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Graphene to fluorographene and fluorographane: a theoretical study

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Please note that terms and conditions apply. IOP PUBLISHING NANOTECHNOLOGY Nanotechnology 24 (2013) 035706 (8pp) doi:10.1088/0957-4484/24/3/035706 Graphene to fluorographene and fluorographane: a theoretical study

R Paupitz1, P A S Autreto2, S B Legoas3, S Goverapet Srinivasan4,AC T van Duin4 and D S Galvao˜ 2

1 Departamento de F´ısica, IGCE, Universidade Estadual Paulista, 13506-900, Rio Claro, SP, Brazil 2 Instituto de F´ısica ‘Gleb Wataghin’, Universidade Estadual de Campinas, 13083-970, Campinas, SP, Brazil 3 Departamento de F´ısica, CCT, Universidade Federal de Roraima, 69304-000, Boa Vista, RR, Brazil 4 Department of Mechanical and Nuclear Engineering, Penn State University, University Park, PA 16801, USA

E-mail: [email protected] and galvao@ifi.unicamp.br

Received 27 September 2012, in final form 27 November 2012 Published 21 December 2012 Online at stacks.iop.org/Nano/24/035706 Abstract We report here a fully reactive molecular dynamics study on the structural and dynamical aspects of the fluorination of graphene membranes (fluorographene). Our results show that fluorination tends to produce defective areas on the graphene membranes with significant distortions of carbon–carbon bonds. Depending on the amount of incorporated fluorine atoms, large membrane holes were observed due to carbon atom losses. These results may explain the broad distribution of the structural lattice parameter values experimentally observed. We have also investigated the effects of mixing hydrogen and fluorine atoms on the graphene functionalization. Our results show that, when in small amounts, the presence of hydrogen atoms produces a significant decrease in the rate of fluorine incorporation onto the membrane. On the other hand, when fluorine is the minority element, it produces a significant catalytic effect on the rate of hydrogen incorporation. We have also observed the spontaneous formation of new hybrid structures with different stable configurations (chair-like, zigzag-like and boat-like) which we named fluorographane. S Online supplementary data available from stacks.iop.org/Nano/24/035706/mmedia (Some figures may appear in colour only in the online journal)

1. Introduction chemical methods, which include the use of quantum dots [6], strain [7], nanoribbons [8–10], chemical modification through The discovery of new carbon-based materials has been oxidation [11–16] and hydrogenation [17–19]. In this way, frequent in the past few decades. Recent examples of partial graphene functionalization with suitable elements, in these materials are colossal nanotubes [1] and graphene [2]. order to transform the carbon hybridization from sp2 to Graphene is a two-dimensional array of hexagonal units of sp2 sp3, has been tried to solve the problem of its gapless bonded C atoms with very unusual and interesting electronic nature. Theoretical and experimental works have indicated and mechanical properties [3]. Because of these electronic that hydrogen, oxygen and, recently, fluorine are good properties, graphene is considered one of the most promising candidates to open the band gap. The resulting structure from materials for future electronics [4]. However, in its pristine these processes are the so-called graphene oxide (GO) [20], state graphene is a gapless semiconductor, which creates graphane [17] and fluorographene (FG) [21]. limitations for a graphene-based transistor electronics [5]. GO has been produced by exposure of graphite to Much effort has been devoted to trying to find a route liquid oxidizing agents and it is basically a graphene sheet to open, in a controlled way, a gap in the graphene band randomly and inhomogeneously decorated with hydroxyl structure. The most common strategies explore physical and and epoxy groups. The chemical route through this singular

