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Journal ArticleDOI

Pressure-induced interlinking of carbon nanotubes

15 Nov 2000-Physical Review B (American Physical Society)-Vol. 62, Iss: 19, pp 12648-12651

Abstract: We predict new forms of carbon consisting of one- and two-dimensional networks of interlinked single-wall carbon nanotubes, some of which are energetically more stable than van der Waals packing of the nanotubes on a hexagonal lattice. These interlinked nanotubes are further transformed with higher applied external pressures to more dense and complicated stable structures, in which curvature-induced carbon ${\mathrm{sp}}^{3}$ rehybridizations are formed. We also discuss the energetics of the bond formation between nanotubes and the electronic properties of these predicted novel structures.

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Pressure-induced interlinking of carbon nanotubes
T. Yildirim,
O. Gu
C¸. Kılıc¸,
and S. Ciraci
NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
Department of Materials Science, University of Pennsylvania, Philadelphia, Pennsylvania 19104
Physics Department, Bilkent University, Ankara 06533, Turkey
Received 1 August 2000
We predict new forms of carbon consisting of one- and two-dimensional networks of interlinked single-wall
carbon nanotubes, some of which are energetically more stable than van der Waals packing of the nanotubes
on a hexagonal lattice. These interlinked nanotubes are further transformed with higher applied external
pressures to more dense and complicated stable structures, in which curvature-induced carbon sp
izations are formed. We also discuss the energetics of the bond formation between nanotubes and the electronic
properties of these predicted novel structures.
Carbon nanotubes, originally discovered as by-products
of fullerene synthesis,
are now considered to be the build-
ing blocks of future nanoscale electronic and mechanical de-
vices. It is therefore desirable to have a good understanding
of their electronic and mechanical properties and the interre-
lations between them. In particular, single-wall carbon nano-
tubes SWNT’s provide a system where the electronic prop-
erties can be controlled by the structure of the nanotubes and
by various deformations of their geometries.
The physical
properties can also be altered by intertube interactions be-
tween nanotubes packed in hexagonal lattices, as so called
The intertube interactions in nanoropes can be probed by
applying external pressure to vary the intertube distance.
For fullerenes, such high-pressure studies have yielded many
interesting results including new compounds such as the
pressure-induced polymeric phases of C
It is, therefore,
of interest to inquire if similar covalent bonding can occur
between the nanotubes in a rope. This could have important
consequences for nanoscale device applications and compos-
ite materials that require strong mechanical properties since
nanoropes consisting of interlinked SWNT will be signifi-
cantly stronger than nanoropes composed of van der Waals
packed nanotubes.
A recent Raman study on SWNT ropes carried out up to
25.9 GPa Ref. 7 showed that the mode intensities and en-
ergies are not completely reversible upon pressure cycling,
suggesting irreversible pressure-induced changes in the
structure. In another high-pressure study Chesnokov et al.
observed a very large volume reduction and high compress-
ibility, signaling the presence of a microscopic volume-
reducing deformation other than van der Waals compression.
Some of these pressure-induced effects are tentatively attrib-
uted to possible crushing or flattening the nanotube cross
section from circular to elliptical or hexagonal.
by these reports, we investigated possible new pressure-
induced ground-state structures for (n,0) nanotube ropes
from first-principles total energy calculations using the pseu-
dopotential method within the generalized gradient
GGA. We observed an elliptical distortion
of the nanotubes under pressure and subsequent curvature-
induced carbon rehybridization, giving rise to one- or two-
dimensional interlinked networks of nanotubes. This is
somewhat reminiscent to the pressure-induced polymeriza-
tions of C
The first-principles total energy and electronic structure
calculations were carried out using the pseudopotential plane
wave code
We used plane waves with an energy
cutoff of 500 eV. With this cutoff and using ultra soft pseu-
dopotentials for carbon,
the total energy converges within
0.5 meV/atom. For the Brillouin zone integration, we used
between 3 3 6to5 5 7 k points according to the
Monkhorst-Pack special k-point scheme.
This method has
already been applied to many carbon systems, including
fullerenes and cubane with remarkable success.
In this report, we present calculations on nanoropes con-
sisting of 5,0, 6,0, 7,0, 9,0, and 6,6 nanotubes. For
simplicity, we model the nanoropes as a hexagonal lattice of
nanotubes. We further assume that we have only one nano-
tube per unit cell. 6,0 nanotubes are perfectly compatible
with the hexagonal lattice i.e.,
120°). However in the
optimized structure, hexagonal carbon rings of one nanotube
face hexagonal rings from the neighboring tubes Fig. 1a兲兴.
From studies of fullerenes, we know that the energy can be
reduced by rotating every other tube such that their CC
bonds face the center of the hexagonal faces of the neighbor-
FIG. 1. Optimized structures
of the vdW a兲共6,0, b兲共7,0, and
one-dimensional interlinked c
7,0 nanotube lattices. The inter-
linked structure shown in c has
lower energy than vdW packed
7,0 nanotubes shown in b.
PRB 62
0163-1829/2000/6219/126484/$15.00 12 648 ©2000 The American Physical Society

