CARBON 90 (2015) 34– 43

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Self-assembly of fullerenes and graphene flake: A molecular dynamics study

Jia-wei Feng a, Hong-ming Ding a, Yu-qiang Ma a,b,* a Collaborative Innovation Center of Advanced Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China b Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou 215006, China

ARTICLE INFO ABSTRACT

Article history: The interaction between graphene and other materials is of great importance for its poten- Received 9 January 2015 tial applications in nanotechnology. In this paper, by using all atom molecular dynamics Accepted 27 March 2015 simulations, we systematically investigate the self-assembly of fullerenes (diameter from Available online 3 April 2015 0:7to2:3 nm) and graphene at room temperature (300 K). It is found that single fullerene can be wrapped by graphene nanoribbon (GNR) due to the van der Waals interaction between them. However, if the GNR is wide enough, the fullerene will only bind to the sur- face of GNR. To overcome the bending energy of wide GNR, we further use multiple fullere- nes, and find that they can self-assemble into various structures. Importantly, fullerenes show dramatically different behaviors as the size changes. Giant fullerenes can work together to scroll a very large graphene from the corner, while this effect is weakened or even disappears in the cases of smaller ones. Finally, we also find that the wrapping process can be completely retarded by adding a substrate below the graphene flake. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction attracted a lot of interest because of its remarkable structure [15–18]. GNS not only has some similar mechanical and elec- Graphene, as a two-dimensional thin film material, has trical properties with carbon nanotube (CNT) (e.g., water received great attention due to its unique electrical and transportation behaviors [19–21]), but also represents unique mechanical properties since it was firstly exfoliated from features such as tunable inner space [22]. A report by the bulk graphite [1]. With the development of nanotechnol- Buehler et al. has shown that graphene can be assembled into ogy, various experimental methods have been applied to fab- nanoscroll under high aspect ratio to minimize the surface ricate graphene with desired geometry [2–5]. Besides, the energy [16]. Moreover, graphene can be guided to scroll on a physical and chemical properties of graphene can be easily CNT, forming a stable core–shell nanostructure [23,24]. controlled [6–8], which makes graphene a promising candi- Other rod-like materials such as silicon nanowire, iron nano- date for real applications such as nanoelectronic devices [9], wire, etc. can also activate the scrolling of graphene [25,26]. biofunctional materials [10,11], solar cells [12] and sea water Recently, molecular dynamics simulations even show that a desalination [13,14]. drop of water or ionic liquid can fold graphene into different However, planar graphene is unstable and can be kinds of nanostructures [27–29]. Experimentally, the encap- deformed into graphene nanoscroll (GNS), which has also sulation of metal nanoparticle by graphene has also been

* Corresponding author at: Collaborative Innovation Center of Advanced Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China. E-mail address: [email protected] (Y.-q. Ma). http://dx.doi.org/10.1016/j.carbon.2015.03.071 0008-6223/Ó 2015 Elsevier Ltd. All rights reserved. CARBON 90 (2015) 34– 43 35

