Geometric and Electronic Structure of Closed Graphene Edges - The

Letter pubs.acs.org/JPCL

Geometric and Electronic Structure of Closed Graphene Edges Alejandro Lopez-Bezanilla,*,† Jessica Campos-Delgado,‡ Bobby G. Sumpter,† Daniel L. Baptista,‡ Takuya Hayashi,§ Yoong A. Kim,§ Hiroyuki Muramatsu,§ Morinobu Endo,§ Carlos A. Achete,‡ Mauricio Terrones,∥ and Vincent Meunier⊥ †

Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, Tennessee 37831-6493, United States Materials Metrology Division, National Institute of Metrology, Avenida Nossa Senhora das Graças 50, Xerém, Duque de Caxias, Brazil § ICST - Institute of Carbon Science and Technology, Shinshu University, Nagano, Japan ∥ Department of Physics, Department of Materials Science and Engineering & Materials Research Institute, The Pennsylvania State University, 104 Davey Laboratory, University Park, Pennsylvania 16802-6300, United States ⊥ Department of Physics, Astronomy, and Applied Physics & Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, New York 12180, United States ‡

ABSTRACT: We report theoretical and experimental results on single and multiple looped graphene sheets. Experimental images of stable closed-edge structures in few-layer graphene samples obtained by high-resolution transmission electron microscopy (HRTEM) are compared with firstprinciples density functional theory calculations. We demonstrate that the electronic structure of a graphene nanoribbon is not significantly perturbed upon closing. By contrast, a significant modulation of the electronic structure is observed for closed-edge graphene structures deposited on a planar graphene substrate. This effect is due to an enhanced reactivity of the looped (coalesced) edges observed experimentally. The coexistence of different degrees of curvature in the graphene sheet induced by folding indicates that these materials could be used for surface chemistry engineering. SECTION: Physical Processes in Nanomaterials and Nanostructures

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increased van der Waals (vdW) attraction between the sheets of closed-edge graphene. Moreover, coalesced edges could be thermally produced on graphene edges by subjecting the material to temperatures above 1500 °C under an inert atmosphere.9,10 Closed-edge graphene can be viewed as a hybrid structure that combines in a single graphitic material the flat geometry of graphene with the curvature of small diameter nanotubes, offering the possibility to experiment locally with the properties of one structure while the other remains untouched. Because of curvature effects governing local hybridization, the physics of such looped structures could have important implications on the chemical functionalization of graphene and their use in nanoelectronics. For example, the covalent anchoring of functional groups on the surface of a pristine graphene sheet11 is limited to chemistries involving radicals able to induce a local sp3 hybridization of the carbon atomic orbitals. These local modifications of the perfect sp2 hybridization could significantly change the electronic properties of closed-edge (or looped) graphene. For example, the reduced backscattering

ver the past two decades, significant efforts have been devoted to the synthesis and characterization1 of novel carbon allotropes, such as fullerenes, carbon nanotubes, and graphene.2,3 The fascinating physicochemical and electronic properties of these systems continue to attract the attention of researchers and engineers across disciplines4 in an attempt to integrate carbon-based materials into future generations of electronic, optoelectronic, and energy storage devices. A form of graphene, called grafold,5 introduces a kind of graphitic geometry consisting of single- or multilayer graphene where the edges are rolled back onto themselves. As the edges of two or more layers interact with the extended surface, the energy balance between the interacting layers and the mechanical tension in the looped part eventually determine the details of the atomic stacking. Looped (or coalesced) edges have been obtained experimentally using various methods, including the folding of graphene edges with an atomic force microscope (AFM) or scanning transmission microscope (STM) tip observed almost two decades ago6,7 and other high-temperature techniques.8 Today, more sophisticated methods allow the control of the morphology and structure of graphene folds via chemical vapor deposition (CVD) or its transfer process.3 In nature, coalesced edges of sufficiently large graphitic domains are very stable when high energies are in play, since the elastic energy penalty due to folding can be easily compensated by the © 2012 American Chemical Society

