Quantum Chemical Molecular Dynamics Studies of Bilayer Graphene

May 5, 2015 - It is extremely interesting to note that an octagon formation was found, which was presumably surrounded by alternate permutation of ...
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Quantum Chemical Molecular Dynamics Studies of Bilayer Graphene Growth on a Ni(111) Surface Menggai Jiao,†,‡ Kai Li,† Ying Wang,*,† and Zhijian Wu*,† †

State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China ‡ University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China S Supporting Information *

ABSTRACT: The mechanism of bilayer graphene nucleation and growth has been investigated by using quantum chemical molecular dynamics simulations. The results indicate that the presence of embedded nickel atoms in the upper-layer (first-layer) graphene has little impact on the evolution mechanism of the second-layer graphene precursor. The nucleation process occurs after the rapid precipitation of internal carbon atoms along with the degradation of nickel catalyst and the formation of discrete carbon polyyne chains. The second-layer graphene exhibits an attachment-limited growth on the rugged Ni(111) surface. The quality of the second-layer graphene can be reduced, and large structural holes are induced when the metal atoms are involved in the upper-layer graphene. On the contrary, high-quality upper-layer graphene can act as an excellent template for the growth of the second-layer graphene. These simulations, therefore, suggest that through carefully controlling the growth conditions, different kinds of bilayer graphene can be fabricated in a layer-by-layer mode on the Ni(111) surface.

1. INTRODUCTION Graphene, a two-dimensional honeycomb lattice with sp2hybridized carbon atoms, has shown a wealth of extraordinary properties such as high carrier mobility,1 superior thermal conductivity,2 and large surface area.3 Such outstanding properties cause it to have great potential for a wide range of applications in supercapacitors,4 flexible and transparent electrodes,5 electronic devices,2 etc. However, the lack of a band gap in monolayer graphene, due to the inherent symmetry in its structure, has imposed great restrictions for many of its applications. Hence, realizing a band gap is of central importance for functional electronic and optoelectronic devices. In such circumstances, huge efforts have been devoted to open the band gap of graphene, including patterning nanoribbons6 or using special substrates.7 Especially notable progress is the synthesis of bilayer graphene films, which has been actively pursued to open the band gap of graphene and further broaden the application of graphene in the electronics industry.8−15 Recently, a continuously tunable band gap was demonstrated in bilayer graphene by employing a perpendicular electric field, opening up a new era for the applications of graphene in electronic and photonic devices.16−19 The exploitation of the intriguing properties in graphene depends largely on the development of controllable graphene growth. Chemical vapor deposition (CVD) is an effective technique in producing large-area high-quality graphene on various metals, such as Ni,20 Cu,21 Ir,12 and alloys.22 Substrates with very low C solubility, such as Cu, yield predominantly monolayer graphene due to the self-limiting nature of the growth process.21,23 Nevertheless, the growth of bilayer © XXXX American Chemical Society

graphene on Cu can be realized under certain growth conditions.8,9,11,24,25 Several reports have demonstrated that bilayer graphene growth on Cu is a quite complicated and timeconsuming process.9,11 Also, the related mechanisms are uncertain, and there are a lot of debates on this aspect (e.g., “on-top” mechanism,9,11,24 “underlayer” mechanism,8,25 etc.). In contrast, for metals with high carbon solubility, such as Ni,26 carbon atoms dissolve into the bulk catalyst at high growth temperature and can readily segregate, resulting in multilayer graphene formation during the cooling process. A previous experimental study indicated that bilayer graphene grew in a layer-by-layer mode by carbon segregation on Ru(0001).27 Soon afterward, the growth of bilayer graphene on Ir(111)12 by the same method was elucidated by Nie et al., and a bottom-up growth mechanism of bilayer graphene was proposed. Among the previous studies, of particular interest is Ni(111), which is an excellent substrate for commensurate graphene growth due to the negligible mismatch between them.28,29 Single-layer formation of graphene was found to be a thermodynamically stable surface termination,28 which can be attributed to the lowering of the surface energy of metal covered by monolayer graphene.30 Monolayer graphene was assumed to grow with segregation in the initial stage, followed by the formation of a subsequent layer of graphene.31 Recently, the sequential growth of graphene following a complete surface coverage of the preceding layer in a bottom-up mode was Received: January 12, 2015 Revised: March 30, 2015