+08$33.00 10957-4484/13/035706 c 2013 IOP Publishing Ltd Printed in the UK & the USA Nanotechnology 24 (2013) 035706 R Paupitz et al structure may turn out to be one of the most effective ways used to obtain large-scale functionalized materials. Graphane [17] was theoretically predicted in 2007 and consists of a single-layer structure with fully saturated (sp3 hybridization) carbon atoms with C–H bonds in an alternating pattern (up and down with relation to the plane defined by the carbon atoms). Its two most stable conformations are the so called chair-like (H atoms on both sides of the plane) and boat-like (H atoms alternating in pairs) [17]. The graphane-like experimental realization has been reported by different groups [22–24]. More recently, Elias et al [19] demonstrated the existence of graphane formation from graphene membranes through its fully hydrogenation, and showed that graphene membranes with both surfaces exposed to atomic H exhibited a compressed crystal lattice [3]. Despite these promising results, the hydrogenation of graphene was observed to be an easily reversible process even at moderate temperatures, which compromises the use of graphane in applications where such stability is required. Figure 1. Graphane, fluorographane and fluorographene structures investigated here. (a), (d) and (g) are chair-like, (b), (e) and (h) are One way to open the gap and create more stable graphene zigzag-like, and (c), (f) and (i) are boat-like conformations. The derivatives has been through the use of more reactive species structures (a)–(c) correspond to graphane or fluorographene than hydrogen [21]. Graphene covered with fluorine could be (colored circles represent H or F atoms, in up (blue) and down a good option because it is a 2D analogue of the well-known (orange) configurations). (d)–(f) and (g)–(i) correspond to fluorographane (1F) and (2F) structures, respectively (blue (orange) materials: Teflon, which is composed of fluorinated 1D carbon circles as H up (down) atoms, and dark (light) green circles as F up chains, and graphite fluoride (GrF), a multi-layer graphene (down) atoms). The structures were geometrically optimized fluoride. However, obtaining FG from mechanical cleavage of without constraints. The highest possible symmetry groups for each graphite fluoride has proved to be a very difficult task. one of the ideal structures are indicated in the panels. Recently, new methods for the creation of FG were achieved [21, 25]. One of the most successful process has 2. Methodology been one in which graphene is exposed to atomic F formed by decomposition of xenon difluoride (XeF ). It was shown 2 The hydrogen and fluorine incorporation processes on that the resulting FG exhibits a strong insulating behavior at graphene were studied with molecular dynamics (MD) room temperature and high stability up to 400 ◦C. However, techniques using reactive force fields (ReaxFF [27–29]), as Raman measurements also indicate that, even if the process implemented in the large-scale atomic/molecular massively takes a long time, the resulting sample presents some regions parallel simulator (LAMMPS) code [30]. ReaxFF is a with carbon atoms that are not bonded to fluorine atoms reactive force field developed by van Duin, Goddard III and the coverage saturation can vary depending on the and co-workers for use in MD calculations, allowing the method adopted for fluorination [21]. Also claimed was the simulation of many types of chemical reactions. ReaxFF existence of a hybrid structure containing fluorine and bonded has some characteristics which are similar to those found hydrogen atoms, resulting in different FG configurations. in standard non-reactive force fields, like MM3 [31]. In this Theoretical ab initio studies have supported the idea of the kind of force field, the system energy is divided into partial existence of two FG configurations. These configurations energy contributions associated with, amongst others, valence have small differences in the formation energy, but a large angle bending and bond stretching, as well as non-bonded van interconversion energy barrier [26]. Nevertheless, in spite der Waals and Coulomb interactions [29, 28, 27]. However, of the importance of this problem, no detailed theoretical in the case of ReaxFF, one main difference is that it can investigation on the dynamics of graphene fluorination has handle bond formation and dissociation (making/breaking been carried out. bonds) as a function of bond order values. ReaxFF was In the present work we have investigated, using fully parametrized against DFT calculations, being the average reactive molecular dynamics methods, the structural and deviation between the heats of formation predicted by the dynamical aspects of the fluorination mechanism, leading theory (ReaxFF) and by the experiment equal to 2.8 and to FG formation from graphene structures. We have also 2.9 kcal mol−1, for non-conjugated and conjugated systems, investigated H and F incorporations with mixed atmospheres respectively [3]. In figure2 we present the DFT data and in order to evaluate the effect of a second chemical element the ReaxFF results related to the development of the ReaxFF in the hydrogenation and/or fluorination processes. For these C/F parameters used in the present work. This involves bond cases new configurations with F and H atoms bonded to the breaking (figure2(a)), angle distortions and rotation around a membranes were observed to spontaneously form (figure1). FC–CF double- and single-bond (figures2(b) and (c)). For all