Received: May 18, 2012 Accepted: July 20, 2012 Published: July 21, 2012 2097

dx.doi.org/10.1021/jz300695h | J. Phys. Chem. Lett. 2012, 3, 2097−2102

The Journal of Physical Chemistry Letters

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Figure 1. A few-layer graphene segment with closed edges with an eight-frame sequence showing the evolution of vacancies (following the arrows, the times (min:sec) at which the images were taken are (1) 00:00, (2) 08:00, (3) 16:30, (4) 18:30, (5) 28:30, (6) 31:00, (7) 33:00, and (8) 33:16). In the first frame, the layers are perpendicular to the electron beam; as vacancies grow, they cause the tilting of the segment until in the last frame the layers are completely parallel to the beam and the triple loop is perpendicular to the e-beam and in focus. Arrows in frame 1 point to organic adsorbates anchored to the graphene surface. (b) Sequence frame with superimposed lines that highlight the contours of the revealed triple loop (time = 33:28). The considered distances are schematically illustrated in panel c. (d) Histrogram of the measured interlayers distances where the numbers at the right correspond to the average values.

Figure 2. In all cases, the looped modeled system is shown below each band diagram panel. (a-i) Energy bands and (a-ii) DoS comparison for a closed-edge zGNR and a flat zGNR composed of 55-C dimers across the ribbon width. The loop diameter is D ∼ 11.6 Å. (b) Similar comparison for a closed-edge aGNR and a flat GNR, composed of 68-C dimers across the ribbon width. The loop diameter is D ∼ 11.3 Å. (c) Band diagram (c-i) and DoS (c-ii) of two concentric closed-edge zGNRs. The diameters of the inner and outer loops are D1 = 10.4 Å and D2 = 16.9 Å. (d) Similar to panel c for three concentric closed-edge zGNRs. The diameters of the inner, intermediate, and outer loops are D1 = 10.2 Å, D2 = 16.8 Å, and D3 = 23.3 Å, respectively. (e,f) Top view of the zigzag and armchair looped ribbons, respectively, to observe the evolution in the atom stacking between layers.

upon chemical attachment to the surface of carbon nanotubes with CCl2 functional groups has been broadly predicted for the so-called “open” configuration.12 The adsorption of CCl2 radicals have been shown to break C−C bonds of the graphitic substrate, thus restoring the π-conjugation, and opening a pathway to covalently functionalize conjugated networks.13 The

highly dependent desorption barrier of greatly curved graphene permits the attachment of CCl 2 and prevents stable functionalization on flat graphene.14,15 The combination of flat graphene and highly strained graphene (loops) in a given nanostructure suggests the distinct possibility of functionalizing 2098



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the high-temperature treatment and the subsequent ultrasonic dispersion in organic solvents used for sample preparation. However, a low dose of electrons is generally sufficient to remove these contaminants, which are loosely bound to the graphene layers via π−π interactions. In particular, at the early stages of our experiments, we found that these adsorbates cover the surface of the sample (indicated by arrows in frame 1 of Figure 1), and, as expected, electron bombardment during the observation effectively cleans the aggregates located on the flat areas of the sample (as shown by green arrows). Interestingly, we found that the aggregates attached to the looped edges (marked with red arrows) are more stable under e-beam irradiation. In all ribbon samples we studied, it was always noted that the adsorbates deposited on the flat regions vanish soon after electron beam irradiation, whereas the fragments close to the edges remained anchored for longer periods of time during electron beam irradiation. The binding energy of an external addend to the surface of a graphitic system is directly related to the degree of curvature of the binding site.17 The different degrees of curvature found along a looped zigzag GNR (zGNR) suggest that the sp2 hybridization of planar regions is modified at the higher curvature region of the fold, with a higher degree of hybridizations occurring for carbon atoms located in the most curved region of the loop. Thus, we posit that the stabilization of the aggregates along the edges (looped regions) is possibly due to the presence of highly curved graphene that locally promotes a stronger binding energy than perfectly flat π−π interactions. Jia, et al.18 demonstrated that the edge terminations of pristine CVD-grown GNRs could be stabilized into either zigzag or armchair, if electron irradiation in conjunction with Joule heating are applied. Therefore, we expect that the high temperature annealed nanoribbons studied here would exhibit coalesced edges (loops) exhibiting zigzag or armchair terminations. Both armchair and zigzag ribbons have been considered in the theoretical models, allowing a convenient implementation of periodic boundary conditions in the DFTbased modeling. Examination of the electronic structure reveals how the electronic and magnetic properties of a closed-edge graphene nanoribbon are modified compared to flat sheets; in particular, different physicochemical properties are noted. The zigzag boundaries along the hydrogen-terminated edge of flat zGNRs and the bipartitioned graphitic network allow the πelectrons in the ground state to localize at the zigzag edges, thus exhibiting a ferromagnetic ordering along a given edge, and an antiferromagnetic ordering across the ribbon width.19 The coupling interaction between the edge states decreases exponentially as the ribbon width increases. First-principles calculations have revealed that zGNRs are metallic in the ferromagnetic metastable configuration, and they exhibit semiconducting behavior in the antiferromagnetic state.20 In our computational model, the ribbon is folded, and both edges are in front of each other, as in a bilayer configuration. Thus, the interlayer interaction is predominant, and the antiparallel configuration vanishes, yielding a ferromagnetic spin coupling between layers. This additional interaction amplifies the π*states dispersion, as shown in Figure 2a, and leads to spin states with a ferromagnetic coupling both along the edges and between the layers. Figure 2a shows a comparison of the band structure and density of states (DoS) of a flat and a closed-edge zGNR with the same number of C atoms in the unit cell. Both systems contain 110 C atoms and the flat ribbon is 11.5 nm wide. The DFT-based results show that such a zGNR can be

