- Email: [email protected]
Carbon nanotube encapsulated fullerenes: a unique class of hybrid materials
17 December 1999
Chemical Physics Letters 315 Ž1999. 31–36 www.elsevier.nlrlocatercplett
Carbon nanotube encapsulated fullerenes: a unique class of hybrid materials Brian W. Smith a , Marc Monthioux b, David E. Luzzi a
a,)
Department of Materials Science and Engineering, UniÕersity of PennsylÕania, 3231 Walnut Street, Philadelphia, PA 19104-6272, USA b CEMES, UPR A-8011 CNRS, BP 4347, F-31055, Toulouse Cedex 4, France Received 24 May 1999; in final form 19 July 1999
Abstract We report the discovery of elongated fullerene capsules contained within single-wall carbon nanotubes, as well as new findings pertaining to encapsulated, self-assembled chains of C 60 . The observed structures comprise a new, complete class of hybrid materials: hemispherically-capped graphene cylinders of various lengths within carbon nanotubes. Short capsules and chains comprised of only a few C 60 molecules spontaneously jump nanometer distances along the axis of the containing tube. A model explaining this behavior is proposed. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Since their discovery, single-wall carbon nanotubes ŽSWNTs. have stimulated widespread scientific interest due to their promising electronic and mechanical properties. However, the processes by which SWNTs are synthesized are still unrefined, and even purified nanotube material invariably contains other carbon structures. The pulsed laser vaporization ŽPLV. of graphite in the presence of certain metallic catalysts is a proven technique for synthesizing SWNTs w1x. Although C 60 is also produced by PLV, most of it is removed from the raw material in successive purification steps w2x. Nevertheless, C 60 has been found inside SWNTs in the form of self-assembled chains even after this purification w3x. Such assemblies could conceivably exhibit electronic and
) Corresponding author. Fax: q1-215-898-8296; e-mail: [email protected]
mechanical properties that differ from those of empty tubes. It is consequently important to investigate this new class of materials. A paramount question is whether C 60 is the only structure produced inside SWNTs by PLV and purification. In this Letter, we report on the search for other carbon structures within SWNTs. In addition, we address the unique behaviors of encapsulated C 60 that have been directly observed.
2. Experimental The nanotube material investigated in this work was synthesized by PLV, acid purified, and vacuum annealed at Rice University in the manner described in Ref. w2x. Small pieces were torn away from the material and fixed inside a 3 mm slot grid to be placed inside a high-resolution transmission electron microscope ŽHRTEM.. At the tear, the SWNTs that
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 8 9 6 - 9
32
B.W. Smith et al.r Chemical Physics Letters 315 (1999) 31–36
are pulled away from the bulk are suitable for imaging. This preparation technique does not subject the specimen to any additional chemical or thermal processing. Isolated SWNTs were imaged in a JEOL 4000EX HRTEM at an accelerating voltage of 100 kV. Magnification was determined using polyaromatic carbon shells present in the specimen, whose lattice fringes have a well-defined spacing of 0.34 nm. The HRTEM image of a fullerene is a projection of the specimen potential onto a plane oriented perpendicular to the electron beam. The image has maximum contrast where the beam encounters the most carbon atoms, which occurs where it is tangent to the molecule’s graphene-like walls. Thus, the image of a SWNT consists of two dark parallel lines whose separation is equal to the tube’s diameter, and the image of a C 60 molecule is a circle 0.7 nm in diameter.