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Figure 3. Incorporation of F and H atoms on a graphene membrane at 300 K. BF(H)/BC is the ratio between bonded fluorines (hydrogens) and the number of carbon atoms of the membrane. F and F80H20 refer to the fluorination process with pure (F) and mixed (F and H) atmospheres, respectively. Black solid curve is associated with the ratio BH/BC in the fluorination process carried out in mixed atmospheres. See text for discussions.

3. Results and discussions

Molecular dynamics (MD) simulations can provide relevant structural information that can help us to interpret exper- imental data in complex phenomena such as the covalent functionalizations of graphene structures exposed to hydrogen and fluorine atoms. In this work, we simulated these processes through the use of MD simulations using reactive force fields. Large graphene membranes were exposed to hydrogen and fluorine (pure and mixed at different relative concentrations) atmospheres at different temperatures. From Figure 2. ReaxFF versus DFT energies: (a) C–F bond dissociation these simulations we analyzed the dynamics of hydrogen in CH3–CF2–CH3, (b) C–C–F angle bending in (CH3)3–CF and fluorine incorporations. In particular, we have analyzed (continuous lines) and F–C–F angle bending (dashed lines) in the rate of atom incorporation in time and the consequent CH3–CF2–CH3 and (c) C–C–C–C torsion angle bending in structural features, such as, the dominant configurations CF –CF –CF –CF and F–C–C–F torsion angle bending in 3 2 2 3 and their geometries. Many and different ideal (defectless) F2C–CF2 (dashed lines). Carbon atoms are colored brown while fluorine and hydrogen atoms are colored green and white structures can possibly form with hydrogen and fluorine respectively. Reaxff energies are represented by blue lines while atoms. Some of them are indicated in figure1. For details, DFT energies are red. The relevant geometric coordinate is indicated see section2. through red colored bonds. Angles are expressed in degrees. 3.1. Graphene to fluorographene these cases we found good agreement between ReaxFF and Initially, we investigated the incorporation rate of fluorine on DFT. the graphene membrane at 300 K. The results are presented The systems considered in our simulations are composed in figure3 (dashed curve). From this figure it is possible to of large graphene membranes (initially with dimension identify two regimes, an initial one in which the number of ∼160 A˚ × 160 A,˚ about 10 000 carbon atoms) embedded into fluorine atoms bonded to the membrane increases at a high a pure (F) or mixed (F and H) atmospheres, using a constant rate, and a second one where this rate (the slope of the curve) volume simulation box. The considered number of atoms in becomes very low, indicating the system is near a saturation the atmospheres was varied from the same up to twice the point. number of carbon ones, and they were randomly distributed At higher temperatures (example, 500 and 650 K), on both sides of the membrane. The typical time for a our results show that the graphene membranes experience complete simulation run was 1.0 ns, considering timesteps significant structural damages. As we are interested in the of 1.0 fs (performing about 106 MD steps) and using a cases where we can have a gap opening but still preserving Langevin thermostat. Smaller timesteps were also considered, the graphene-like structures, in the following we restricted our obtaining results which are consistent with those obtained in analysis to the cases around 300 K, since the observed damage the simulations discussed in the text. was not extensive for this temperature.

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Figure 4. Representative snapshots from the molecular dynamics simulations of the fluorination process. F atoms are indicated in red. (a) Initial configuration. (b) Early stage of simulation with randomly distributed F atoms. (c) Intermediate stage. (d) Final stage.