graphene-based structures in the looped regions, thus preserving the original hyperconjugated graphitic network. In this paper we provide further understanding of the local physicochemical properties of single and multiple looped graphene sheets using high-resolution transmission electron microscopy (HRTEM) in conjunction with first-principles calculations. Here, the loops are observed in high-temperature heat-treated graphitic nanoribbon (GNR) samples. The experimental findings are rationalized using density functional theory (DFT)-based calculations. We observed that edge closing does not significantly perturb the original electronic structure of a suspended pristine flat layer. By contrast, a significant modulation of the electronic structure is observed for closed-edge graphene structures deposited on a planar graphitic substrate. These findings are based on the modification of the local hybridization of each graphene-like system, in which molecular-orbitals are found to vary from sp2 to sp2.5 across the looped/curved regions. We first describe the experimental observations of a triplelooped structure, which results from the formation of several “holes” on a graphene segment with six layers, induced by an electron beam. This particular segment was part of a CVDgrown GNR that was heat treated at 2800 °C.10 The morphology of the GNRs consists of micrometer-long beltlike structures, ∼100 nm wide and ∼10 nm thick. The graphene sheets are arranged in parallel to the main nanoribbon axis. In its pristine form, the GNRs account for stacked graphene sheets with bare open edges. After this high-temperature treatment, we confirmed by Raman spectroscopy and transmission electron microscopy (TEM) that a significant change in the structure occurred: the crystallinity of the graphene layers was enhanced, and adjacent graphene edges coalesced, forming the so-called “loops”. During annealing, the edges of a double-layer graphene would coalesce to form a loop, a four-layer graphene would coalesce to form a double loop, and so forth.5 (For detailed sample characterization, see the Materials and Methods section). The details and mechanisms for the underlying processes of “hole” formation are the subject of a separate communication.16 Figure 1 illustrates eight individual frames of a recorded sequence. In the first frame (t = 0), a six-layer graphene is perpendicular to the electron beam, and the sharp lines represent the looped edges. As time evolves (in the sequence defined by arrows, which occurs over a period of ca. 33 min.), we observed the onset of vacancy formation and the subsequent propagation at the base of the six-layered section. The holes “drilled” in the few-layer graphene cause the flat layers to bend and tilt progressively toward the e-beam, until the sheets align parallel to the beam and the cross section of the triple loop is captured (eighth frame, bottom left of Figure 1a and Figure 1b). DFT calculations of concentric loops reveal distances of 0.33 nm, an inner gap of a single loop of 1 nm, a width of 1.7 nm for a double loop (four layers of graphene) and 2.33 nm for a triple loop (six layers of graphene) (see lower panel of Figure 2d). Measurements performed on the experimental images reveal that the loop-to-loop separation is ∼0.33 nm, and the loop width is ∼2.75 nm, while the inner distance of the loop is, on average, 0.94 nm (see Figure 1b,c,d). Therefore, we can conclude that the DFT results are in good agreement with the experimental observations, albeit smaller due to the use of LDA, which is known to systematically overbind. Residues such as carbon adsorbates, including graphene-like platelets, are commonly observed in TEM, and are attributed to 2099



