NANO LETTERS
Structure and Dynamics of Carbon Nanoscrolls
2004 Vol. 4, No. 5 881-884
Scheila F. Braga,*,† Vitor R. Coluci,†,‡ Sergio B. Legoas,†,§ Ronaldo Giro,† Douglas S. Galva˜o,† and Ray H. Baughman‡ Instituto de Fı´sica “Gleb Wataghin”, UniVersidade Estadual de Campinas, C.P. 6165, 13083-970 Campinas SP, Brazil, and NanoTech Institute and Department of Chemistry, UniVersity of Texas, Richardson, Texas 830688 Received February 19, 2004
ABSTRACT Carbon nanotube scrolls (CNSs) provide an interesting form of carbon that ideally consists of a single sheet of graphite that is spiral wrapped to form a nanotube. We here use molecular dynamics simulations to investigate CNS formation, stability, and the structural effects due to charge injection. CNS formation is seen to automatically occur when a critical overlap between sheet layers is achieved for the partially curled sheet. We find that charge injection causes unwinding of the CNSs, which might be important for the application of CNSs as nanomechanical actuators.
Single walled nanotubes (SWNTs) comprise a single graphite sheet that is wound to make a seamless cylinder. Concentric arrays of these SWNTs are nested like the layers of a tree trunk to make multiwalled nanotubes (MWNTs). While the present cost of producing high quality SWNTs limits commercial applicability, MWNTs are much less expensive and are available in relatively large quantities. There is a third type of carbon nanotube, called nanotube scrolls, which promises to be less expensive to produce than SWNTs and are like SWNTs in that they can comprise a single sheet of graphite. These carbon nanotube scrolls (CNSs) are formed by the jelly roll-like wrapping of a graphite sheet to form a nanotube. Scroll whiskers were first reported by Bacon in 1960.1 Recent synthesis efforts2,3 provide simple, lowtemperature routes to CNSs. One route involves intercalation of graphite flakes with potassium metal followed by exfoliation with ethanol to make a dispersion of carbon sheets. After sonication to assist exfoliation and spiral wrapping of the graphite sheets, carbon nanoscrolls are formed (see video01 in Supporting Information). Reflecting previous difficulties in the synthesis of pure CNSs, comparatively few investigations of CNSs have been reported.4-8 Because of the novel scroll topology, their properties should differ from those of either SWNTs or MWNTs. For example, in contrast to SWNTs and MWNTs, CNSs provide interlayer galleries that can be intercalated with donors and acceptors, and the nanotube diameter can expand to accommodate the volume of the intercalant. This * Corresponding author. E-mail:
[email protected]. † Universidade Estadual de Campinas. ‡ University of Texas. § Current address: Departamento de Fı´sica, Universidade Federal do Amazonas, 69077-000 Manaus AM, Brazil. 10.1021/nl0497272 CCC: $27.50 Published on Web 04/15/2004
© 2004 American Chemical Society
feature is potentially important for a rich variety of applications, from hydrogen storage to energy storage in supercapacitors or batteries.3 In important initial calculations on CNSs,9-11 continuum elasticity theory was applied to analyze the structure and stability of scrolls. However, this approach cannot reveal atomic-level features of structure, and dynamic calculations have not been done. While static molecular mechanics calculations have also been described, only pairwise atom-atom interactions were considered.12 In this work we report the first molecular mechanics investigations for CNS structures that consider more than pairwise atom-atom interactions. Molecular dynamics simulations were used to investigate structural evolution for selected CNS configurations. We have analyzed both neutral and charged CNSs in order to investigate the effects of charge injection on scroll geometry. SWNT artificial muscles are already known, and the CNSs provide a new type of actuation (scroll unwinding), so these results are of interest for possible nanoscale actuator applications. While CNSs can likely exist that are based on the spiral wrapping of a few stacked sheets of graphite, we here consider only single sheet scrolls. Various CNS structures were generated by rolling a graphene sheet into a truncated Archimedean-type spiral13 by rotation around the y1 axis defined by the angle θ shown in Figure 1. We have used the following nomenclature: the geometry produced is zigzag for θ ) 0, armchair for θ ) 90°, and chiral for 0 < θ < 90°. We restricted investigation of the evolution of structure during scroll formation by considering initial structures of two types: R (Figure 1b), where there are no uncurled regions of the sheet, and β (Figure 1c), where flat and curled regions of the sheet simultaneously exist. Although there are many other possible initial structures, the basic structural features can be ad-
Figure 1. (a) The unwrapped honeycomb lattice of a graphene sheet (width W and height H). Here x1 and y1 are the scroll axes, which are rotated by an angle θ with respect to the reference coordinate system xy. The scroll is generated by wrapping the sheet around the axis y1. Examples of (b) R and (c) β-type CNSs (with θ ) 45°) and their cross sections are shown.