During the fluorination process, the carbon atoms which distinct. For instance, while in the hydrogenation processes are bonded to fluorine ones have their sp2 hybridization the formation of uncorrelated domains is quite common [3, transformed into a partially sp3-like hybridization. This 33], for the fluorination we did not observe domain formation, transformation from a planar to a tridimensional structure which is in accordance with [32]. DFT-based potential energy has electronic consequences and has been extensively studied, curve at a B3LYP/6-31g∗∗ level of theory indicates that F as mentioned earlier. For these reasons, it is important to atoms bind to coronene molecules in a barrierless process understand the geometry of the fluorinated system and to with a binding energy of 20 kcal mol−1, consistent with our compare it with graphane under the same conditions. ReaxFF-based energies. This barrierless chemisorption of F In figure4 we present representative snapshots from atoms onto coronene (or graphene in general) could explain a 0.5 ns MD simulation of the fluorination process at the absence of domains of F atoms on graphene. 300 K for a atmosphere composed only of F atoms. Initially, In figure5(a) we present histograms of second neighbor figure4(a), we have a graphene membrane almost perfectly distances (related to the unit cell lattice) at the final planar, immersed in a fluorine atmosphere. In figure4(b) configuration of a graphene membrane and FG at the same is shown an early stage of simulation, when several atoms temperature. The FG cell size was calculated to be ∼1.3% of the gas are already randomly bonded to the membrane. larger than that of graphene in vacuum. How these histograms In figures4(c) and (d) are presented the final fluorination evolve in time can be seen in the animated histograms in the stages. A better visualization of the whole process can be supplementary materials (available atstacks.iop.org/Nano/24/ obtained from the videos in the supplementary materials 035706/mmedia). The mean values of these distributions are (available atstacks.iop.org/Nano/24/035706/mmedia). These in good agreement with experimental results reported by results showed that at the early stages of fluorination, Geim and co-workers [21]. Time evolution of these mean the opposite side ortho position is the most common values is shown in figure5(b), where three regimes are C–F configuration for adjacent F atoms. This favors the identified. These regimes are related to the time changes of formation of chair domains, as observed in the fluorination fluorination rate (see figure3). In our simulations, typical advanced stages. These results are consistent with reported F–C bond distances are about 1.4 A,˚ which agree well with DFT calculations for graphite fluorides [26]. Although the theoretical ab initio [34] and experimental [35] results. fluorination and hydrogenation processes can both lead to Recently, some discrepancies between theoretical results effectively functionalized graphene structures and share some and experimental data for the band gaps and Young’s moduli common dynamical aspects, there are some ones that are quite of fluorinated structures indicated that experimental samples

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Figure 6. Hydrogen rate incorporation as a function of time for pure (H) and mixed (80% of H atoms and 20% of F atoms) atmospheres.

Figure 5. Effect of fluorination on second neighbor carbon distances. (a) Distribution of the second neighbor carbon–carbon distances for pure graphene and fluorinated membranes at 300 K. Figure 7. Representative snapshots from the molecular dynamics Vertical lines indicate the mean value of these distances for simulations of the H and F atoms incorporation process. H atoms graphene and fluorographene. (b) Mean second neighbor are represented in yellow and F atoms in red. (a) Early stage of carbon–carbon distances during the fluorination process. There are simulation when fluorine atoms are the dominating incorporation three regimes of mean values variation, indicated by r1, r2 and r3. species. (b) Final stage, when H domains are formed around F See text for discussions. atoms. See text for discussions.