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Figure 3. Geometric structures of a closed-edge GNR (a) and a double-loop GNR (b) with zigzag edges over a graphene substrate. In a, distances are D1 = 8.3 Å, D2 = 3.4 Å and D3 = 3.3 Å. In b, D1 = 9.7 Å, D2 = 16.7 Å, D3 = 3.2 Å, D4 = 3.7 Å, and D5 = 3.5 Å.

with a minimum of D3 = 3.2 Å, to the flat region where the separation reaches the D5 = 3.5 Å. In the intermediate zone between the curved and the flat region, the interlayer distance reaches a maximum of D4 = 3.7 Å. The observed distances correspond to the typical π-stacking distances of graphitic layers. As a result of the interaction with the outermost layer, the inner closed layer decreases its diameter with respect to the single free-standing case of Figure 2. Similar to the case of multiple loops discussed above (Figure 2c,d), the dispersion of the π- and π*-states corresponding to the closed edge over a flat substrate are greatly altered with respect to the freestanding ribbon, in this case decreasing over the whole BZ. This suggests that a free-standing ribbon might be preferred for electronic purposes due to the good preservation of the π character of the electronic states when the flat surface of the structure is not in contact with a substrate. Experimental HRTEM observations have clearly demonstrated that the bare edges of graphene layers could coalesce forming multiple loops via Joule heating22 or high-temperature treatments above 1500 °C.10 However, and to the best of our knowledge, a complete study of the way single-, double-, and triple-loops behave has not been studied (theoretically) hitherto. We have carried out detailed HRTEM imaging for different types of loops forming in GNRs heat treated at 2800 °C. These high resolution images allow direct comparison to the DFT-determined structures for the double- and triplefolded GNRs. In particular, Figure 4a shows an experimental HRTEM image of multilayered coalesced graphene edges from thermally treated GNRs. The fully relaxed geometries of two and three concentric loops are superimposed to the experimental images in Figure 4b,c, showing an excellent agreement between experimental and computed atomic positions. These HRTEM images of the edges reveal an effective 180° curving of the graphitic sheets at the edge, which actually corresponds to two or more graphene sheets whose edges coalesced to form a looped structure. The hexagonal planes join in pairs, forming nanoloops at the edges of the graphitic sheets. As previously reported for boron nitride compounds, these nanoarches have multilayer walls.23 The edge coalescence process is assumed to take place in order to minimize the number of dangling bonds at the border of the hexagonal layers. It is noteworthy that the different loop configurations observed in Figure 4 indicate that the loop morphology is dependent on the graphene layers underneath

