Journal ArticleDOI

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.
Topics: , Carbon nanotube (61%), Carbon nanobud (57%), Carbon (53%)

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T. Yildirim,
1
O. Gu
¨
lseren,
1,2
C¸. Kılıc¸,
3
and S. Ciraci
3
1
NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
2
Department of Materials Science, University of Pennsylvania, Philadelphia, Pennsylvania 19104
3
Physics Department, Bilkent University, Ankara 06533, Turkey
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
3
rehybrid-
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,
1,2
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.
3–5
The physical
properties can also be altered by intertube interactions be-
tween nanotubes packed in hexagonal lattices, as so called
‘‘nanoropes.’’
The intertube interactions in nanoropes can be probed by
applying external pressure to vary the intertube distance.
6–8
For fullerenes, such high-pressure studies have yielded many
interesting results including new compounds such as the
pressure-induced polymeric phases of C
60
.
9
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.
10
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.
8
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.
8
Motivated
by these reports, we investigated possible new pressure-
induced ground-state structures for (n,0) nanotube ropes
11
from ﬁrst-principles total energy calculations using the pseu-
dopotential method within the generalized gradient
approximation
12
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
60
.
9
The ﬁrst-principles total energy and electronic structure
calculations were carried out using the pseudopotential plane
wave code
CASTEP.
13
We used plane waves with an energy
cutoff of 500 eV. With this cutoff and using ultra soft pseu-
dopotentials for carbon,
14
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.
15
This method has
already been applied to many carbon systems, including
fullerenes and cubane with remarkable success.
16
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
7,0 nanotube lattices. The inter-
linked structure shown in c has
lower energy than vdW packed
7,0 nanotubes shown in b.
PHYSICAL REVIEW B 15 NOVEMBER 2000-IVOLUME 62, NUMBER 19
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 therefore 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 3 hybridization. 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 behavior. 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 20 C 20 C 24 C 24 C 28 C 28 C 36 C 36 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 3 ) 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 3 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 12 649BRIEF REPORTS 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. 17 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 60 molecules 20 meV/atom. 18 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 2 E/da 2 13.7 eV/Å 2 ) than the 1D interlinked phase (d 2 E/da 2 3.3 eV/Å 2 ) and sixteen times stiffer than the vdW nanoropes (d 2 E/da 2 0.8 eV/Å 2 ). 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 C–C 1.644 Å, is signiﬁcantly elongated for an sp 3 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. 5 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. d C–C indicates the smallest distance between two carbon atoms of nearest neighbor nanotubes. 12 650 PRB 62 BRIEF REPORTS which is found to be a band insulator with a band gap of 2 eV. 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 3 bonded square carbon rings, while other parts consist of graphitelike sp 2 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 3 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 ¨ BI ˙ TAK under Grant No. TBAG-1668197 T 116. 1 S. Iijima, Nature London 354,561991. 2 S. Iijima, T. Ichihashi, and Y. Ando, Nature London 356, 776 1992. 3 N. Hamada, S. Sawada, and A. Oshiyama, Phys. Rev. Lett. 68, 1579 1992. 4 C. J. Park, Y. H. Kim, and K. J. Chang, Phys. Rev. B 60, 10 656 1999. 5 O. Gu ¨ lseren et al. unpublished. 6 J. R. Wood, M. D. Frogley, E. R. Meurs, A. D. Prins, T. Peijs, D. J. Dunstan, and H. D. Wagner, J. Phys. Chem. B 103, 10 388 1999. 7 U. D. Venkateswaran, A. M. Rao, E. Richter, M. Menon, A. Rinzler, R. E. Smalley, and P. C. Eklund, Phys. Rev. B 59, 10 928 1999; A. K. Sood, Pallavi V. Teredesai, D. V. S. Muthu, R. Sen, A. Govindaraj, and C. N. R. 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B 62, 7625 2000. 17 We note that the transition path should be calculated in order to obtain the actual barriers between the different phases, which is not done in this paper. 18 G. B. Adams, J. B. Page, O. F. Sankey, and M. O’Keeffe, Phys. Rev. B 50, 17 471 1994. PRB 62 12 651BRIEF REPORTS Citations More filters Journal ArticleDOI Abstract: We investigate curvature effects on geometric parameters, energetics, and electronic structure of zigzag nanotubes with fully optimized geometries from first-principle calculations. The calculated curvature energies, which are inversely proportional to the square of radius, are in good agreement with the classical elasticity theory. The variation of the band gap with radius is found to differ from simple rules based on the zone folded graphene bands. Large discrepancies between tight binding and first-principles calculations of the band gap values of small nanotubes are discussed in detail. 