Computational Materials Science 68 (2013) 391–395

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Computational Materials Science

journal homepage: www.elsevier .com/locate /commatsci

A possible self-healing mechanism in damaged graphene by heat treatment

Jianwei Zhu a, Daning Shi a,b,⇑a Department of Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, Chinab Key Laboratory for Intelligent Nano Materials and Devices of The Minister of Education, Nanjing 210016, China

a r t i c l e i n f o

Article history:Received 1 July 2012Received in revised form 27 August 2012Accepted 30 October 2012Available online 13 December 2012

Keywords:DamageSelf-healingGrapheneHeat treatmentMolecular dynamics simulation

0927-0256/$ - see front matter Crown Copyright � 2http://dx.doi.org/10.1016/j.commatsci.2012.10.041

⇑ Corresponding author at: Department of Physicsnautics and Astronautics, Nanjing 210016, China. Tel.

E-mail address: shi@nuaa.edu.cn (D.N. Shi).

a b s t r a c t

As an emerging candidate of high-performance electrical and mechanical devices, graphene may be dam-aged unexpectedly by external force or constant strain in practical applications, resulting in the lifespanand performance degradation in graphene-based devices. Here, nano-damage in suspended graphenemonolayer is created via a rigid C60 molecule. By applying molecular dynamics simulations, we show thatthe self-healing procedure happens under adequate heat treatment. It suggests an efficient two-stageself-healing mechanism in damaged graphene: local curvature introduced by defects around the damageand curved surface smoothed via defects reconstruction which leads to damage shrinking. In addition,our simulations indicate that thermal fluctuation and the size of damage determine the self-healing capa-bility of graphene. These results may offer additional insights for realizing self-healing nano-devices com-posed of graphene.

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1. Introduction

Since the discovery of graphene in 2004 [1,2], great efforts havebeen made by hundreds of researchers to use them in the study ofdevice applications. Recent progress has been made in manufactur-ing high-performance devices such as transparent films [3], tran-sistors [4] and optical biosensors [5]. Structural damage anddefects, such as holes and vacancies are not thermodynamicallydominant in graphene due to their high formation energies, butthey do appear during growth, by chemical treatment or in irradi-ation environments [6,7]. The presence of these structural changesis known to introduce features attractive for applications, such asmagnetism [8,9], enhanced chemical activity [10,11] and functionas metallic wires [12]. Despite of this, defects are well-known totheir ability to increase carriers scattering, thereby deterioratingthe performance of graphene-based devices. It has been revealedthat even small defects are responsible for degradation in electricaltransport of graphene obtained by the exfoliation or chemicalreduction of graphene oxide platelets [13,14]. The dramatic reduc-tion of charge carrier mobility in graphene generated by microme-chanical cleavage has also been ascribed to nonhexagons [15].Besides, weaker bonds around damage undoubtedly affect thethermal conductivity and reduce the mechanical strength of graph-ene. In this point of view, the healing capability in graphene is cru-cial for maintaining graphene-based devices with high electrical

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conductivities and, naturally, excellent thermal and mechanicalproperties.

High temperature evaporation is a fascinating method to re-move the damage from graphene, typically for those samples byhydrocarbon gas with thermal annealing or electrical joule heating.For example, utilizing atomic layer etching technology, the hydro-carbon gas might decompose by thermal annealing to supply car-bon atoms that can heal the damage on the graphene surfacelayer [16]. In theoretical side, the heat treatment can be simulatedby molecular dynamics (MD) method. Carbon nanotubes are foundto hold powerful self-healing capability at high temperatures[17,18], while the ability of self-healing in damaged graphene islack of study in theory. Specifically, the underlying healing mech-anisms in damaged graphene are far from clear. There are lots ofpossible mechanisms for the healing process. In most cases, theresidual catalyst impurities are ineluctable in samples preparedby the chemical vapor deposition method, so that the catalystmay play a positive role on the procedure. Moreover, vacanciescan be healed by the assistance of impurities such as NO and COmolecules [19], which cannot be well predicted in experiments.Now a natural question arises: what will happen if damagedgraphene undergoes heat treatment without the assistance ofhydrocarbon gas and impurities? Therefore it is our motivationto have a comprehensive study of the structural evolution in dam-age at a wide range of temperatures.