Table 1. ReaxFF results for the total potential energy for some of still contain appreciable amounts of defects [26]. One of these the possible configurations for graphane, fluorographene, and defects could be some kind of H contamination. In order fluorographane with 1 (1F) and 2 (2F) fluorine atoms. Results are in to investigate the effect of hydrogen contamination on the eV/atom. fluorination processes, we carried out a series of simulations Chair Zigzag Boat for atmospheres containing both F and H atoms. In figure3 we Graphane −5.65 −5.54 −5.61 present the results for the case of an atmosphere composed Fluorographane (1F) −5.73 −5.66 −5.70 of 80% F and 20% H. As we can see from the figure, there Fluorographane (2F) −5.83 −5.78 −5.81 is a decrease in the rate of the fluorine incorporation in Fluorographene −6.14 −5.96 −6.00 relation to a pure F atmosphere. The black solid curve in figure3 indicates that, even at low concentration, hydrogen incorporation is also observed. An effect that can play an have also decided to investigate whether the opposite could important role in this process is the fact that H gas can act like occur, i.e., how small quantities of the highly reactive fluorine a reducing agent for the mobility of F atoms, decreasing the would affect the hydrogenation processes. In this sense, we frequency of C–F collisions and, consequently, decreasing the studied the dynamics of graphene membranes embedded in rate of incorporation. We can also consider the competition hydrogen atmospheres contaminated with fluorine atoms. In for the reactive sites between F and H as another component figure6 we present the results for the rate of hydrogen in retarding the fluorination process. incorporation as a function of time for pure and mixed (H and F) atmospheres. As can be seen from the figure, after 3.2. Fluorine as a catalyst for hydrogen incorporation 200 ps the number of incorporated H atoms is significantly increased for the case of mixed atmospheres. The F atoms As the presence of H atoms into the F atmosphere was seem to work as a catalyst for H atom incorporation. In shown to significantly affect the rate of F incorporation, we figure7 we present representative snapshots of the MD

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Table 2. Barriers, reaction energy and transition state C–H distance for the binding of H on graphene and F-graphene. Reaction Reaction Barrier energy (kcal mol−1) C–H distance (A)˚ energy (kcal mol−1) H on graphene 4.42 1.744 −36.42 H on F-graphene: Same side ortho position 6.07 1.904 −46.84 Same side metaposition 9.9 1.698 −27.47 Same side paraposition 1.98 1.792 −42.55 Opposite side orthoposition 1.36 1.944 −63.4 Opposite side metaposition 11.0 1.714 −27.63 Opposite side paraposition 3.89 1.82 −38.97 simulations for the mixed atmosphere. At the early stages (figure7(a)) we observed that F atoms are always the first ones to be incorporated on the graphene membrane and their presence causes strong geometrical deformations on the honeycomb lattice, creating highly reactive sites, making easier the bonding of H atoms and causing the H clustering around the attached F. In these conditions C–H bonds are formed initially in the neighborhood of adsorbed fluorines and, after subsequent H incorporation, large regions of fluorinated graphane can be formed (figure7(b)). We called this new configuration fluorographane. Three fluorographane configuration patterns were identified. The H and F were observed in chair-like, boat-like and zigzag-like pattern configurations (see figure8). Chair is known to be the lowest energy configuration for graphane [17] and it is the most frequently found in our simulations. The observed structures included not only graphene with separated hydrogenated and fluorinated regions, but also organized regions in which F and H form one of those three patterns shown in figure8. These results can be better understood when we analyze the specific energy of the different configurations. In tables1 and2 we present the potential energy, barriers and reaction energies for graphane, fluorographene and fluorographane. In table1 we present the total ReaxFF potential energy (depicting essentially the atomization energy) values for the different structures considering the cases with the presence of 1 and 2 fluorine atoms in the unit cell. For all cases considered here we can see from the table that the chair configurations Figure 8. Structural configurations formed during the incorporation are the most stable conformers, followed by the boat ones. process in a mixed atmosphere (80% of H atoms and 20% of F The zigzag conformation results in a less stable structure. It atoms). (a) chair-like, (b) zigzag-like and (c) boat-like is also observed that the structural stability increases with configurations. In the figures, yellow represents H atoms while red the number of fluorine atoms. The small energy differences represents F atoms. for the different configurations can explain the simultaneous presence of the three main configurations (chair-like, boat-like favorably to the ortho position on the opposite side of and zigzag-like) in our MD simulations. the graphene sheet (opposite with respect to the fluorine In order to further evaluate the consistency of our MD atom). Based on the barriers, the relative ease of H results, we calculated the ReaxFF-based barriers and reaction binding to various positions on the F-graphene sheet can > > energies for the binding of a hydrogen atom to a pristine be summarized as: opposite side ortho same side para > > > graphene sheet and to a F-graphene sheet (i.e. graphene opposite side para same side ortho same side meta functionalized with a single fluorine atom). Six different opposite side meta. See also the discussions related to figure2 positions, as shown in figure9, for the binding of a in section2. hydrogen atom to the F-graphene sheet, were considered for the calculation. The relative energies as a function 4. Summary and conclusions of the atomic distances are presented in figure 10. The barriers and the reaction energies are summarized in table2. We have used a fully reactive molecular dynamics approach From these numbers, it can be seen that H binds most in order to study the structural and dynamical effects of the