223 citations Journal ArticleDOI Salim Ciraci1, Sefa Dag1, Taner Yildirim2, Oguz Gulseren1 +2 moreInstitutions (3) Abstract: Carbon nanotubes, in which the two-dimensional hexagonal lattice of graphene is transformed into a quasi-one-dimensional lattice by conserving the local bond arrangement, provide several structural parameters for engineering novel physical properties suitable for ultimate miniaturization. Recent interest in nanoscience and nanotechnology has driven a tremendous research activity in carbon nanotubes, which has dealt with a variety of problems and produced a number of new results. Most of the effort has gone into revealing various physical properties of nanotubes and functionalizing them in different ways. This paper covers a narrow region in this enormous research field and reviews only a limited number of recent studies which fit within its scope. First, we examine selected physical properties of bare carbon nanotubes, and then study how the mechanical and electronic properties of different tubes can be modified by radial strain, structural defects and adsorption of foreign atoms and molecules. Magnetization of carbon nanotubes by foreign atom adsorption has been of particular interest. Finally, we discuss specific device models as well as fabricated devices which exploit various properties of carbon nanotubes. 114 citations Journal ArticleDOI Boris Ni1, Rodney Andrews2, David Jacques2, Dali Qian2 +4 moreInstitutions (3) Abstract: The modification of bundled single-walled and multiwalled carbon nanotubes is examined using a combination of computational and experimental methods. The computational approach is classical molecular dynamics simulations using the many-body reactive empirical bond-order potential parametrized by Brenner. The simulations consider the deposition of CH3+ at incident energies of 10, 45, and 80 eV. They predict the chemical functionalization of the nanotubes, the formation of defects on the nanotube walls, and the formation of cross-links between neighboring nanotubes or between the walls of a single nanotube. They also illustrate the manner in which the number of walls in the nanotube and incident energy affect the results. In the experiments, multiwalled nanotubes with about 40 shells (average diameter of 25 nm) are synthesized by chemical vapor deposition. CF3+ ions are deposited at incident energies of 10 and 45 eV, and then the nanotubes are examined with X-ray photoelectron spectroscopy and scanning elec... 112 citations Journal ArticleDOI Abstract: We performed high pressure resonant Raman experiments on well characterized purified single-wall carbon nanotubes up to40\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$using argon as pressure transmitting medium. We used two different excitating wavelengths, at$632.8\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$and$514.5\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. In contrast with other studies no clear sign of phase transformation is observed up to the highest studied pressure of$40\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. Our results suggest that the progressive disappearance of the radial breathing modes observed while increasing pressure should not be interpreted as the sign of a structural phase transition. Moreover, a progressive change of profile of the tangential modes is observed. For pressures higher than$20\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$the profile of those modes is the same for both laser excitations. We conclude that a progressive loss of resonance of single-wall carbon nanotubes under pressure might occur. In addition, after high pressure cycle we observed a decrease of intensity of the radial breathing and tangential modes and a strong increase of the$D\$ band.

97 citations

Journal ArticleDOI
Boris Ni1, Susan B. Sinnott1Institutions (1)
Abstract: Classical molecular dynamics simulations are used to investigate the responses of bundles of single-walled carbon nanotubes to compressive and shear forces between two sliding diamond surfaces The forces on the atoms in the simulations are determined using a many-body reactive empirical potential for hydrocarbons coupled to Lennard–Jones potentials The simulations predict that the nanotubes can be subjected to high shear forces prior to wear because of their flexibility The response to the applied shear forces is sliding of the bundle or a combination of sliding and rolling, where the exact responses depend on the orientation and bonding of the nanotube bundle to the sliding surfaces No rolling of carbon nanotubes against other nanotubes in the bundle is predicted to occur in any of the orientations considered

88 citations

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