbon atoms are been eliminated from the 12
pentagons in the fullerene surface. If all the generated defects during C2 sublimation can
be healed efficiently, the number of pentagons in the fullerene will keep constant. Thus
the sublimation rate mains steady, because 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 high quality during the sublimation.
Fig 3. A pentagon acts as both a source and a sink 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 3 ab shows the defect formation after removing a C2 from a pentagon. A 5|7|5
topological defect formation was created after the C2 removal. The 5|7|5 can be viewed as
a pentagon plus a 5|7 pair, 5+5|7, which means an extra topological defects, 5|7 pair, was
created after the C2 removal. Hence removing C2 from isolated pentagon is less clean
than the ‘Rice mechanism’.
The topological defect, 5|7, created after C2 removal is well known a two
dimensional (2D) edge dislocation in 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 C 2
from the pentagon leads the 5|7 climb one step simply. So the 5|7 is mobile in the
fullerene surface at the sublimation temperature. Once a 5|7 meet another pentagon it
may be annealed by another C2 removal or a SW bond rotation. Generally, there are two
principle ways to anneal topological defects in the fullerene: two adjacent pentagons with
one heptagon can be annealed to one pentagon by removing a C2 (cd in fig.3) and two
separated pentagons and a heptagon can be annealed to a pentagon by rotating a C-C
bond (ef in fig. 3). Above analysis shows that pentagon can be taken as both the source
and drain of topological defects (e.g, 5|7) in fullerene surafce.
It is interesting to note that 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 the extra 5|7 topological defect is by 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.
A modified Monte-Carlo dynamic simulation was used to study the carbon removal
channel and the sublimation process of large fullerene. The initial fullerene is an
icosahedral C720. 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. Follow the C2 removal, the most
energetic preferred bond rotation was performed to annealing the topological defect
formation until the energy can’t be further reduced by any possible SW transformation.
The simulation was performed with the Tesorff-Brenner potential31.
Fig 4abcd show a typical process of annihilate 5|7 defect observed in the
dynamic simulation. This process start with two separated pentagons in the fullerene
surface (a). The created 5|7 climbs one step by another C2 removal (bc) and then it was
annihilated by one SW step (cd).
a
b
c
d
Figure 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).
With efficient annealing, a large fullerene can avoid big hole formation and maintain
its high quality close structure during the sublimation process. The snapshots in Fig. 4
clearly show that the large fullerene has polyhedron structure as experimentally observed.
Discussion and Conclusion
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 prove that such a “shrink-wrap” mechanism indeed operates
during the fullerene formation process. Our results also agree 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.
In summary, large fullerenes produced by electric breakdown of carbon nanotubes
were found to shrink continuously until the formation of a C60, and finally the C60
disintegrated and vanished. The shrinkage process involved both C2 pair removal and SW
transformation. In this context, the present paper provides the first microscopic
explanation for a series of novel phenomena observed in carbon nanotubes and fullerenes
at high temperatures. Theoretically analysis indicates that the constant sublimation rate
during is related to the energetic preferred sublimation channel from the pentagons. And
after each removal, the annealing of the created 5|7 topological defect is very important to
maintain the high quality fullerene structure.
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 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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Supporting Materials:
Supporting Figure S1. HRTEM images showing the fullerene formation on the carbon
nanotube surfaces when the nanotubes are Joule heated to high temperatures. (a) and (b)
are the same nanotube before and after Joule heating, respectively. The bias voltage is
2.14 V and the current is 107 A. The arrowheads point out single shell giant fullerenes.
Supporting Figure S2, Theoretical model show that how Shrink-Wrap works on C60. It
need pre-bond-rotation, and create two adjacent pentagons. Removing C2 from adjacent
pentagons will create no any extra defects.
Supporting Movie M1