3. Results Various microscopy, diffraction and spectroscopy techniques have not previously detected contained C 60 so it might be expected that such assemblies are anomalous. To the contrary, in this work fullerenes are commonly observed within both isolated tubes and tubes that comprise ropes. It has not been possible to determine the density with which each tube is filled, and tubes containing fullerenes appear to be segregated on the micron scale. C 60 is the most frequently observed encapsulate, but other derivative structures are seen as well. Examples of these various observed structures are shown in Fig. 1. All of the structures in this figure belong to a set of hybrid structures. This is an infinite set, explicitly described as ‘‘hemispherically-capped graphene cylinders that are 0.7 nm in diameter contained within 1.4 nm diameter SWNTs,’’ where the length of the cylinder is a variable structural parameter. The limiting members of this set are thus C 60 Žhaving a cylinder of zero length. within a 1.4 nm diameter SWNT, and a 0.7 nm diameter SWNT of ‘infinite’ length within a 1.4 nm diameter SWNT. ŽAn equivalent description of this set is thus C 60q10 n @ SWNT, where n is an integer G 0.. In practice, the latter case corresponds to where the
inner tube fills the length of the outer tube completely. Such two-wall, co axial t ubes ŽCATs. may be thought of as the smallest observed multiwall tubes. Multiwall tubes have not been previously observed in PLV produced material, and those produced by other techniques are generally much larger in diameter w4x. In the nanotube samples of this study, two-wall CATs were less abundant than SWNTs containing encapsulated C 60 . Fig. 1a shows a 1.4 nm diameter SWNT containing a self-assembled chain of collinear C 60 molecules. Even accounting for error in measurement due to the large depth of field of the microscope, there is obvious variability in the separations of adjacent C 60 molecules within the nanotube. The images of some are distinct, while others are so close that they appear to be tangent, or paired. An example of the latter case is indicated with an arrow. Pairing of C 60 is commonly observed in such chains. Fig. 1b shows an image of a SWNT containing several members of the set of encapsulated fullerenes. A segment of CAT is seen adjacent to a 2.2 nm long capsule, a C 70 molecule, and two C 60 molecules. From the figure, it is clear that different types of encapsulates can exist within a single SWNT. Two of the three smaller internal molecules have their equilibrium shape: both C 60 and C 70 have Žminor. diameters of 0.7 nm and thus are commensurate with the size of a 1.4 nm diameter nanotube cavity. The 2.2 nm capsule, however, contains ; 180 carbon atoms Žif it is assembled in the manner of an elongated C 70 .. The equilibrium shape of an individual, isolated fullerene having this many carbon atoms has a more uniform distribution of the 12 pentagons on the shell, thereby imparting spherical-like symmetry instead of the observed cylindrical-like symmetry. The capsule is thus a metastable configuration. During observation, it was discovered that these hybrid structures exhibit certain dynamic behaviors. The chronological sequence of images in Fig. 2, taken at ; 30 s intervals, demonstrates the motion of C 60 molecules inside a SWNT. Fig. 2a shows a chain of five C 60 molecules inside the otherwise hollow tubule cavity. In Fig. 2b, the same molecules are split into a pair, which has remained almost stationary, and a triplet, which has contiguously jumped ; 2 nm relative to the tube towards the right-hand side of the image. In Fig. 2c, one C 60
B.W. Smith et al.r Chemical Physics Letters 315 (1999) 31–36 Fig. 1. HRTEM micrographs of 1.4 nm diameter SWNTs that contain: Ža. a self-assembled chain of C 60 molecules; and Žb. a long section of two-wall tube terminating at a 2.2 nm long capsule, a C 70 molecule, and two C 60 molecules. The feature in the center of Žb. is likely a carbonaceous impurity adsorbed on the outside of the tube. Scale bar 2 nm.
33
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B.W. Smith et al.r Chemical Physics Letters 315 (1999) 31–36
B.W. Smith et al.r Chemical Physics Letters 315 (1999) 31–36
molecule has diffused back towards the left-hand side of the image, turning the former pair into a triplet and the former triplet into a pair. This behavior occurs spontaneously and in an apparently stochastic manner during observation. C 60 molecules tend to remain paired when stationary and may be imaged in different positions because they are sometimes latent for 10–20 s between jumps. In instances where a jump occurs during the exposure of a film, dim images of the molecules are observed only in the starting and finishing positions. Since a typical exposure time is 4 s, each jump must occur within a small fraction of a second. This behavior has been observed for single C 60 molecules, chains of various lengths, and short Ž; 2 nm. capsules. Under the present experimental conditions, chains containing 2–5 molecules are most often seen to jump. Each jump is typically 1–10 nm.