Figure 2. Change in total energy (relative to an undistorted graphene sheet) during the wrapping of a single graphite sheet to make a CNS. The torsion plus inversion (EBend) and van der Waals energies (EvdW) are shown in the inset graph.
dressed using these two structure types. We investigated structures containing up to ∼20000 carbon atoms, which precludes the use of quantum methods. The evolution of the scroll structure was simulated using molecular dynamics methods for different temperatures (up to 300 K). In average, each simulation was carried out for a period of 50 ps, in time steps of 1 fs. Geometrical optimizations and molecular dynamics simulations were carried out using a standard molecular force field which includes van der Waals, bond stretch, bond angle, bending, electrostatic, and torsional terms.14 This methodology had been proved to be very effective in the study of the structural and dynamical properties of carbon structures.15,16 CNS formation is dominated by two major energetic contributions, the elastic energy increase caused by bending the graphite sheet (decreasing stability) and the free energy decrease generated by the van der Waals interaction energy of overlapping regions of the graphite sheet (increasing stability). Figure 2 shows the changes in per-carbon energy ∆E (relative to the energy of an undistorted graphene sheet) during structure evolution for an armchair R-type Archimedean 882
Figure 3. Temporal evolution of structure and relative energy ∆E obtained from dynamics simulations for R-type structures at 5 K. Structures of representative simulation points are indicated.
spiral scroll. Before sheet overlap occurs (configurations 1 up to 8, Figure 2), increases in the curvature of the graphene sheet increases the torsion and inversion contributions to sheet strain energy, thereby making the rolled structure less stable relative to an undistorted graphene sheet. This implies that the transition from graphene to these structures must be energy assisted (e.g., through sonication2,3 in present experimental methods). As the rolling continues and surface overlapping regions appear (configuration 9, Figure 2, for instance) the van der Waals contributions increase the structural stability. There is a critical value of layer overlap above which the rolling process evolves spontaneously as a result of van der Waals interlayer forces. This critical limit value depends on the initial sheet dimensions and the orientation of the sheet relative to the axis about which curling occurs. For the structure indicated in Figure 2 (W ) 30.06 and H ) 121.46 Å, H being the wrapped scroll axis) this is approximately an overlap of two rows of hexagons in each layer of the graphene sheet. The final structure can even be more stable than its parent graphene sheet (configuration 10, Figure 2). There is a critical minimum inner diameter (∼20 Å) for scroll stability, which seems to be consistent with experimental observations.7 For smaller diameters, the bending contributions outweigh the van der Waals energetic gain and the structure is unstable (see inset, Figure 2). We have carried out dynamic simulations for different initial configurations in order to understand the importance of graphene sheet width and length, the chiral angle θ (Figure 1) of wrapping, and the effect of initial curling type and extent (R or β). In Figure 3 we present the results for two representative cases. We considered a square R-type layer (W ) L ) 100 Å) curled about the chiral axes providing θ ) 90° and 45°. Figure 3 shows the temporal energy profiles for the cases where the critical overlap limit for spontaneous rolling has not been yet obtained at the start of the experiment (left), so the structure uncurls, and for when the structure evolves into self-rolled scrolls (right) because the initial structure has sufficient overlap within the sheet layers. We Nano Lett., Vol. 4, No. 5, 2004
Figure 4. Relative energy ∆E of optimized scroll structures as a function of their (a) height H for W ) 107.78 Å; and (b) width W for H ) 30.54 Å. All initial structures are truncated Archimedeantype spirals13 with an internal diameter of ∼20 Å and θ ) 0 (corresponding to a zigzag CNS).