stabilized by ∼100 meV by folding it back onto itself and allowing the C atoms to interact in a bilayer configuration. Note in Figure 2b that, in contrast to the closed-edge zGNR, the closed-edge armchair GNR (aGNR) displays very similar electronic properties compared to the corresponding flat geometry. Both structures contain 126 C atoms, and the flat ribbon is 7.5 nm wide. The band structure diagram of a freestanding double-looped graphene sheet is shown in Figure 2c. Compared with the single-loop shown in Figure 2a, the dispersion of the π*-states corresponding to one of the loops decreases around the Γ-point and increases in the second third of the Brillouin zone (BZ) for both π and π* states. The second π and π* bands corresponding to the other monolayer are slightly distorted but remain flat in this zone. Similar conclusions are valid for the triple-loop for which the dispersion of two of the π and π* bands is enhanced upon mutual interaction, as shown in Figure 2c. This observation clearly indicates a fold-induced band interaction. Regarding the geometrical properties of the closed-edges graphene, several differences can be noticed depending on the number of concentric layers. In our experiments, we identified six planar structures connected in pairs by means of loops of different diameters. For the simplest case of a single-loop, Figure 2e,f shows a top view of zigzag and armchair loop GNRs fully relaxed by means of a DFT. The A−A long-distance stacking found in the looped region progressively disappears moving away from the closed edge. As soon as the C atoms in the bilayer start to interact through vdW forces, a lateral displacement that gradually reaches an A−B stacking away from the folded edge occurs, as predicted by atomistic simulations reported in ref 21. The diameter of the various free-standing closed-edge structures studied here for single and concentric loops are reported in the caption of Figure 1. The geometries and distances between a graphene layer and single- and double-loops are shown in Figure 3. The diameter of the looped region is decreased with respect to the freestanding configuration due to the constraint imposed by the substrate. The typical vdW equilibrium distance of ∼3.3 Å is observed between consecutive parallel flat regions. In the multiple loop structure shown in Figure 3b), the interaction between concentric layers leads to larger diameter geometries in comparison to the single-loop case. Different interlayer distances between the external looped sheets and the flat substrate are observed when moving from the looped region, 2100



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density approximation (LDA)26 was adopted27 for the exchange correlation functional, and the Troullier−Martins scheme28 was employed to describe the interaction between ionic cores and localized pseudoatomic orbitals. All atoms were relaxed with a maximum force tolerance of 0.01 eV/Å. The lattice parameter along the periodic direction was determined by minimizing the stress component below 0.02 GPa. During geometry optimizations, 48 k-points were used to sample the one-dimensional BZ. The numerical integrals were performed on a real space grid with an equivalent cutoff of 300 Ry.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

Figure 4. (a) HRTEM images of looped edges in GNRs exhibiting two and three concentric loops. In b and c, the closed-edge ribbons calculated with DFT-based tools are superimposed on the images of panel a, showing an excellent agreement between experimental and computed positions.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

these loops. In addition, more complex edge morphologies such as multilayer loops have been observed after Joule heating due to the much higher annealing temperatures (e.g., 3000 °C). In summary, we have presented details of theoretical and experimental results on single and multiply coalesced graphene nanoribbons into loops. The experimental characterization of stable coalesced edge structures (loops) in few-layer graphene samples obtained by HRTEM are in good agreement with quantum mechanical DFT calculations of the electronic and geometrical structures. The fully relaxed geometry and electronic state distribution of multilayers in a closed geometry confirm that the stacking of multiple layers leads to the shrinking of the radius of curvature within the inner loops as compared to the single-loop. The DFT-based results show that edge coalesced regions preserve the original electronic state distribution of both armchair and zigzag flat ribbons, although a modification of the edge π and π* states was observed for the single zigzag-edged loop. The π-states of multiple loops near the Fermi level are disturbed in this case, exhibiting an enhanced localization at the Γ-point and dispersion at the X point of the BZ. We believe that the coexistence of different degrees of curvature along the same structure would induce different degrees of reactivity, suggesting a novel and controllable way for band engineering through functionalization of different reactive molecules on graphene surfaces at both flat and looped edges.

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ACKNOWLEDGMENTS This research used computational resources of the Oak Ridge Leadership Computing Facility, located in the National Center for Computational Sciences at Oak Ridge National Laboratory, and the computational resources of the National Energy Research Scientific Computing Center, which are supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22750 and Contract No. DEAC02-05CH11231, respectively. The research was supported by the Center for Nanophase Materials Sciences (CNMS), sponsored at Oak Ridge National Laboratory by the Division of Scientific User Facilities, U.S. Department of Energy. V.M. was supported in part by New York State under NYSTAR contract C080117. Research at RPI (VM) was also sponsored in part by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-12-2-0023. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government.