4. Discussion The overwhelming majority of SWNTs that form the outer tubes of the hybrid structures are 1.3–1.4 nm in diameter, which is the proper size for a nested C 60 -sized fullerene to maintain a preferred, graphitic Van der Waals separation Ž0.3 nm. from the tube’s walls. Thus it is possible that the presence, or absence, of contained C 60 et al. is strongly correlated to a tube’s diameter. Furthermore, it has been shown that SWNTs can contain molecules in metastable states. It is likely that the surrounding SWNT acts as a structural template that is essential for the formation of these endo-structures. Such hybrid assemblies could conceivably have interesting properties; for example, a CAT is expected to have greater flexural strength than an empty SWNT of the same outer diameter. The observation of small separations between contained C 60 molecules, as indicated in Fig. 1a, invites the question of whether they might exist in a dimerized or polymerized state. Since it is known that thin C 60 films photopolymerize under UVrvisi-
35
ble light w5x, it is possible that dimerization could have occurred during handling of the specimen outside of the microscope. The center-to-center separation between C 60 molecules in a pair is often 0.9 nm, which is consistent with a ŽC 60 . 2 dimer to within the resolution of the microscope w6x. The spontaneous motion of C 60 along the tubule axis is a common observation in sparsely filled SWNTs under the experimental conditions. The observed latency between jumps suggests that contained C 60 is stabilized in certain fixed positions, but the fact that motion does occur implies that the only interactions between C 60 and the surrounding tube are weak Van der Waals interactions. Accordingly, motion must require an activation energy that is of the same order as the summed Van der Waals binding energies of interaction, where the energy of a carbon–carbon Van der Waals interaction is of the order of 10y2 eV w7x. It is possible that motion is thermally induced. This would account for the statistical occurrence since each jump is expected to derive from the thermally induced vibrations of the constituent carbon atoms. However, small-amplitude oscillations of C 60 molecules should occur with greater frequency than large jumps. Such oscillations are not observed at room temperature. Thermally induced large-amplitude jumps in the absence of small-amplitude oscillations requires that the interaction between the C 60 molecules and the SWNT is governed by a narrow and deep potential. However, this is unlikely given the expected weak Van der Waals interactions. A more satisfactory explanation of the observed C 60 diffusion involves interactions between the incident electron beam and the specimen that occur during TEM observation. An electron beam is ionizing radiation, and electrons bound to carbon atoms in C 60 can be induced to undergo electronic transitions or to be entirely liberated according to the cross-sections for each process. The former could lead to the production of a dipole moment in a C 60 molecule, and the latter leaves a molecule with a net positive charge. Charged particles will sense an attractive or
Fig. 2. C 60 molecules spontaneously diffusing inside a 1.4 nm diameter SWNT: Ža. at 0 s; Žb. after ; 30 s; and Žc. after ; 60 s. From Ža. to Žb., a triplet has jumped 2 nm from its initial position towards the right-hand side of the image. From Žb. to Žc., a single C 60 molecule has jumped back towards the left. Scale bar 2 nm.
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B.W. Smith et al.r Chemical Physics Letters 315 (1999) 31–36
repulsive potential, and so beam-induced excitations could conceivably drive C 60 motion. Since electronic excitations and decays are statistically governed, and since beam-driven diffusion requires that two charged states exist simultaneously, this model accounts for the latency time that is observed between jumps. It is supposed that a particular jump is arrested either if the Coulomb potential is removed by the decay of an excited state or if another intermolecular interaction suddenly predominates. For the strongest case in which the concurrent ionization of two carbon atoms causes two C 60 molecules to become singly charged, the repulsive potential will be much higher than the Van der Waals binding energy. Thus motion may be driven, which suggests that it could be controlled.
5. Conclusions We have shown that a variety of fullerenes exist inside SWNTs, including C 60 molecules and 0.7 nm diameter fullerene capsules of various lengths. These hybrid structures comprise a new and distinct class of molecular assemblies. Many of these structures
spontaneously jump during observation, and this dynamic behavior could conceivably be driven by beam–specimen interactions.
Acknowledgements Material for this study was provided by R.E. Smalley’s group at Rice University. Financial support was provided by DOE grant DE-FC0286ER45254, NSF grant DMR98-02560, and NATO.
References w1x A. Thess et al., Science 273 Ž1996. 483. w2x A.G. Rinzler et al., Appl. Phys. A 67 Ž1998. 29. w3x B.W. Smith, M. Monthioux, D.E. Luzzi, Nature ŽLondon. 396 Ž1998. 323. w4x S. Iijima, Nature ŽLondon. 354 Ž1991. 56. w5x A.M. Rao et al., Science 259 Ž1993. 955. w6x G.W. Wang, K. Komatsu, Y. Murata, M. Shiro, Nature ŽLondon. 387 Ž1997. 583. w7x R. Eisberg, R. Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, Wiley, New York, 1985, p. 444.