can see that the profile during uncurling is quite similar for chiral angles of θ ) 45° and θ ) 90° (Figure 3, left). The energy for the θ ) 45° starting structure is lower than for the θ ) 90° starting structure, since the bending strain energy to obtain initial overlap of sheet layers is lower for curling around the diagonal of the sheet than for curling around the sheet side. However, the energy minima shown for the θ ) 90° structure (Figure 3, right) are much lower than for the θ ) 45° structure, since further wrapping the former structure eventually maximizes the overlap energy relative to the strain energy. Due to this more favorable energy for the structure with θ ) 90°, the θ ) 45° structure will eventually evolve into either a θ ) 0° or θ ) 90° structure. These results suggest that the scroll formation will likely preferentially occur by curling about a chiral axis that differs from the chiral axis of the final CNS. These wrapping and unwrapping processes can be better understood by analyzing videos 0204 from the molecular dynamics simulations (Supporting Information). An example of a shift from a scroll angle of θ ) 60° to θ ) 0° (both of which correspond to an zigzag CNS) can be seen in video 05. For a fixed helical angle the height(H)/width(W) ratio for the graphene sheet strongly affects scroll stability. This is shown in Figure 4 where relative energy is plotted as a function of H and W for the case of a CNS having θ ) 0. The axis about which wrapping occurs is parallel to the height direction. For a fixed W (H) the relative stability with respect to the parent graphene sheet increases with increasing H (W). The decrease in per carbon energy (increase in stability) with increasing W is steeper than for increasing H. This can be explained in terms of an increase in the exposed edges as H increases, which decreases stabilization. These results are in agreement with continuum models.11 Note that the energy advantage of the scrolled nanotubes should approach roughly the van der Waals binding energy of graphite (about 2 kcal/mol carbon) as both H and W increase indefinitely, which is a much larger stabilization energy than shown in Figure 4. Nano Lett., Vol. 4, No. 5, 2004
Figure 5. (a) Total (ETotal), (b) van der Waals (EVdW), and (c) torsion plus inversion (EBend) energy changes during the dynamical process of scroll formation for R and β-types (θ ) 0, W ) 146, and H ) 45 Å, T ) 5 K).
The energetics of scroll formation, from a rectangular sheet initially curled in R- and β-types, are compared in Figure 5. CNS formation from the R-type configuration is energetically more favorable and faster than for the β configuration. This can be seen from the initial energy values and from the slope of the ETotal curves (Figure 5a). The R-type allows the simultaneous movement of both overlaped edges in opposite directions, causing faster CNS formation (video 06, Supporting Information). This feature can be also be seen in Figure 5b where the fast van der Waals gain for the R-type is clearly observed. On the other hand, the β-type configuration presents a more complex behavior, especially for EBend, where geometrical changes in the flat graphene region occur at the same time that the CNS is being formed (video 07). Despite these different behaviors, both types of initial geometries can generate the same CNSs by the self-rolling process. For larger structures both tubular and conical shape scrolls can arrise. Figure 6 shows a CNS obtained from a simulation of β-type initial structure with W ) 215 and H ) 230 Å. The structural features observed in this simulated CNS are in good qualitative agreement with the available experimental data.3 Dimensional changes useful for actuator applications are observed upon charge injection in SWNTs.17 Small amounts of charge injection in the neutral state of SWNTs (either positive or negative) can result in either expansion or contraction due to quantum mechanical effects, depending upon the structure of the SWNT.18,19 However, large amounts of charge injection, relative to the neutral state, always result in expansion due to Coulombic repulsion. Unlike SWNTs or MWNTs, CNSs can be intercalated between sheet layers, which can increase the achievable actuation strain relative to those for SWNTs. To evaluate the Coulombic contribution to actuation, we have used molecular mechanics and the method of charge equilibration.20 Starting from neutral CNSs with optimized geometry, various densities of charge were injected into the system and equilibrated before new geometry/energy optimization. We 883
Figure 6. Three-dimensional view of a CNS of 19 210 atoms obtained from dynamics simulation. The simulation was carried out at 300 K during 48 ps using a β-type structure with θ ) 60°. A conical shaped scroll with ∼2.5 turns can be seen.
In summary, in this work we have studied structural and dynamical properties of carbon nanoscrolls (CNSs) using molecular dynamics simulations. Our results show that the CNSs can have a lower energy than the precursor graphene and that scroll formation is a self-sustained curling process after a critical overlap area is reached. This curling is predicted to occur on a picosecond time scale, even at 5 K. Consistent with observations, CNSs having an inner diameter smaller than about 20 Å are unstable with respect to an increase in this diameter, and conical scrolls can be trapped as a metastable state. Depending upon the initial shape and dimensions of the graphite sheet, the lowest energy activated state for self-rolling can have a chiral angle that differs from that developed during the rolling process. We find that charge injection causes unwinding of the CNSs, which might be important for the application of CNSs as nanomechanical actuators. Acknowledgment. The authors acknowledge financial support from the Brazilian agencies CAPES, FAPESP, CNPq, IMMP/MCT, and the Robert A. Welch Foundation. We also acknowledge the use of computational facilities at CENAPAD-SP. Supporting Information Available: Videos mentioned in this letter. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) (2) (3) (4) (5) (6) (7) (8)
Figure 7. Nanoscroll structure as a function of charge-per-carbon (expressed as percentages).