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The Journal of Physical Chemistry C verified on Ni(111),32 consistent with the case of Ir(111)12 and Ru(0001).27 Although the high carbon solubility of Ni generally results in the formation of less-desired multilayer graphene, numerous experimental studies have demonstrated that the growth of layer-controlled and high uniform graphene can be realized through modulating the experimental conditions in the CVD process.20,33,34 Bilayer graphene films have been synthesized successfully on Ni(111) lately.13−15 However, scalable synthesis of high-quality bilayer graphene is still in its infancy, and the underlying growth mechanism is less understood or even controversial. How the second-layer graphene grows following the first layer is still an open question. Therefore, understanding the complicated growth mechanism of bilayer graphene is demanding and of vital importance for further optimizing the experimental conditions to achieve high-quality bilayer graphene. In this aspect, computer simulation is demonstrated to be a powerful tool to explore the graphene growth process at the atomic scale.35 Nevertheless, theoretical work concentrating on bilayer graphene growth is still rare,10 and the underlying mechanism is far from clear. In this study, we aim to address the bilayer graphene growth mechanism on a Ni(111) surface with a bottom-up mode by employing quantum chemical molecular dynamics (QM/MD) simulations. We will elucidate how the second-layer graphene grows on the Ni(111) surface underlying one perfect or defect graphene layer (with one carbon atom substituted by a nickel atom). In particular, we will show that the embedded nickel atoms in the upper-layer (first-layer) graphene have little impact on the evolution mechanism of the second-layer graphene. However, the quality of the upper-layer graphene influences directly the topology of the second-layer graphene. Through controlling the quality of the first-layer graphene, we can fabricate different kinds of structural holes involved in the second-layer graphene and extend the applications of graphene as a membrane material.36,37

that was already formed on the nickel surface, named the P model system (Figure 1a). Considering the high temperature

Figure 1. Optimized geometries of the (a) P and (b) D model systems employed for QM/MD simulations. Brown and cyan spheres represent Ni and C atoms, respectively.

used in the graphene CVD growth process, metal atoms are likely to be activated and to be involved in the precursor of graphene. Such phenomena have been observed during graphene formation on Ni(111),48,49,52 Fe(111),49 and even Cu(111)53,54 surfaces. Thus, a monolayer graphene in which a carbon atom is substituted by a nickel atom was considered as another model to represent the upper layer of graphene, named the D model system (Figure 1b). The Ni atoms in the bottom layer were fixed throughout the simulations to mimic the bulk effect. Periodic boundary conditions were employed, and a vacuum region of 10 nm in the direction perpendicular to the surface was applied to avoid interactions between adjacent surfaces. The initial structures were optimized at 0 K before being equilibrated at 1180 K for 10 ps. Then, 10 geometries were chosen from the interval between 5 and 10 ps with corresponding velocities as starting points for subsequent QM/ MD simulations in each model, labeled as lp−10p for the P model and 1d−10d for the D model. Afterward, the growth of the second-layer graphene was induced by the addition of one carbon atom to a randomly chosen interstitial site in the Ni(111) structure at regular intervals of 5 ps, in a manner similar to that of our previous simulations of graphene nucleation.48,50 During the first 250 ps carbon addition simulations, 50 carbon atoms were inserted into the subsurface of nickel substrate to simulate the precipitation process. Then we stopped inserting atomic carbon and annealed these structures at 1180 K for a further 100 ps to investigate the second-layer graphene growth mechanism on the Ni(111) surface with an upper-layer graphene.

2. COMPUTATIONAL METHOD 2.1. Quantum Chemical Molecular Dynamics Simulations. All simulations in this study were performed with nonequilibrium QM/MD simulations based on the selfconsistent charge density functional tight-binding (SCCDFTB) method38 including van der Waals correction (the dispersion term is the universal force field, UFF) (SCC-DFTBD). The standard trans3d-0-139 and mio-0-138 parameter sets were employed. The SCC-DFTB-D wave function, energy, and gradient were computed “on-the-fly” at each step of the dynamics, as implemented in the DFTB+ program.40 Since the studied systems contain many near-degenerate nickel d orbitals and unsaturated dangling carbon bonds, a fractional orbital occupation in Fermi−Dirac distribution was employed with an electronic temperature (Te)41,42 of 3000 K to improve convergence of the SCC-DFTB-D equations. The equations of motion of nuclei were integrated by employing the Velociy− Verlet algorithm43 (Δt = 1 fs) for the time propagation. The nuclear temperature (Tn) was held constant at 1180 K in the NVT ensemble throughout the simulations via a Nosé−Hoover chain thermostat.44 The same technique has been successfully employed before in the nonequilibrium MD studies of carbon nanotube and graphene nucleation and growth.45−51 2.2. Model System. In this study, a three-layer Ni(111) slab was established, and then a 5 × 5 supercell of graphene was employed to represent the upper-layer (first-layer) graphene