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(a) (b)

(c) (d)

(e) (f)

Figure 9. Possible conformations for hydrogen atom binding to F-Graphene: (a) same side ortho binding, (b) opposite side Figure 10. Potential energy surface for H binding on orthobinding, (c) same side metabinding, (d) opposite side fluorographene, indicated by FG: (a) same side binding, (b) opposite metabinding, (e) same side parabinding, (f) opposite side side binding. The potential energy surface for hydrogen binding on parabinding. Carbon atoms are colored brown while fluorine and graphene is shown in (a) and (b) for reference. hydrogen atoms are colored green and white, respectively.

atstacks.iop.org/Nano/24/035706/mmedia). On the other incorporation of H and F atoms on graphene membranes, hand, previously exposing graphene to a diluted hydrogen exposed to pure and mixed (F20H80 and F80H20) atomic atmosphere can reduce the structural damage created by fluorine and hydrogen gaseous atmospheres. Our results fluorination. We hope that the present work can stimulate showed that the fluorination process occurs without correlated further experimental works along these research lines. domain formation (which was observed in graphanes) and resulted in a fluorographene structure which has a unit cell 1.3% larger than that observed for graphene. At high Acknowledgments temperatures, the fluorine atoms induce significant damage to the membrane, with extensive formation of holes and carbon This work was supported in part by the Brazilian Agencies losses. CNPq, CAPES, FAPESP. Ricardo Paupitz is grateful for We have also considered the dynamics of chemical the financial support of Fapesp (grant 2011/17253-3) and functionalizations of mixed atmospheres of fluorine and Fundunesp (grant 01409/11). The authors wish to thank M hydrogen atoms. For the case of an atmosphere of F80H20, Z S Flores for very useful discussions. ACTvD and SGS the presence of hydrogen atoms results in an expressive acknowledge funding from the Air Force Office of Scientific decrease in the rate of fluorine atoms incorporated into the Research under AFOSR-MURI Grant FA9550-10-1-0563. membrane. For the opposite corresponding case (F20H80), the presence of fluorine atoms acts as a catalyst for the References hydrogenation, increasing the rate of hydrogen incorporation. Our results also indicate that the rate of hydrogenation [1] Peng H et al 2008 Phys. Rev. Lett. 101 145501 on graphene membranes can be significantly improved by [2] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, previously exposing the graphene structures to diluted fluorine Dubonos S V, Grigorieva I V and Firsov A A 2004 Science atmosphere (see video 7 in the supplementary materials, 306 666