have considered charge densities equal to 0.01, 0.015, and 0.02 e- per carbon atom. In Figure 7 we show superimposed images of charged CNSs for different injected charge values. An increase in the scroll radius was observed with increasing charge density. In contrast with CNTs, where comparable axial and radial geometrical changes occur upon charge injection,19 the fractional radial expansions for CNSs are much larger than the axial expansions. This can be understood because this radial expansion of the CNSs involves changes in van der Waals distances, rather than largely covalent bond distances. To have an independent verification of this scroll unwinding due to charge injection, we have also carried out quantum mechanical calculations21 for small nanotube structures. Both methodologies, classical and quantum mechanics, presented the same qualitative results, i.e., the predominant effect of charge injection is an increase in scroll diameter. 884
(9) (10) (11) (12) (13)
(14) (15) (16) (17)
(18) (19) (20) (21)
Bacon, R. J. Appl. Phys. 1960, 31, 283. Shioyama, H.; Akita, T. Carbon 2003, 41, 179. Viculis, L. M.; Mack, J. J.; Kaner, R. B. Science 2003, 299, 1361. Amelinckx, S.; Bernaerts, D.; Zhang, X. B.; Van Tendeloo, G.; Van Landuyt, J. Science 1995, 267, 1334. Mordkovich, V. Z.; Baxendale, M.; Yoshimura, S.; Chang, R. P. H. Carbon 1996, 34, 1301. Maniwa, Y.; Fujiwara, R.; Kira, H.; Tou, H.; Nishibori, E.; Takata, M.; Sakata, M.; Fujiwara, A.; Zhao, X.; Iijima, S.; Ando, Y. Phys. ReV. B 2001, 64, 073105. Zhou, O.; Fleming, R. M.; Murphy, D. W.; Chen, C. H.; Haddon, R. C.; Ramirez, A. P.; Glarum, S. H. Science 1994, 263, 1744. Ruland, W.; Schaper, A. K.; Hou, H.; Greiner, A. Carbon 2003, 41, 423. Lavin, J. G.; Subramoney, S.; Ruoff, R. S.; Berber, S.; Toma´nek, D. Carbon 2002, 40, 1123. Toma´nek, D.; Zhong, W.; Krastev, E. Phys. ReV. B 1993, 48, 15461. Toma´nek, D. Physica B 2002, 323, 86. Seton, R. Carbon 1996, 34, 69. The truncated Archimedean-type spiral is defined by the parametric equation r ) aφ + a0, where a and a0 are nonzero constants, and r and φ are the usual cylindrical coordinates. The parameter a is related to the initial interlayer spacing d as a ) d/2π, where d ) 3.4 Å. Universal 1.02 Molecular Force Field, available from Accelrys, Inc. as part of Cerius2 suite programs. http://www.accelrys.com. Baughman, R. H.; Galva˜o, D. S. Nature (London) 1993, 365, 735. Legoas, S. B.; Coluci, V. R.; Braga, S. F.; Coura, P. Z.; Dantas, S. O.; Galva˜o, D. S. Phys. ReV. Lett. 2003, 90, 055504. Baughman, R. H.; Cui, C.; Zakhidov, A. A.; Iqbal, Z.; Barisci, J. N.; Spinks, G. M.; Wallace, G. G.; Massoldi, A.; De Rossi, D.; Rinzler, A. G.; Jaschinski, O.; Roth, S.; Kertesz, M. Science 1999, 284, 1340. Gartstein, Y. N.; Zakhidov, A. A.; Baughman, R. H. Phys. ReV. Lett. 2002, 89, 045503. Verissimo-Alves, M.; Koiller, B.; Chacham, H.; Capaz, R. B. Phys. ReV. B 2003, 67, 161401. Rappe´ A. K.; Goddard, W. A. J. Phys. Chem. 1991, 95, 3358. AM1 Semiempirical calculations for scroll nanotubes containing 400 carbon atoms with charge injection values of -1 and -2%.
NL0497272 Nano Lett., Vol. 4, No. 5, 2004