ing nanotubes. This would double the unit cell for 6,0
nanotubes. We will not pursue this here because we are
mainly interested in the potential for covalent bonding be-
tween nanotubes.
9,0 nanotubes are also compatible with hexagonal sym-
metry. Furthermore the relative orientation of the nanotubes
are optimal energetically i.e., CC bonds face the center of
the hexagonal faces of adjacent nanotubes. 5,0 and 7,0
nanotubes are not compatible with hexagonal symmetry and
is expected to deviate from the ideal value of
120°. We find that when one bond is along the a axis, the
total energy is minimized when the b axis is aligned so that
it brings the CC bonds of one nanotube to the center of
hexagonal faces of adjacent nanotubes. For 5,0 and 7,0
nanotubes this occurs when
(360/5) 1 72.0° and
(360/7) 2 102.857°, respectively. These values are very
close to the values
72.46° and 102.35° obtained from the
first-principles structural optimization.
The pressure dependence of these lattices of nanotubes
was determined by calculating the total energy as a function
of nanotube separation i.e., a and b) while the other param-
eters, including atom positions, c, and
are optimized. We
observe that 7,0 nanotubes become elliptically distorted
with applied pressure i.e., decreasing nanotube-nanotube
distance. At a critical pressure, we observe a structural
phase transformation from the van der Waals nanotube lat-
tice as shown in Figs. 1a and 1b兲兴 to a new lattice in
which the nanotubes are interlinked along the 110 direc-
tion, where the strain of the nanotube is largest Fig. 1c兲兴.
The covalent bonding between nanotubes is therefore the
result of curvature-induced rehybridization of the carbon or-
bitals. The same structural transformation was observed for
the other (n,0) nanoropes and the results are summarized in
Table I. The structure of each of these one-dimensionally
interlinked nanoropes is orthorhombic space group Cmcm),
with two nanotubes per unit cell. The relationship between
the conventional orthorhombic cell and the primitive one is
shown in Fig. 2a.
Figure 2 also shows the local environment of the carbon
atoms involved in the interbonding of the nanotubes for 6,0
and 7,0. In the first case, the covalent bonding occurs be-
tween carbon atoms on two hexagonal rings Fig. 2b兲兴.We
believe this process is slightly less favorable than covalent
bonding between carbons on a hexagonal ring and those in-
volved in an intratube CC bond which occurs for the 7,0
case Fig. 2c兲兴. In both cases, the bond distances are com-
parable to those in diamond, indicating sp
The bond angles vary from about 100° to 120°, indicating
some strain. From Table I, we see that the energy of the
interlinked phase is actually lower than the van der Waals
vdW lattices for 5,0 and 7,0 nanotropes. For the 9,0
nanorope, the energy difference is relatively small. Regard-
less of the energies relative to that of unlinked nanotubes, an
interlinked phase is stable once it is formed, because break-
ing the intertube bonds requires jumping over a significant
energy barrier.
To quantitatively study the bonding mechanism, we cal-
culated the total energies of the different phases as a function
of the lattice constant i.e., applied pressure. The result for
7,0 nanotubes is summarized in Fig. 3. The energies of the
vdW and the one-dimensional interlinked 1DI phases cross
TABLE I. Various structural parameters and the total energies of the optimized structures of (n,0) vdW lattices and one-dimensional
interlinked 1DI nanoropes as shown in Fig. 1. The band gaps of all the structures listed here are found to be zero, indicating metallic
Properties 5,0兲共5,0兲共1DI兲共6,0兲共6,0兲共1DI兲共7,0兲共7,0兲共1DI兲共9,0兲共9,0兲共1DI
Formula C
Space group Cmcm Cmcm P6/mmm Cmcm Cmcm Cmcm P63/mcm Cmcm
a b Å 7.408 7.079 8.364 7.762 9.250 8.432 10.389 9.532
c Å 4.208 4.190 4.212 4.223 4.218 4.205 4.219 4.209
72.46 125.39 120.00 121.96 102.35 119.15 120.00 111.97
Density (g/cm
) 1.8119 2.331 1.8713 2.2176 1.5849 2.1415 1.8213 2.0245
Energy/C eV 155.694 155.802 155.843 155.868 155.946 155.969 156.049 156.042
FIG. 2. a A view along the c axis of the 1D interlinked (n,0)
nanotube lattice. The shaded rectangular region is the orthorhombic
unit cell. Local structure of carbon atoms involved in the intertube
bonding dotted lines between two b兲共6,0 and c兲共7,0 nano-
tubes. The sp
hybridization occurs between two hexagonal faces
for 6,0 nanotubes and between a hexagonal face and a CC bond
for 7,0 nanotubes.
PRB 62