7 Nanotechnology 24 (2013) 035706 R Paupitz et al [3] Flores M Z S, Autreto P A S, Legoas S B and [18] Ryu S, Han M Y, Maultzsch J, Heinz T F, Kim P, Galvao˜ D S 2009 Nanotechnology 20 465704 Steigerwald M L and Brus L E 2008 Nano Lett. 8 4597 [4] Cheng S H, Zou K, Okino F, Gutierrez H R, Gupta A, Shen N, [19] Elias D C et al 2009 Science 323 610 Eklund P C, Sofo J O and Zhu J 2010 Phys. Rev. B [20] Eda G and Chhowalla M 2010 Adv. Mater. 22 2392 81 205435 [21] Nair R R et al 2010 Small 6 2773 [5] Withers F, Dubois M and Savchenko A K 2010 Phys. Rev. B [22] Lueking A D, Gutierrez H R, Fonseca D A, Narayanan D L, 82 73403 van Essendelft D, Jain P and Clifford C E B 2006 J. Am. [6] Ponomarenko L A, Schedin F, Katsnelson M I, Yang R, Chem. Soc. 128 7758 Hill E W, Novoselov K S and Geim A K 2008 Science [23] Boukhvalov D W, Katsnelson M I and Lichtenstein A I 2008 320 356 Phys. Rev. B 77 35427 [7] Guinea F, Katsnelson M I and Geim A K 2010 Nature Phys. [24] Casolo S, Lovvik O M, Martinazzo R and Tantardini G F 2009 6 30 J. Chem. Phys. 130 054704 [8] Han M Y, Ozyilmaz B, Zhang Y and Kim P 2007 Phys. Rev. [25] Robinson J T et al 2010 Nano Lett. 10 3001 Lett. 98 206805 [26] Leenaerts O, Peelaers H, Hernandez-Nieves A D, [9] Li X, Wang X, Zhang L, Lee S and Dai H 2008 Science Partoens B and Peeters F M 2010 Phys. Rev. B 82 195436 319 1229 [27] van Duin A C T, Dasgupta S, Lorant F and Goddard W A III [10] Han M, Ozyilmaz B, Zhang Y, Jarillo-Herero P and 2001 J. Phys. Chem. A 105 9396 Kim P 2007 Phys. Status Solidi b 244 4134 [28] van Duin A C T and Damste´ J S S 2003 Org. Geochem. 34 515 [11] Stankovich S, Dikin D A, Piner R D, Kohlhaas K A, [29] Chenoweth K, van Duin A C T and Goddard W A III 2008 Kleinhammes A, Jia Y, Wu Y, Nguyen S B T and J. Phys. Chem. Ruoff R S 2007 Carbon 45 1558 A 112 1040 [12] Gilje S, Han S, Wang M, Wang K L and Kaner R B A 2007 [30] Plimpton S 1995 J. Comput. Phys. 117 1 Nano Lett. 7 3394 [31] Allinger N L, Yuh Y H and Lii J H 1989 J. Am. Chem. Soc. [13] Gomez-Navarro C, Weitz R T, Bittner A M, Scolari M, 111 8551 Mews A, Burghard M and Kern K 2007 Nano Lett. 7 3499 [32] Ribas M A, Singh A K, Sorokin P B and Yakobson B I 2011 [14] Ruoff R 2008 Nature Nanotechnol. 3 10 Nano Res. 4 143 [15] Wu X, Sprinkle M, Li X, Ming F, Berger C and [33] Chandrachud P, Pujari B S, Haldar S, Sanyal B and De Heer W A 2008 Phys. Rev. Lett. 101 26801 Kanhere D G 2010 J. Phys.: Condens. Matter 22 465502 [16] Kaiser A B, Gomez-Navarro´ C, Sundaram R S, [34] Han S S, Yu T H, Merinov B V, van Duin A C T, Burghard M and Kern K 2009 Nano Lett. 9 1787 Yazami R and Goddard W A 2010 Chem. Mater. 22 2142 [17] Sofo J O, Chaudhari A S and Barber G D 2007 Phys. Rev. B [35] Sato Y, Itoh K, Hagiwara R, Fukunaga T and Ito Y 2004 75 153401 Carbon 42 3243

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