Chemical Physics Letters 315 Ž1999. 31–36 www.elsevier.nlrlocatercplett
Carbon nanotube encapsulated fullerenes: a unique class of hybrid materials Brian W. Smith a , Marc Monthioux b, David E. Luzzi a
a,)
Department of Materials Science and Engineering, UniÕersity of PennsylÕania, 3231 Walnut Street, Philadelphia, PA 19104-6272, USA b CEMES, UPR A-8011 CNRS, BP 4347, F-31055, Toulouse Cedex 4, France Received 24 May 1999; in final form 19 July 1999
Abstract We report the discovery of elongated fullerene capsules contained within single-wall carbon nanotubes, as well as new findings pertaining to encapsulated, self-assembled chains of C 60 . The observed structures comprise a new, complete class of hybrid materials: hemispherically-capped graphene cylinders of various lengths within carbon nanotubes. Short capsules and chains comprised of only a few C 60 molecules spontaneously jump nanometer distances along the axis of the containing tube. A model explaining this behavior is proposed. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Since their discovery, single-wall carbon nanotubes ŽSWNTs. have stimulated widespread scientific interest due to their promising electronic and mechanical properties. However, the processes by which SWNTs are synthesized are still unrefined, and even purified nanotube material invariably contains other carbon structures. The pulsed laser vaporization ŽPLV. of graphite in the presence of certain metallic catalysts is a proven technique for synthesizing SWNTs w1x. Although C 60 is also produced by PLV, most of it is removed from the raw material in successive purification steps w2x. Nevertheless, C 60 has been found inside SWNTs in the form of self-assembled chains even after this purification w3x. Such assemblies could conceivably exhibit electronic and
) Corresponding author. Fax: q1-215-898-8296; e-mail: [email protected]
mechanical properties that differ from those of empty tubes. It is consequently important to investigate this new class of materials. A paramount question is whether C 60 is the only structure produced inside SWNTs by PLV and purification. In this Letter, we report on the search for other carbon structures within SWNTs. In addition, we address the unique behaviors of encapsulated C 60 that have been directly observed.
2. Experimental The nanotube material investigated in this work was synthesized by PLV, acid purified, and vacuum annealed at Rice University in the manner described in Ref. w2x. Small pieces were torn away from the material and fixed inside a 3 mm slot grid to be placed inside a high-resolution transmission electron microscope ŽHRTEM.. At the tear, the SWNTs that
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 8 9 6 - 9
32
B.W. Smith et al.r Chemical Physics Letters 315 (1999) 31–36
are pulled away from the bulk are suitable for imaging. This preparation technique does not subject the specimen to any additional chemical or thermal processing. Isolated SWNTs were imaged in a JEOL 4000EX HRTEM at an accelerating voltage of 100 kV. Magnification was determined using polyaromatic carbon shells present in the specimen, whose lattice fringes have a well-defined spacing of 0.34 nm. The HRTEM image of a fullerene is a projection of the specimen potential onto a plane oriented perpendicular to the electron beam. The image has maximum contrast where the beam encounters the most carbon atoms, which occurs where it is tangent to the molecule’s graphene-like walls. Thus, the image of a SWNT consists of two dark parallel lines whose separation is equal to the tube’s diameter, and the image of a C 60 molecule is a circle 0.7 nm in diameter.