each other at about a 9.0 Å with an energy barrier of only
46 meV/unitcell 552 K. The pressure required to attain this
lattice constant is only about 0.3 GPa for the vdW phase,
indicating that polymerization of vdW 7,0 nanoropes could
occur at modest pressures and temperatures.
Once the in-
terlinked phase is reached, the energy barrier required to
break the bonds and obtain free nanotubes is about 0.7 eV
25 meV/atom, which is comparable to that of 1D polymer-
ized C
molecules 20 meV/atom.
Figure 3 also shows that another interlinked phase of 7,0
nanotubes becomes the ground state for lattice parameter
smaller than 8.0 Å. In this new phase the nanotubes are in-
terlinked along both a and b axes see Fig. 4a兲兴. This two-
dimensional interlinked 2DI structure is about four times
stiffer i.e., d
13.7 eV/Å
) than the 1D interlinked
phase (d
3.3 eV/Å
) and sixteen times stiffer than
the vdW nanoropes (d
0.8 eV/Å
We observe that applying even higher pressures yields
more complicated and denser phases for many of the nano-
ropes studied here see Fig. 4. For 9,0 nanoropes, we find
that the nanotubes are interlinked along three directions
forming a hexagonal network. The length of the intertube
bond, d
1.644 Å, is significantly elongated for an sp
CC bond. The two-dimensional interlinked phase of 7,0
nanotubes is further transformed to a denser structure at 30
GPa Fig. 4c兲兴. By comparison, 6,6 nanotubes do not form
an interlinked structure up to a pressure of 60 GPa. Rather
the nanotubes are hexagonally distorted such that the local
structure of the nanotube faces is similar to that in graphite
sheets Fig. 4c兲兴. Furthermore, releasing the pressure yields
the original structure, indicating that the distortion is purely
elastic. Similar calculations are currently underway for other
(n,m) nanotubes. However, we expect similar results for
other types of tubes.
A detailed discussion of the electronic band structure and
density of states of the predicted structures will be presented
elsewhere, however all the structures reported here except
one in Fig. 4c兲兴 are found to be metal. The dispersion of the
bands near Fermi level in a direction perpendicular to the
tube axis is found to be around 0.5 eV, making the vdW
nanoropes metallic even though the individual tubes are in-
sulating such as 7,0 nanotubes or semiconducting with a
small band gap. The structural changes clearly have strong
effects on the electronic properties and therefore should be
detected in the pressure dependence of various transport
properties of nanoropes. From our calculations we expect
two effects to be observed. First, on the initial pressure cycle
one should observe an irreversible effect in the resistivity
due to the polymerization of the nanotubes. Second, the ap-
plied pressure will induce a reversible deformation of the
circular cross section, which will change the metallic behav-
ior of the nanotubes.
For example, the 7,0 nanorope,
which is found to be metallic at ambient pressure, transforms
to a high-density phase as shown in Fig. 4c at 30 GPa,
FIG. 3. Planar lattice constant variation of the total energy of
7,0 nanotube ropes in three different phases. Inset shows the view
of the structures along the c axis. The zero of energy was taken to
be the energy of vdW packing of the nanotubes.
FIG. 4. Various high density phases of carbon nanotubes. a
Two-dimensional interlinked 2DI structure of 5,0 nanotubes,
consisting of rectangularly distorted nanotubes interlinked on a 2D
network. b A hexagonal network of 9,0 nanotubes, in which
9,0 nanotubes are interlinked along a, b, and 110 directions. c
A very dense structure of 7,0 nanotubes obtained under 30 GPa
pressure. d The optimized structure of 6,6 nanotubes under P
53 GPa. Nanotubes are distorted in such a way that the local
nearest-neighbor structure is somewhat similar to graphite sheets.
indicates the smallest distance between two carbon atoms of
nearest neighbor nanotubes.
12 650 PRB 62

which is found to be a band insulator with a band gap of 2
The new pressure-induced, high-density phases reported
here can also be important host lattices for intercalation and
sorption. For instance, the high-density phase of 7,0 nano-
ropes Fig. 4c兲兴 has an interesting structure in which some
parts of the lattice are very strained containing sp
square carbon rings, while other parts consist of graphitelike
bonded carbon atoms 28% of all atoms. In this struc-
ture, there are still interstitial sites that would accommodate
other species such as alkali metals.
In summary, we have presented first-principles calcula-
tions of the structures and electronic properties of various
nanoropes. We find that small nanotubes in a rope are dis-
torted elliptically with applied pressure and then are co-
valently bonded to each other at the positions of highest
curvature point of nanotubes by sp
hybridization of the car-
bon orbitals. For small nanotubes, the resulting one-
dimensional chains of elliptic carbon nanotube structure are
found to be energetically more stable than the circular van
der Waals nanoropes. Higher applied pressures resulted in
more dense and complicated structures. Thus pressure in-
duced polymerization of the nanotubes may provide a way of
synthesizing novel carbon base materials with interesting
physical properties. For example interlinking of the nano-
tubes may improve the mechanical performance of compos-
ites based on these materials. It will be an experimental chal-
lenge to confirm the structures predicted here. A difference
NMR spectrum of two identical samples; one treated with
pressure and the other not, may give some evidence for the
new phases. Similar difference measurements by ESR and
Raman could be equally valuable.
We thank D. A. Neumann, R. L. Cappelletti, and J. E.
Fischer for many fruitful discussions and critical reading of
the manuscript. This work is partially supported by the Na-
tional Science Foundation under Grant No. INT97-31014
and TU
TAK under Grant No. TBAG-1668197 T 116.
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