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REFERENCES

(1) Sun, Z.; James, D. K.; Tour, J. M. Graphene Chemistry: Synthesis and Manipulation. J. Phys. Chem. Lett. 2011, 2, 2425−2432. (2) Novoselov Novoselov, K. S. Nobel Lecture: Graphene: Materials in the Flatland. Rev. Mod. Phys. 2011, 83, 837−849. Geim, A. K. Nobel Lecture: Random Walk to Graphene. Rev. Mod. Phys. 2011, 83, 851− 862. (3) Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K. The Electronic Properties of Graphene. Rev. Mod. Phys. 2009, 81, 109. (4) Rao, C. N. R.; Sood, A. K.; Voggu, R.; Subrahmanyam, K. S. Some Novel Atrributes of Graphene. J. Phys. Chem. Lett. 2010, 1, 572− 580. (5) Kim, K.; Lee, Z.; Malone, B. D.; Chan, K. T.; Alemán, B.; Regan, W.; Gannett, W.; Crommie, M. F.; Cohen, M. L.; Zettl, A. Multiply Folded Graphene. Phys. Rev. B 2011, 83, 245433. (6) Hiura, H.; Ebbesen, T. W.; Fujita, J.; Tanigaki, K.; Takada, T. Role of sp3 Defect Structures in Graphite and Carbon Nanotubes. Nature 1994, 367, 148−151. (7) Roy, H.-V.; Kallinger, C.; Sattler, K. Study of Single and Multiple Foldings of Graphitic Sheets. Surf. Sci. 1998, 407, 1−6.

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MATERIALS AND METHODS The studied material consists of CVD-grown GNRs subjected to a high-temperature annealing after synthesis. The GNRs were synthesized through the pyrolysis of ethanol/ferrocene/ thiophene solutions, as described previously.5 In this work, TEM studies were carried out using a TITAN FEI 80/300 transmission electron microscope equipped with a single Cscorrector, which was operated at 80 kV in parallel TEM mode. We also performed electron microscopy studies using a JEOL JEM-2100F equipped with two Cs-correctors, and it was operated at 120 kV and 80 kV. The DFT-based calculations of the electronic and geometric structures were performed with the SIESTA code24,25 using a double-ζ basis set with additional polarization orbitals to optimize the geometry of the closed-edge armchair and zigzag ribbons and to determine the electronic properties. The local 2101