In the current work, the self-healing capability of pure graphenewith nano-damage is investigated by MD simulations. A rigid C60

molecule is used to penetrate a monolayer graphene to producenano-damage. Details of structural evolution of the damage areidentified under different thermal temperatures. We propose a

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392 J.W. Zhu, D.N. Shi / Computational Materials Science 68 (2013) 391–395

possible two-stage mechanism to explain the capability of self-healing behavior in graphene. Moreover, we find that self-healingdepends on thermal fluctuation and the damage size. Since damageis unavoidable in practical applications, it is expected that the self-healing mechanism will be applied to promote limited lifespan andsimultaneously improve degraded performance of graphene-baseddevices.

2. Methods

In the framework of our MD simulations, the interatomic inter-actions are modeled with the adaptive intermolecular reactiveempirical bond-order (AIREBO) potential [20,21], which includescovalent bonding using both a bond order parameterized REBO po-tential and a 4-body potential that describes various dihedral anglepreferences, as well as long-ranged van der Waals interactionsusing standard Lennard–Jones 12-6 format. This potential reliablydescribes binding energies, lattice constant and bond length. Inparticular, it has a satisfied capability of describing the formationand breaking of carbon bonds [22]. In our simulations, the cut-offdistance of covalent C–C bonds is set to be 2.0 Å in order to avoidparticularly high bond force and therefore leads to non-physicalbehavior [23]. A velocity Verlet algorithm is used to integrate theNewton equations of motion with a time step of 0.5 fs.

The graphene monolayer is exfoliated from graphite with thenearest neighbor distance equals to 1.42 Å. The graphene sheethas a size of 12.8 Å (armchair direction) � 14.8 Å (zigzag direction).The boundary of graphene sheet considered is held rigid, and theremaining atoms in the center part are free to evolve with canon-ical ensemble (i.e. constant number of atoms, volume and temper-ature, NVT). Nosé–Hoover chain thermostat [24] is adopted toprovide optimal conservation of energy and minimize the fluctua-tion in temperature. The system is firstly relaxed at zero tempera-ture to minimize its energy by using conjugate gradient method,and is then gradually increased up to a high temperature within20 ps, after which it is kept at the temperature lasted for 30 ps.In order to observe self-healing behavior, we use a rigid C60 mole-cule to make nano-damage in graphene. The C60 molecule is ini-tially placed 6.5 Å above the graphene, after thermalequilibration the C60 molecule starts to penetrate the graphenesheet with a constant velocity of 5 Å/ps. The evolution of the pro-

Fig. 1. The deformation process of gra

duced nano-damage is then carefully monitored under the fixedtemperature.

3. Results and discussions

Fig. 1 illustrates the procedure of a rigid C60 molecule straininga graphene sheet with frozen edges up to destruction. Fig. 1ashows the initial structure, in which the C60 molecule is placed6.5 Å above the graphene monolayer. The deformation procedureis followed by Fig. 1b with flexure value d1. Fig. 1c correspondsto the point of critical strain with deflection d2. The snapshot withdamage is presented in Fig. 1d, where the flexure value is d3. Fig. 2shows the dependence of pressure of the graphene sheet alongz-direction (normal to graphene, Pz) from deflection (d) with tem-peratures ranging from 250 K to 3400 K, where Pz is defined asPN

k ðmkv2kz þ rkzfkzÞ=s, s is the area of the graphene sheet, N is the to-

tal number of atoms. The characteristic noise-like profiles of thecurves from MD simulations are smoothed out by the ensembleaveraging per 1 ps. It is demonstrated that below 1700 K Pz-dcurves have little relevant to temperatures within elastic limit.However, the critical strain and its corresponding pressuredecrease with increasing temperature. This thermal perturbationinduced softening phenomenon has also been revealed in our pre-vious study on graphene nanoribbons [25].

When the C60 molecule breaks the graphene sheet, it causes for-mation of a nano-hole and dangling bonds surrounded by breakingoriginal hexagonal rings or even making some atoms out of thesurface. Thermal perturbations may lead to the rotation or refor-mation of the bonds which produces nonhexagonal rings. In de-tails, we take the case of temperature at 3000 K as an example;the final morphology of the force-damaged graphene is shown inFig. 3b–c, where Fig. 3c is the partially enlarged drawing ofFig. 3b in the damaged region. Three typical micro-structuresaround the damage are arrowed in Fig. 3c, including a hexagon(arrow a), a short carbon linear atomic chain (LAC) with five atoms(arrow b) and a pentagon (arrow c). At first glance, the LAC is theedges of three hexagons. However, the distance between atoms 1and 2 (arrowed in Fig. 3c) is 2.89 Å, and the distance betweenatoms 3 and 4 is 3.28 Å. These values are far beyond critical C–Ccovalent bond length. After the C60 molecule gets through thegraphene sheet, the deformed atoms rebound in the directionopposite to the motion of C60 molecule. Noticeable Pz with a lapse

phene with a rigid C60 molecule.