3. Results Various microscopy, diffraction and spectroscopy techniques have not previously detected contained C 60 so it might be expected that such assemblies are anomalous. To the contrary, in this work fullerenes are commonly observed within both isolated tubes and tubes that comprise ropes. It has not been possible to determine the density with which each tube is filled, and tubes containing fullerenes appear to be segregated on the micron scale. C 60 is the most frequently observed encapsulate, but other derivative structures are seen as well. Examples of these various observed structures are shown in Fig. 1. All of the structures in this figure belong to a set of hybrid structures. This is an infinite set, explicitly described as ‘‘hemispherically-capped graphene cylinders that are 0.7 nm in diameter contained within 1.4 nm diameter SWNTs,’’ where the length of the cylinder is a variable structural parameter. The limiting members of this set are thus C 60 Žhaving a cylinder of zero length. within a 1.4 nm diameter SWNT, and a 0.7 nm diameter SWNT of ‘infinite’ length within a 1.4 nm diameter SWNT. ŽAn equivalent description of this set is thus C 60q10 n @ SWNT, where n is an integer G 0.. In practice, the latter case corresponds to where the
inner tube fills the length of the outer tube completely. Such two-wall, co axial t ubes ŽCATs. may be thought of as the smallest observed multiwall tubes. Multiwall tubes have not been previously observed in PLV produced material, and those produced by other techniques are generally much larger in diameter w4x. In the nanotube samples of this study, two-wall CATs were less abundant than SWNTs containing encapsulated C 60 . Fig. 1a shows a 1.4 nm diameter SWNT containing a self-assembled chain of collinear C 60 molecules. Even accounting for error in measurement due to the large depth of field of the microscope, there is obvious variability in the separations of adjacent C 60 molecules within the nanotube. The images of some are distinct, while others are so close that they appear to be tangent, or paired. An example of the latter case is indicated with an arrow. Pairing of C 60 is commonly observed in such chains. Fig. 1b shows an image of a SWNT containing several members of the set of encapsulated fullerenes. A segment of CAT is seen adjacent to a 2.2 nm long capsule, a C 70 molecule, and two C 60 molecules. From the figure, it is clear that different types of encapsulates can exist within a single SWNT. Two of the three smaller internal molecules have their equilibrium shape: both C 60 and C 70 have Žminor. diameters of 0.7 nm and thus are commensurate with the size of a 1.4 nm diameter nanotube cavity. The 2.2 nm capsule, however, contains ; 180 carbon atoms Žif it is assembled in the manner of an elongated C 70 .. The equilibrium shape of an individual, isolated fullerene having this many carbon atoms has a more uniform distribution of the 12 pentagons on the shell, thereby imparting spherical-like symmetry instead of the observed cylindrical-like symmetry. The capsule is thus a metastable configuration. During observation, it was discovered that these hybrid structures exhibit certain dynamic behaviors. The chronological sequence of images in Fig. 2, taken at ; 30 s intervals, demonstrates the motion of C 60 molecules inside a SWNT. Fig. 2a shows a chain of five C 60 molecules inside the otherwise hollow tubule cavity. In Fig. 2b, the same molecules are split into a pair, which has remained almost stationary, and a triplet, which has contiguously jumped ; 2 nm relative to the tube towards the right-hand side of the image. In Fig. 2c, one C 60
B.W. Smith et al.r Chemical Physics Letters 315 (1999) 31–36 Fig. 1. HRTEM micrographs of 1.4 nm diameter SWNTs that contain: Ža. a self-assembled chain of C 60 molecules; and Žb. a long section of two-wall tube terminating at a 2.2 nm long capsule, a C 70 molecule, and two C 60 molecules. The feature in the center of Žb. is likely a carbonaceous impurity adsorbed on the outside of the tube. Scale bar 2 nm.
33
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B.W. Smith et al.r Chemical Physics Letters 315 (1999) 31–36
B.W. Smith et al.r Chemical Physics Letters 315 (1999) 31–36
molecule has diffused back towards the left-hand side of the image, turning the former pair into a triplet and the former triplet into a pair. This behavior occurs spontaneously and in an apparently stochastic manner during observation. C 60 molecules tend to remain paired when stationary and may be imaged in different positions because they are sometimes latent for 10–20 s between jumps. In instances where a jump occurs during the exposure of a film, dim images of the molecules are observed only in the starting and finishing positions. Since a typical exposure time is 4 s, each jump must occur within a small fraction of a second. This behavior has been observed for single C 60 molecules, chains of various lengths, and short Ž; 2 nm. capsules. Under the present experimental conditions, chains containing 2–5 molecules are most often seen to jump. Each jump is typically 1–10 nm.