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(8) Ni, Z.; Wang, Y.; Yu, T.; You, Y.; Shen, Z. Reduction of Fermi Velocity in Folded Graphene Observed by Resonance Raman Spectroscopy. Phys. Rev. B 2008, 77, 235403. (9) Liu, Z.; Suenaga, K.; Harris, P. J. F.; Iijima, S. Open and Closed Edges of Graphene Layers. Phys. Rev. Lett. 2009, 102, 015501. (10) Campos-Delgado, J.; Kim, Y. A.; Hayashi, T.; Morelos-Gómez, A.; Hofmann, M.; Muramatsu, H.; Endo, M.; Terrones, H.; Shull, R. D.; Dresselhaus, M. S.; et al. Thermal Stability Studies of CVD-Grown Graphene Nanoribbons: Defect Annealing and Loop Formation. Chem. Phys. Lett. 2009, 469, 177−182. (11) Niyogi, S.; Bekyarova, E.; Hong, J; Khizroev, S.; Berger, C; de Heer, W; Haddon, R. C. Covalent Chemistry for Graphene Electronics. J. Phys. Chem. Lett. 2011, 2, 2487−2498. (12) Lee, Y.-S; Marzari, N. Cycloaddition Functionalizations to Preserve or Control the Conductance of Carbon Nanotubes. Phys. Rev. Lett. 2006, 97, 116801. (13) Liu, C.; Zhang, Q.; Stellacci, F.; Marzari, N.; Zheng, L.; Zhan, Z. Carbene-Functionalized Single-Walled Carbon Nanotubes and Their Electrical Properties. Small 2011, 7, 1257−1263. (14) Margine, E. R.; Bocquet, M.-L.; Blase, X. Thermal Stability of Graphene and Nanotube Covalent Functionalization. Nano Lett. 2008, 8, 3315−3319. (15) Lopez-Bezanilla, A.; Triozon, F.; Latil, S; Blase, X.; Roche, S. Effect of the Chemical Functionalization on Charge Transport in Carbon Nanotubes at the Mesoscopic Scale. Nano Lett. 2009, 9, 940− 944. (16) Campos-Delgado, J.; Baptista, D. L.; Lopez-Bezanilla, A.; Sumpter, B.; Meunier, V.; Kim, Y. A.; Muramatsu, H.; Hayashi, T.; Endo, M.; Terrones, M.; Achete, C. A. Nano-drilling of Few Layer Graphene Assisted by Metal Nanoparticles at Low Accelerating Voltages. (In preparation). (17) Gülseren, O.; Yildirim, T.; Ciraci, S. Tunable Adsorption on Carbon Nanotubes. Phys. Rev. Lett. 2001, 87, 116802. (18) Jia, X.; Hofmann, M.; Meunier, V.; Sumpter, B. G.; CamposDelgado, J.; Romo-Herrera, J. M.; Kong, J.; Terrones, M.; Dresselhaus, M. S. Controlled Formation of Sharp Zigzag and Armchair Edges in Graphitic Nanoribbons. Science 2009, 323, 1701−1705. (19) Fujita, M.; Wakabayashi, K.; Nakada, K.; Kusakabe, K. Peculiar Localized State at Zigzag Graphite Edge. J. Phys. Soc. Jpn. 1996, 65, 1920−1923. (20) Cresti, A.; Nemec, N.; Biel, B.; Niebler, G.; Triozon, F.; Cuniberti, G.; Roche, S. Charge Transport in Disordered GrapheneBased Low Dimensional Materials. Nano Res. 2008, 1, 361−394. (21) Zhang, J.; Xiao, J.; Meng, X.; Monroe, C.; Huang, Y.; Zuo, J.-M. Free Folding of Suspended Graphene Sheets by Random Mechanical Stimulation. Phys. Rev. Lett. 2010, 104, 166805. (22) Jia, X.; Campos-Delgado, J.; Gracia-Espino, E. E.; Hofmann, M.; Muramatsu, H.; Kim, Y. A.; Hayahsi, T.; Endo, M.; Kong, J.; Terrones, M.; Dresselhaus, M. S. Loop Formation in Graphitic Nanoribbon Edges Using Furnace Heating or Joule Heating. J. Vac. Sci. Technol. 2009, 27, 1996−2002. (23) Nistor, L. C.; Van Tendeloo, G.; Dinca, G. Crystallographic aspects related to the high pressure-high temperature phase transformation of boron nitride. Philos. Mag. 2005, 85, 1145−1158. (24) Soler, J.; Artacho, E.; Gale, J.; Garcia, A.; Junquera, J.; Ordejón, P.; Sanchez-Portal, D. The SIESTA Method for Ab Initio Order-N Materials Simulation. J. Phys.: Condens. Matter 2002, 14, 2745−2779. (25) Ordejon, P.; Artacho, E. Soler Self-Consistent Order-N DensityFunctional Calculations for Very Large Systems. Phys. Rev. B 1996, 53, 10441−10444. (26) Ceperley, D. M.; Alder, B. J. Ground State of the Electron Gas by a Stochastic Method. Phys. Rev. Lett. 1980, 45, 566−569. (27) We also explicitly considered the effects of vdW interactions in the relaxation of the atomic positions by using the so-called vdW-DF2 functional approach. These calculations were performed to ensure the accuracy of the computed geometries within the LDA approach. With respect to the electronic calculations, strictly speaking, the non-local vdW correlation is not defined for spin-polarized systems. The vdWDF approach can be used to obtain accurate geometric and binding

energies, but to obtain the spin polarized electronic structure, the PBE functional was used (see Klimes, A; et al. Phys. Rev. B 2011, 83, 195131. ). No major differences were observed between the approaches. Thus, the LDA was chosen for the overall study. We note that LDA is also more suitable than the GGA to explore weakly interacting systems such as the π-stacking interaction on sp2-like materials. (See Tournus, F.; Latil, S.; Heggie, M. I.; Charlier, J.-C. Phys. Rev. B 2005, 72, 075431. (28) Troullier, N.; Martins, J. L. Efficient Pseudopotentials for PlaneWave Calculations. Phys. Rev. B 1991, 43, 1993.

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Geometric and Electronic Structure of Closed Graphene Edges - The

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