3. RESULTS AND DISCUSSION 3.1. Nucleation Mechanism of the Second-Layer Graphene. 3.1.1. P Model System. We will initially discuss the simulation process of the P model system. Final structures of trajectories 1p−10p after 350 ps of simulation are provided in Figure S1 (Supporting Information). In Figure 2a, we take trajectory 1p as a representative example to show the dynamics of the second-layer graphene nucleation and growth underneath one perfect graphene layer. Other trajectories show similar features. The simulation process for trajectory 1p is given in Movie S1 (Supporting Information). The populations of different polygonal carbon rings observed in trajectory 1p are quantified in Figure 2b as a function of the simulation time. Ring populations of the individual trajectories 1p−10p are provided in Figure S2 (Supporting Information). It is seen immediately from Movie S1 that, once the internal carbon atoms were inserted into bulk Ni, they precipitated very fast to B

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internal carbon atoms. In addition, the upper-layer graphene was also not static and moved backward or forward, becoming incommensurate with the catalyst from the preferred alignment. In the previous studies,12,15 bilayer graphene was found to nucleate preferentially under rotational graphene domains that are weakly bound to the substrate. Therefore, it is reasonable to deduce that this horizontal motion of the upper-layer graphene, along with the constant thermal fluctuations, weakened the interaction between the upper-layer graphene and Ni substrate, which favored the growth of the carbon network underneath the upper-layer graphene. In the first 50 ps, most of the carbon atoms were scattered and participated in the Ni−C−Ni bridge structures, which have been investigated extensively during graphene nucleation on Fe(111),49 Ni(111),52 and Cu(111).53 Hence, their diffusion was impeded significantly. As more and more carbon atoms precipitated from the inside, Ni−C bond gradually yielded to the formation of C−C bonds, due to the more favorable thermodynamic stability of C−C bond. As seen from the snapshot at 115.0 ps in Figure 2a, different lengths of polyyne chains were already preferentially formed with the terminal Ni− C σ bonds. Meanwhile, some of the nickel atoms that originally bonded with carbon atoms went back to the catalyst surface gradually. This polyyne chain leading to graphene precursor formation is similar to the observation of single-layer graphene growth on a Ni(111) surface.29,48,49 The upper-layer graphene, however, suppressed the three-dimensional growth of the carbon structure, such as nanoarches (domelike structure), which are often observed when single-layer graphene grows on uncovered metal surfaces.55−57 Nucleation of an extended sp2 structure was observed via the cross-link of polyyne chains, as shown in Figure 2a. A pentagon was formed at first at 126.2 ps, although the vibration of polyyne chains was hindered by the surrounding nickel atoms (Ni−C σ bond) to some extent. Therefore, the growth mechanism of the second-layer graphene in this context again followed closely in nature the “pentagon first” mechanism, as in the nucleation of graphene and carbon nanotubes on transition metals.45,47,49 Thereafter, plenty of pentagons emerged swiftly due to their superiority from the dynamic point of view (see the snapshot of 165.4 ps in Figure 2a). A concomitant formation of several hexagons was also observed during this period (Figure 2b). In the subsequent ca. 185.0 ps, rings condensed further and several pentagons converted to hexagons, resulting in a more thermodynamically stable network (see Figure 2b). It is extremely interesting to note that an octagon formation was found, which was presumably surrounded by alternate permutation of pentagons and hexagons, forming a new 5− 8−5 defect-like54,58 structure embedded in the graphene precursor. Analogous structures were frequently observed in other trajectories, such as 5p, 6p, 9p, and 10p (Figure S1, Supporting Information). This is because the curvature of the networked carbon structure needs to match that of the flat Ni(111) surface. In the 5−8−5 defect-like structure, the positive curvature of the pentagon is compensated by the negative curvature of the octagon in the immediate vicinity of the pentagon. It is noted that this 5−8−5 defect-like structure formation is different from Haeckelite growth, where heptagons with a negative curvature are ideal polygonal shapes to balance the positive curvature induced by pentagons.47 3.1.2. D Model System. Now we will discuss the growth of the second-layer graphene in the D model system. Trajectory 2d typifies the growth of the second-layer graphene precursor in