observed [30,31]. The authors claimed that the interaction than 1 104 eV or the 2-norm of the global force vector is between metal nanoparticle and oxygenated defects on gra- less than 1 106 eV=A),˚ followed by an MD run until equili- phene accounts for this phenomenon. However, nanoparticle brated (total energy and structure of the system keep is very different from one-dimensional nanorods above. So it unchanged for 500 ps). is still unclear how nanoparticles roll up graphene and make itself encapsulated. 3. Results and discussion Here, by using molecular dynamics simulations, we choose fullerene as a prototype to investigate the self-assembly of 3.1. Self-assembly of one fullerene and GNR nanoparticles and graphene. Actually, the fullerene–graphene composite was found to exhibit photoinduced electron trans- Our simulation results show that fullerene with appropriate fer, which indicates that the composite can be a candidate for size can activate the scrolling of GNR. As illustrated in fabrication of all-carbon solar cells [7,32]. Fullerenes with dif- Fig. 1a, one C540 is firstly put at one end of the GNR with a ferent numbers of atoms (from 60 to 540) are used to mimic width of 3:6 nm. After energy minimization, we observe that the nanoparticles with different sizes (diameter from 0.7 to the C540 exhibits an icosahedral shape (Fig. 1a, 0 ps), which is : 2 3 nm). As we will show below, a single large fullerene can in accordance with previous report [40] and validates the be wrapped by graphene nanoribbon (GNR), forming a core– choice of force field. In the beginning, the C540 firstly binds shell structure, and the self-assembly of two fullerenes and to the surface of GNR and diffuses to the corner. Then, the GNR shows more versatile configurations. Further, the effects corner of GNR gradually adsorbs to the surface of C540 (from of fullerene size and number on the assembly will also be 10 to 30 ps). After that, the GNR wraps around the fullerene investigated in details. and finally reaches a fully wrapped state (we name it as core–shell structure) at 87 ps. Such core–shell structure 2. Modeling and methods remains unchanged until the end of the simulation, which implies that it’s quite stable. Here, we consider a system comprised of one graphene flake In order to elucidate the driving force of this phenomenon, and one or more fullerenes. Fullerenes with different sizes we calculate the total potential energy (Etotal), the energy of the single GNR (EGNR), the energy of fullerene (EFUL) and the (i.e., C60,C180,C240,C320 and C540) are chosen. Besides, since graphene is an isotropic elastic material, the choice of edge interaction energy between GNR and fullerene (Einter). The shape doesn’t affect its mechanical properties [33]. For the interaction energy is defined as sake of simplicity, we chose armchair-edged graphene flakes Einter ¼ Etotal EGNR EFUL: ð1Þ along X direction unless otherwise stated. Zigzag-edged gra- As shown in Fig. 1b, the total energy keeps nearly constant phene will also be briefly studied for comparison. Hydrogen during the first 50 ps. And we can observe a slight increase atoms are covalently bonded to the edges of graphene flake of the E (Fig. 1c) and a slight decrease of the E to stabilize the carbon atoms with dangling bonds. All GNR inter (Fig. 1d). We don’t show the E because the energy of fuller- together, three types of systems are constructed. The first FUL ene doesn’t change (i.e., it behaves like a rigid nanoparticle) one contains single fullerene and graphene, with the size of during the whole simulation time. As shown in Fig. 1a, in graphene ranging from 0:4 8:5nm2 to 6:0 8:5nm2. The the beginning, the fullerene seeks an appropriate config- second one is almost the same as the first one, except that uration (i.e., binding to the corner) for the following wrapping we include two fullerenes with the same type in the system process. If the fullerene bends the GNR from the edge, there and elongate the GNR to 16:0 nm. The third one contains mul- will be a sharp increase of EGNR compared to bending from tiple fullerenes (three to six) and one graphene flake with size the corner which results from the increase of the bending from 0:4 16:0nm2 to 16:0 16:0nm2. energy. The bending energy (Ebend) is given by [16] All the simulations are carried out by using the LAMMPS Z 1 package [34]. The adaptive intermolecular reactive empirical E ¼ Dj2ðx; yÞdxdy; ð2Þ bend 2 bond-order (AIREBO) potential function is applied to describe A the bonded and nonbonded interactions [35]. This potential where D is bending rigidity, j is the mean curvature at ðx; yÞ has been proven to be one of the most successful potential and the integral is calculated over the bending area. It should functions to describe the intra- and intermolecular interac- be noted that the energy change of an elastic membrane (gra- tions in hydrocarbon systems [36–38]. Simulations are per- phene) mainly comes from two aspects, i.e., the elastic energy formed in the NVT ensemble at 300 K using the Nose´- and the bending energy. Here, the change of the EGNR mainly Hoover thermostat [39] with a damping constant of 0:1 ps. comes from the bending energy [16]. So it is more energy- We also use 1 K and 500 K to investigate the temperature favorable to initialize the wrapping from the corner. Since dependence. The periodic boundary conditions are applied the structure doesn’t change much in the beginning (see in all directions and the vacuum separations between gra- Fig. 1a), the total energy keeps unchanged during this period. phene flake and box edge are at least 2 nm (i.e., at least Then, after 50 ps, when the GNR wraps around the fullerene,

4 nm between graphene flake and its mirror). The time step we observe a sharp increase of the EGNR (induced by the bend- is 1 fs and data are collected every 1 ps. Initially, one or more ing of GNR) and a decrease of the Einter (induced by the fullerenes are placed in the vicinity of graphene flake. Then, increase of contact area between GNR and fullerene), which we perform steepest descent energy minimization of the sys- overall results in a decrease of the total potential energy. We tems (stop if the change in energy between iterations is less find that the difference of Etotal between the initial and final 36 CARBON 90 (2015) 34– 43

(a)Width (3.6 nm) Length (8.5 nm)

0 ps 10 ps 30 ps 65 ps 87 ps (b) (c)(c) (d) -13360 -9415 0

-13365 -9420 -5 -13370 -10 -9425 -13375 -15 -13380 -9430 -20 Potential energy (eV) -13385 -9435 -25 0 30 60 90 120 0 30 60 90 120 0 30 60 90 120 Time (ps) Time (ps) Time (ps)