4. Discussion The overwhelming majority of SWNTs that form the outer tubes of the hybrid structures are 1.3–1.4 nm in diameter, which is the proper size for a nested C 60 -sized fullerene to maintain a preferred, graphitic Van der Waals separation Ž0.3 nm. from the tube’s walls. Thus it is possible that the presence, or absence, of contained C 60 et al. is strongly correlated to a tube’s diameter. Furthermore, it has been shown that SWNTs can contain molecules in metastable states. It is likely that the surrounding SWNT acts as a structural template that is essential for the formation of these endo-structures. Such hybrid assemblies could conceivably have interesting properties; for example, a CAT is expected to have greater flexural strength than an empty SWNT of the same outer diameter. The observation of small separations between contained C 60 molecules, as indicated in Fig. 1a, invites the question of whether they might exist in a dimerized or polymerized state. Since it is known that thin C 60 films photopolymerize under UVrvisi-
35
ble light w5x, it is possible that dimerization could have occurred during handling of the specimen outside of the microscope. The center-to-center separation between C 60 molecules in a pair is often 0.9 nm, which is consistent with a ŽC 60 . 2 dimer to within the resolution of the microscope w6x. The spontaneous motion of C 60 along the tubule axis is a common observation in sparsely filled SWNTs under the experimental conditions. The observed latency between jumps suggests that contained C 60 is stabilized in certain fixed positions, but the fact that motion does occur implies that the only interactions between C 60 and the surrounding tube are weak Van der Waals interactions. Accordingly, motion must require an activation energy that is of the same order as the summed Van der Waals binding energies of interaction, where the energy of a carbon–carbon Van der Waals interaction is of the order of 10y2 eV w7x. It is possible that motion is thermally induced. This would account for the statistical occurrence since each jump is expected to derive from the thermally induced vibrations of the constituent carbon atoms. However, small-amplitude oscillations of C 60 molecules should occur with greater frequency than large jumps. Such oscillations are not observed at room temperature. Thermally induced large-amplitude jumps in the absence of small-amplitude oscillations requires that the interaction between the C 60 molecules and the SWNT is governed by a narrow and deep potential. However, this is unlikely given the expected weak Van der Waals interactions. A more satisfactory explanation of the observed C 60 diffusion involves interactions between the incident electron beam and the specimen that occur during TEM observation. An electron beam is ionizing radiation, and electrons bound to carbon atoms in C 60 can be induced to undergo electronic transitions or to be entirely liberated according to the cross-sections for each process. The former could lead to the production of a dipole moment in a C 60 molecule, and the latter leaves a molecule with a net positive charge. Charged particles will sense an attractive or
Fig. 2. C 60 molecules spontaneously diffusing inside a 1.4 nm diameter SWNT: Ža. at 0 s; Žb. after ; 30 s; and Žc. after ; 60 s. From Ža. to Žb., a triplet has jumped 2 nm from its initial position towards the right-hand side of the image. From Žb. to Žc., a single C 60 molecule has jumped back towards the left. Scale bar 2 nm.
36
B.W. Smith et al.r Chemical Physics Letters 315 (1999) 31–36
repulsive potential, and so beam-induced excitations could conceivably drive C 60 motion. Since electronic excitations and decays are statistically governed, and since beam-driven diffusion requires that two charged states exist simultaneously, this model accounts for the latency time that is observed between jumps. It is supposed that a particular jump is arrested either if the Coulomb potential is removed by the decay of an excited state or if another intermolecular interaction suddenly predominates. For the strongest case in which the concurrent ionization of two carbon atoms causes two C 60 molecules to become singly charged, the repulsive potential will be much higher than the Van der Waals binding energy. Thus motion may be driven, which suggests that it could be controlled.
5. Conclusions We have shown that a variety of fullerenes exist inside SWNTs, including C 60 molecules and 0.7 nm diameter fullerene capsules of various lengths. These hybrid structures comprise a new and distinct class of molecular assemblies. Many of these structures
spontaneously jump during observation, and this dynamic behavior could conceivably be driven by beam–specimen interactions.
Acknowledgements Material for this study was provided by R.E. Smalley’s group at Rice University. Financial support was provided by DOE grant DE-FC0286ER45254, NSF grant DMR98-02560, and NATO.
References w1x A. Thess et al., Science 273 Ž1996. 483. w2x A.G. Rinzler et al., Appl. Phys. A 67 Ž1998. 29. w3x B.W. Smith, M. Monthioux, D.E. Luzzi, Nature ŽLondon. 396 Ž1998. 323. w4x S. Iijima, Nature ŽLondon. 354 Ž1991. 56. w5x A.M. Rao et al., Science 259 Ž1993. 955. w6x G.W. Wang, K. Komatsu, Y. Murata, M. Shiro, Nature ŽLondon. 387 Ž1997. 583. w7x R. Eisberg, R. Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, Wiley, New York, 1985, p. 444.