Figure 2. (a) Snapshots from trajectory 1p, depicting the evolution of the second-layer graphene precursor at the interface. (b) Populations of polygonal carbon rings from trajectory 1p. Snapshot times are given with respect to the beginning of the simulation. The upper-layer perfect graphene is shown in cyan, and the inserted carbon atoms are highlighted in purple. The location of the periodic boundary is indicated by the red lines. The yellow circles denote the adjacent pentagons and a flower-like structure. The flower-like structure is composed of an octagon surrounded by pentagons and hexagons which are connected sequentially.

the interface between the upper-layer graphene and nickel substrate, although they encountered the obstruction from the surrounding nickel atoms constantly. At the same time, the majority of nickel atoms became quite active, and a lot of them were squeezed out along with the precipitation of carbon precursors to saturate their dangling bonds. This phenomenon, on the other hand, is presumably attributed to the relative strength of Ni−Ni and Ni−C bonds.50 Ultimately, the upper nickel atoms became quite distorted with a large quantity of vacancies. This led to the size (or volume) of the catalyst expanding greatly, which was favorable for the precipitation of C

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the P model system discussed above. It appears that the segregated carbon atoms distributed quite scattered, and almost all of them were involved in Ni−C−Ni structures at the very beginning of the simulation process. The formation of short dispersed polyyne chains, which were constrained by Ni−C bonds, and their subsequent collapse or coalescence, occurred before the ring condensation. As shown in Figure 3, several polyyne chains emerged at 90.5 ps, followed by the formation of a pentagon at 93.5 ps. Then several pentagons and hexagons continued to appear, forming a semioctagon simultaneously at 213.3 ps. At this very moment, the formed graphene precursor possessed a certain rate of curvature. Afterward, as in the P model system, an octagon surrounded by pentagons and hexagons was also observed, resulting in almost zero overall curvature. This process was accompanied by a simultaneous degradation and subsequently a certain degree of recovery of the catalyst surface. It is noted that, because of extremely strong and favorable C−C bonds, the nickel atom in the upper-layer graphene was resubstituted probably by the segregated carbon atom in some cases to form a perfect upper-layer graphene. This self-healing process was observed in trajectories 4d, 5d, and 9d (Figure S4). 3.2. Comparison of the Two Model Systems. It can be inferred from the above discussion that the growth mechanisms of the second-layer graphene in the two model systems bear some analogies to each other. It is observed that the formation and elongation of dispersed polyyne chains occurred before the nucleation and extension of the precursor. This can be corroborated in Figure 4, which depicts the evolution of each individual carbon cluster during the QM/MD simulations. It is seen from Figure 4 and Movies S1 and S2 (Supporting Information) that, in the initial stage up to 50 ps, the formed Cn carbon cluster moieties, almost without exception, were composed entirely of atomic carbon and the short polyyne

this system. The details of this trajectory can be seen in Figure 3a, and the corresponding movie is provided in Movie S2

Figure 3. (a) Snapshots from trajectory 2d, depicting the evolution of the second-layer graphene precursor at the interface. (b) Populations of polygonal carbon rings from trajectory 2d. Snapshot times are given with respect to the beginning of the simulation. The upper-layer defect graphene is shown in cyan, and the inserted carbon atoms are highlighted in purple. The location of the periodic boundary is indicated by the red line. The yellow circles denote a semipolygon and a flower-like structure. The flower-like structure is composed of an octagon surrounded by disordered pentagons and hexagons.

(Supporting Information). Final structures of trajectories 1d− 10d following 350 ps of simulation are presented in Figure S3 (Supporting Information). The ring populations of the newly formed polygonal carbon rings observed in trajectory 2d as a function of time are given in Figure 3b. Ring populations of individual trajectories 1d−10d are depicted in Figure S4 (Supporting Information). The growth mechanism of the second-layer graphene precursor here resembles closely that of

Figure 4. Carbon cluster size evolution in the (a) P and (b) D model systems as a function of the simulation time. Each color indicates a unique carbon cluster observed during the simulation; the way in which the sizes of these colored areas change indicates how these cluster sizes change. In each case, the largest cluster grows by consuming smaller fragments. All data were averaged over 10 trajectories. D

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The Journal of Physical Chemistry C chains of less than C5 at the interface between the substrate and the upper-layer graphene. A particular carbon cluster among them, then, exhibited a gradual growth in the next 50 ps. The growth of the largest cluster started drastically at approximately 100 ps, when more than 90% of the carbon atoms had precipitated to the surface (see Figure 5, which shows the