Fig. 2. Pressure of graphene along the direction normal to graphene (Pz) as afunction of deflection (d) with temperatures ranging from 250 K to 3400 K.

Fig. 3. (a) Pressure along the direction normal to graphene as a function of evolvingtime with temperatures ranging from 250 K to 3000 K. (b) 3-D view of damagedgraphene at t = 1.7 ps and T = 3000 K. (c) Partially enlarged view of figure (b) aroundthe damage. Arrows a, b and c denote three typical morphologies around thedamage.

(a)

(b) t = 2.7 ps (c) t = 10.7 ps (d) t = 23.7 ps

(e) t = 58.7 ps (f) t = 64.7 ps (g) t = 198.7 ps

Fig. 4. (a) Number of atoms surrounding the damage as denoted in Fig. 3c versustime at temperature 3000 K. The time span between two adjacent points is 1 ps.(b)–(g) Structural evolution during the self-healing procedure.

J.W. Zhu, D.N. Shi / Computational Materials Science 68 (2013) 391–395 393

of time are shown in Fig. 3a. With time flying, Pz fluctuatesbetween positive and negative through graphene’s restoring force,corresponding to height fluctuation of the graphene sheet. Mean-while, the amplitude of Pz decrease with time because of energydissipation. Structural evolutions of damage can be monitored dur-ing this oscillatory procedure.

When the temperature reaches an adequate threshold, thedamaged graphene can be self-healed and turns into a stable con-figuration with only small defects. The self-healing procedure gen-erally consists of two stages. First, local curvature around thedamage is created from the nucleation of defects. Second, curvedsurface transforms into smoother surface via the reconstructionof defects, which gradually shrinks the damage till its annihilation.We now take the case of temperature at 3000 K as an illustration.Fig. 4a shows the number of atoms which surround the damage ingraphene evolve with a lapse of time. We learn that in general thenumber becomes less and less with the increasing time, whichimplies that size of the damage gets smaller and smaller until itbecomes a heptagonal ring composed of seven carbon atoms. Toanalyze the self-healing behavior, we divide the procedure into anumber of snapshots by red dotted lines as shown in Fig. 4a. Thecorresponding atomistic view is shown in Fig. 4b–g. More detailsof the evolution of the damage can be observed in a motion picturecompiled from the image size (see Supplementary material). In thefirst stage, the atoms around the damage try to optimize dangling

Fig. 5. Number of atoms surrounding the damage in graphene versus time attemperatures ranging from 250 K to 2500 K. The time span between two adjacentpoints is 1 ps.

394 J.W. Zhu, D.N. Shi / Computational Materials Science 68 (2013) 391–395

bonds to lower their local energies. These atoms have definitelylarger vibrational amplitude than surrounding atoms till danglingbonds, e.g. LACs as arrowed in Fig. 3c, try to arrange themselvesinto a variety of different carbon rings. We can see from Fig. 3b thatthe atoms around the damage are mainly composed of polygons,not only hexagons. These defective edges appear around the dam-age because the release of strain energy and thermal perturbationtry to minimize the number of dangling bonds. These nonhexagonslocally change the curvature in the damaged region. For example,pentagons lead to positive (or spherical) curvature and heptagonsto negative (or saddle-like) curvature. Since heptagons are domi-nant in Fig. 4b, the curvature around the damage remains remark-able. Among these nonhexagons, abundant defects widelyobserved in experiments are extensively distributed around thedamage. For example, we can find the pentagon–heptagon (5-7)pairs as previously proposed in experiments [26,27].