Fig. 1 – (a) Process of self-assembly between C540 and GNR with a width of 3:6 nm and length of 8:5 nm. (b) Etotal, (c) EGNR, and (d)

Einter as a function of time. (A color version of this figure can be viewed online.) structures is about 5 eV, while the thermal fluctuation at 300 K is about 0:026 eV. So the core–shell structure is quite stable at room temperature, in accordance with the sim- (a) ulation result. 12 C540 We can characterize the core–shell structure by the con- GNR centration profiles of GNS and fullerene along X and Y direc- 10 tions (CðXÞ and CðYÞ) (see Fig. 2). The concentration profile is calculated by counting the number of atoms within evenly 8 spaced slices. Then, we define the distance between GNS and fullerene (i.e., d1, d3 and d4) as the distance between 6 C(X) the peaks in concentration profiles (see Fig. 2), which is mea- sured as 0.34, 0.34, and 0:33 nm, respectively. Due to the 4 irregular shape of the open mouth of GNS, we don’t define 2 the distance between the fullerene and the open mouth. It d1 is observed that these distances are close to the shortest dis- tance in the graphite layer, i.e., 0:34 nm, which implies the 0 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 strong adhesion between the fullerene and GNS. X (nm) On the basis of our discussions above, we can see that the (b) wrapping process happens when the decrease of interaction 12 C540 energy is larger than the increase of bending energy of GNR. GNR We can imply that the total energy will not decrease with 10 the wrapping of a sufficiently wide GNR, thus this process is energetically unfavorable. By altering the width of GNR and 8 the size of the fullerene, it is indeed found that there exist two different assembly behaviors, i.e. the binding and wrap- 6 C(Y) ping phases (see Fig. 3). In particular, there may exist two dif- ferent structures (i.e., the rolling structure, the sliding 4 structure) in the wrapping phase. However, we will not distin- 2 guish the two structures in the phase diagram because it’s d3 d4 highly dependent on the initial configuration [23]. As shown in Fig. 3 (black, solid line), the boundary between the two 0 -1.5 -1 -0.5 0 0.5 1 1.5 2 regions increases monotonously with the size of the fuller- Y (nm) ene, which is due to the fact that larger fullerenes will have larger interaction energy with the GNR and thus can over- Fig. 2 – Concentration distribution profiles of the C540 and come larger bending energy of the GNR. GNR in (a) X and (b) Y directions after equilibration. The type Next, we will consider the influence of edge shape and of GNR is the same as that in Fig. 1a. (A color version of this temperature on the interaction between fullerene and GNR. figure can be viewed online.) CARBON 90 (2015) 34– 43 37

6 3.2. Self-assembly of two fullerenes and GNR armchair 300K 5 zigzag 300K armchair 1K We then investigate the self-assembly of two fullerenes with armchair 500K 4 GNR. Similar to the self-assembly of single fullerene with GNR, we observe two distinct phases, i.e., binding and wrap- 3 ping. However, the wrapping of two fullerenes by GNR shows 2 more versatile configurations, namely, disordered wrapping (Fig. 4b), parallel wrapping (Fig. 4c) and vertical wrapping

Width of graphene (nm) 1 (Fig. 4d). And some final configurations of the self-assembly are highly dependent on the dynamic process. For example, 0 0.2 0.4 0.6 0.8 1 1.2 two configurations shown in Fig. 4c are observed for a given Radius of fullerene (nm) system. So we regard the two configurations as single one for the sake of simplicity. Next, we conduct five independent Fig. 3 – Phase diagram of the assembly between single simulations for each system and summarize the most proba- fullerene and graphene as a function of the size of fullerene ble final configuration. As shown in Fig. 4e, the disordered and width of GNR. The lines represent the boundaries wrapping configuration mainly occurs in the self-assembly between wrapping phase (lower region) and binding phase of large fullerenes and GNR with small width. This is because (upper region) under different conditions. The upper inset GNR is highly flexible, and a disordered structure will maxi- shows a snapshot of binding phase. The bottom left one mize its contact area with the large fullerenes (to reduce the and the right one show snapshots of sliding and rolling total energy). With the increase of its width, GNR becomes structures in wrapping phase, respectively. (A color version less flexible and thus it transfers to the parallel wrapping of this figure can be viewed online.) structure, which decreases the EGNR. If we continue to increase the width, GNR will further tend to increase the con-

tact area with itself to decrease the EGNR by adopting a smaller As shown in Fig. 3 (two black lines), the edge shape has little radius. So it pushes the two fullerenes inside and forces the effect on the phase diagram, which implies that the choice of fullerenes to adopt the vertical wrapping configuration. To edge shape doesn’t affect the mechanical properties of GNR. conclude, the final structure depends on the competition