Figure 6. Averaged populations of newly formed carbon rings during 350 ps QM/MD simulations for the (a) P and (b) D model systems.

with the graphene growth on Pd(111).60 As seen in Movies S1 and S2 (Supporting Information), the rapid precipitation of internal carbon atoms resulted in a strong degradation of the catalyst, analogous to Fe(111)-catalyzed CVD graphene growth.49 Hence, the dangling σ bonds in the initial isolated carbon fragments can be sufficiently saturated by the scattered nickel atoms, forming significant Ni−C−Ni bridge structures. Our study also showed that the upper-layer graphene can act as an excellent template for the growth of large-sized domains of bilayer graphene with a particular stacking order, analogous to the previous reports.9−11 Compared with the interlayer growth via van der Waals interaction, the graphene precursor exhibited a faster intralayer growth by carbon aggregation and polyyne chain coalescence at the interface. Carbon atoms or fragments were captured once they diffused to the edge of the graphene precursor at the interface, because of the extremely active dangling bonds. Consequently, bilayer graphene presented a layer-by-layer growth mode with a high anisotropic nature on the Ni(111) surface. On the other hand, some differences do exist between the two model systems. First, a comparison of parts a and b of Figure 6 shows that the second-layer graphene precursor in the P model system exhibited a growth rate slightly lower than that in the D model system. The embedded nickel atom in the D model system played a significant role here. The presence of the nickel atom, which is similar to the step edge in the substrate, favored the quick precipitation of internal carbon atoms. The much more drastic fluctuation of the curves in Figure 5b as compared with that in Figure 5a at the very beginning of the simulation underlines this point. Although the interaction of the embeded nickel atom with the substrate underneath was gradually weakened with the sp2 network formation, it induced the formation of local nickel clusters to some extent (such as 2d, 3d, 6d, 8d, and 10d in Figure S3, Supporting Information), and this fact impeded the precipitation of carbon atoms in a later stage and degraded the quality of the second-layer graphene. It is evident from Figure 6 that the number of hexagons, representing the quality of as-grown

Figure 5. Ratios of subsurface C to total carbon atoms and surface C to total carbon atoms as a function of time for the (a) P and (b) D model systems. All data were averaged over 10 trajectories.

variation ratios of subsurface and surface carbon to total carbon with the time propagation). From then on, the largest carbon cluster enlarged itself by gradually consuming the other smaller fragments. However, the growth rate of the largest carbon fragments was slowed after ca. 170 ps, accompanied by a simultaneous increase of smaller clusters. This seemingly weird phenomenon can be ascribed to the increase of subsurface carbon atoms that failed to precipitate out, which can also be seen from Figure 5. The growth of all carbon clusters gradually saturated after the cease of carbon addition in the simulation. In addition, as seen in Figure 5, in each case, the ratio of surface carbon atoms exhibited a drastic increase, accompanied by a sharp decrease in the ratio of subsurface carbon atoms in the first 50 ps. However, somewhat surprisingly, the quick precipitation of the internal carbon atoms, which is indicated by the quite strong vibrations of curves, did not lead to the rapid growth of the graphene precursor, contrary to the previous study on graphene nucleation from nickel carbides.59 This is in turn reinforced by analyzing Figure 6, which depicts the average population statistics of polygonal ring formation of the two model systems during the growth process. It is evident that nearly no polygonal ring appeared in the first 100 ps simulation, during which the dispersed carbon fragments exhibited little diffusion across the rugged Ni(111) surface due to the constraint of the relatively strong Ni−C interaction. This fact, combined with the space confinement provided by the upperlayer graphene, would make the migration of the polyyne chains more difficult and hence resulted in a relatively long graphene precursor nucleation time. On the basis of the above points, it can be deduced that the second-layer graphene exhibited an attachment-limited growth kinetics, consistent E

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interaction between the substrate and upper-layer graphene and further facilitate the precipitation of internal carbon atoms to grow the graphene precursor at the interface. On the other hand, due to the space confinement, the upper-layer graphene suppresses the formation of carbon nanoarches (domelike structure) and is conducive to the formation of high-quality bilayer graphene. Furthermore, the upper-layer graphene can act as an excellent template for the growth of large-sized domains of bilayer graphene so that a controllable stacking order can be achieved. This opens up the exciting possibility for fabricating scalable bilayer graphene in a layer-by-layer mode on the Ni(111) surface.