In the following stage, the octagons shown in Fig. 4b graduallyevolve into a more stable double vacancies structure with two pen-tagons and one octagon (5-8-5 defect, see Fig. 4c), which is also

t = 2.7 ps t = 12.7 ps (a)

t = 2.7 ps t = 4.7 ps (b)

Fig. 6. Structural evolution of damage in case that

frequently observed in electron microscopy experiments [7]. An-other favorite defect observed in Fig. 4c is composed of two penta-gons and two heptagons (57-57 defect), which is termed inverseStone–Wales (ISW) defect [28]. The formation of these regular de-fects gradually smoothes the previously curved surface. As a conse-quence, the damage in graphene shrinks into a smaller hole asshown in Fig. 4d. Except the 5–7 pairs mentioned above, aStone–Wales (SW) defect with two pentagons and two heptagons(55-77 defect [29]) is observed. Before self-healing procedure com-pletes, a nonagon with one dangling bond is formed in the center ofthe original damage. Since no atoms are lost in the damaging pro-cess and the following self-healing procedure, the graphene canprovide enough carbon atoms to heal the damage by itself. Conse-quently, the final self-healed structure, as shown in Fig. 4f, is acompletely sp2 networked structure although not a purely hexag-onal one, containing only intrinsic defects. The SW (55–77) defecthas high formation energy of 4.5–5.3 eV [29,30], which warrantsits stability even at high temperatures. As illustrated in Fig. 4g, thistype of defect still remains after about 130 ps. Although the finalstructure with defects such as SW (55-77) has small local devia-tions from ideally flat graphene sheet, the total Gaussian curva-tures of graphene remains zero [31].

When the thermal energy is not sufficient to excite the wholedangling bonds reformation, the self-healing procedure is not wellcompleted. Fig. 5 displays the size of damage evolves with time attemperatures ranging from 250 K to 2500 K. It is found that at2500 K, the damage finally evolves into a pentagon within 50 ps,while below this temperature damage with surrounding atomsmore than 10 remains in graphene in the scope of the simulationtime up to 200 ps. We find that the curving process discussedabove accompanies by the nucleation of nonhexagonal rings, andthe smoothing process always happens via defects reconstruction;these two stages are dependent of each other. At low temperatureof 250 K, the local intrinsic curvature is not remarkable around thedamage due to insufficient defects, as shown in Fig. 6a. As a result,the second stage does not happen. Instead, the damage shrinks byanother mechanism, i.e. reconnection of dangling bonds, which isdue to the oscillatory process. On the other hand, at higher temper-ature of 2100 K, although the curved surface is formed via nucle-ation of a small number of defects around the damage, theinsufficient temperature has no ability to activate the smoothing

t = 17.7 ps t = 26.7 ps

t = 8.7 ps t = 15.7 ps

the temperature is 250 K (a) and 2100 K (b).

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mechanism via defects reconstruction. The structural evolution isshown in Fig. 6b. In other words, the atoms around the damagehave poor ability to reform bonds with their neighbor atomsbeyond t = 10 ps. Therefore, the self-healing procedure is stilluncompleted. In these cases, thermal fluctuation cannot provideenough energy to fulfill the self-healing procedure in sp2 lattice.Assisted-healing with the help of other molecules, for example,noble gas [32], CO or NO [19], may act as an additional strategyto heal damaged graphene.

In case of larger damage, the self-healing procedure may not bepurely accomplished via thermal annealing. We confirm this argu-ment by replacing C60 molecule with diamond particles in diame-ters ranging from 20 Å down to 12 Å to make larger damage.Although temperatures increase up to 4000 K which is close tomelting resp. sublimation temperature of graphite 3948 K [31],no complete self-healing behavior is observed. This is understand-able since the size of these holes with diameter in nanometer scaleis far beyond C–C bond length. While in graphene sheet the atomsis lack of ability to move from one region to another due to local-ized phonon modes [33].

4. Conclusions

In conclusion, we show the structural evolution of force-dam-aged graphene sheet by heat treatment via MD simulations. It sug-gests an efficient two-stage mechanism to fulfill the self-healingprocedure in graphene. The first one is to construct a defectiveedge with local curvature. The following corresponds to curvedsurface smoothed by reconstructing defects, which results in dam-age shrinking. In addition, we argue that the thermal energy andthe size of damage also play significant roles on the self-healingcapability. We expect that this self-healing mechanism may pro-vide a new strategy to promote limited lifespan and simulta-neously to improve performance in graphene-based devices, as asupplement of current healing methods, including ion irradiationand chemical treatment.

Acknowledgement

This work was supported by Natural Science Foundation ofJiangsu Province (NSFJS, No. BK2010499).

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