graphene, was lower in the D model system. On the basis of the comparison between Figures S1 and S3, it can be found that more carbon atoms in the D system failed to participate in the growth of the graphene precursor, which is also reflected in Figure 5. Another role played by the embedded nickel atom is to connect the upper and lower graphene. The averaged distance from bottom-layer to upper-layer graphene in the D system was thus shortened compared with that in the P system (2.55 and 2.64 Å, respectively). The strong space restriction in the D model system limited the expansion of the Ni catalyst and prevented further carbon precipitation in the late stage, as observed in Figures S3 and 5. Due to the remarkable kinetic superiority, an extensive body of pentagons was formed promptly in both the P and D model systems, especially in the former (Figure 6). In the initial stage, these pentagons could be stabilized by the isolated nickel atoms that moved out from the substrate. Then several nickel atoms would go down to facilitate the growth of the graphene precursor. However, pentagons could not transform to thermodynamically more stable hexagons immediately, but were trapped in the precursor during the simulation process. Interestingly, a point worth emphasizing now is that the formation of octagonal holes was induced at the interface besides a few heptagons, so that the positive curvature brought by a large amount of pentagons can be remedied excellently. Nonetheless, fewer octagons were formed in the D system, and owing to more unsegregated carbon existing under the secondlayer carbon network, large structural holes were formed in most trajectories of the D system (Figure S3, Supporting Information). These observations indicate that different sizes of holes in graphene may be tunable by controlling the morphology of the first-layer graphene.

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ASSOCIATED CONTENT

S Supporting Information *

Movie S1 showing the evolution of QM/MD simulations of the second-layer graphene precursor at the interface for trajectory 1p for the P model system, Movie S2 showing the evolution of QM/MD simulations of the second-layer graphene precursor at the interface for trajectory 2d for the D model system, Figure S1 showing the structures of trajectories 1p−10p following 350 ps QM/MD simulation for the P model system, Figure S2 showing the polygonal carbon ring populations of the 1p−10p trajectories for the P model system, Figure S3 showing the structures of trajectories 1d−10d following 350 ps QM/MD simulation for the D model system, and Figure S4 showing the polygonal carbon ring populations of the 1d−10d trajectories for the D model system. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b00340.

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4. CONCLUSION The growth of bilayer graphene on a Ni(111) surface have been studied by using QM/MD simulations. The calculations show that the embedded nickel atoms involved in the growth of the upper-layer (first-layer) graphene do not play an important role in the evolution mechanism of the second-layer graphene. The rapid precipitation of internal carbon atoms and the formation of discrete carbon polyyne chains, accompanied by the strong degradation of the nickel catalyst, occur before the nucleation process. The second-layer graphene exhibits an attachmentlimited growth due to the constraint of the Ni−C interaction on the rugged Ni(111) surface. On the other hand, the embedded nickel atom in the upper-layer graphene has an influence on the quality and growth rate of the second-layer graphene. In the case with a high-quality upper-layer graphene, rapid formation of kinetically favorable pentagons induces the formation of an octagonal hole, which is surrounded by pentagons and hexagons. This results in a relatively high-quality bilayer graphene. However, the quality of the second-layer graphene will be reduced if some metal atoms are embedded in the upper-layer graphene, and relatively large structural holes will emerge. Thus, different sizes of holes in the second-layer graphene can be fabricated through carefully controlling the quality of the upper-layer graphene in the growth process and further extend the applications of graphene as a membrane material. The presence of upper-layer graphene (regardless of perfect or defect graphene) has a significant role on the second-layer graphene growth. Its constant horizontal motion and thermal fluctuations around the most favorable sites weaken the

AUTHOR INFORMATION

Corresponding Authors

*Phone: +86-0431-85262801. E-mail: [email protected]. *Phone: +86-431-85262801. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the National Natural Science Foundation of China for financial support (Grants 21203174, 21221061, and 21273219) and the Natural Science Foundation of Jilin Province (Grants 20130522141JH and 20130101179JC-07). We also acknowledge financial support from the Department of Science and Technology of Sichuan Province. The computational resource is partly supported by the Performance Computing Center of Jilin University, China. We are also grateful to the Computing Center of Jilin Province for essential support.

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REFERENCES

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DOI: 10.1021/acs.jpcc.5b00340 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.5b00340 J. Phys. Chem. C XXXX, XXX, XXX−XXX