Actually, the bending constants along the two directions of between EGNR and Einter. With the increase of the width of graphene are very similar, which are measured to be GNR, it will tend to adopt a more compact structure to

0:972 eV and 0:975 eV in X and Y directions, respectively, decrease the EGNR. and are in accordance with previous reports [16]. There is a The boundary between binding region and wrapping bit of deviation in the case of small fullerene, which may be region is also studied. It is found that two fullerenes can acti- a result of the different hydrogen atoms on the edges of vate the scrolling of wider GNR (see Figs. 3 and 4e for compar-

GNR. The temperature dependence is also investigated (see ison) in the case of C180s, C240s, C320s and C540s. For example,

Fig. 3, red and blue lines). It is found that increasing tempera- two C320s can activate the scrolling of GNR with a width of ture hinders the wrapping process, while decreasing tem- 4:8 nm, which is twice as much as the width in the case of perature promotes the wrapping. This is because at high single C320 (2:5 nm). So two fullerenes can work cooperatively temperature, the system prefers large entropy to decrease to roll up wider GNR. the free energy. Thus the graphene flake is not likely to bind closely to fullerene (small entropy). 3.3. Self-assembly of multiple fullerenes and graphene Finally, it is worthwhile to make a comparison with pre- nanosheet vious report, where GNR can be scrolled by a drop of water [27]. Firstly, the folding of GNR by a nanodroplet shows vari- Finally, we investigate the effect of the number of fullerenes ous phases including nonfolding, sliding, rolling and zipping on the assembly, where the number increases from three to phases, which is similar to our phase diagram except the lack six, and compare the results with those in the cases of one of zipping phase, which is probably due to the rigid structure and two fullerenes (see Fig. 5). Generally, it is found that pro- of fullerene. Also, the boundary between folding phase and cess of self-assembly greatly changes when we increase the nonfolding phase increases monotonously with the size of size and number of fullerenes. the nanodroplet. Particularly, we find that a nanodroplet with a diameter of about 1:4 nm can fold GNR with a width up to 3.3.1. Self-assembly of multiple C60s and GNR

0:5 nm. On the contrary, the maximum width of GNR in the As shown in Fig. 5,C60s can roll up graphene with maximum case of fullerene with the same size is about 2:0 nm. In this width of about 0:5 nm, which doesn’t increase when we use sense, the folding by fullerene is more efficient. This is more fullerenes (meaning that there exists little cooperative because that water droplet can be treated as a very soft nano- effect). As shown in Fig. 6a, when we deposit five C60son particle. This is very similar to cellular uptake of an elastic the surface of GNR with a width of 3:6 nm, they gradually nanoparticle, where they reveal that the uptake of a rigid aggregate into close-packed structure due to the attractive nanoparticle is easier than a soft nanoparticle, for that soft interaction between them. And from Fig. 6b, we can see sev- nanoparticle tends to lay on the surface of membrane and eral drops of the interaction between C60s during the aggrega- results in partial or frustrated wrapping [41–43]. tion. After aggregation, we observe a slight bend of GNR (see 38 CARBON 90 (2015) 34– 43

(a) (b) (e) 6 (a) (b) (c) (d) (c) 4

2 (d) Width of graphene (nm)

0 0.2 0.4 0.6 0.8 1 1.2 Radius of fullerene (nm)

Fig. 4 – Snapshot of the (a) binding, (b) disordered wrapping, (c) parallel wrapping, and (d) vertical wrapping structures. (e) Phase diagram of the assembly between two fullerenes and graphene as a function of size of fullerene and width of GNR. (A color version of this figure can be viewed online.)

(green and dashed lines), there is no difference between C60 15 C180 them, indicating that the cooperative effect in aggregated C240 C320 C60s is very limited. C540

10 3.3.2. Self-assembly of multiple C180s/C240s and GNR Interestingly, it is observed that the maximum width of GNR exhibits a non-monotonous dependence on the number of

5 C180s and C240s. For example, four C240s can drive the scrolling Width of graphene of GNR with a width of about 4 nm, larger than that in the

case of five C240s (about 3 nm). This phenomenon may arise 0 from the improper configuration of multiple fullerenes. As 1 2 3 4 5 6 shown in Fig. 7a, we firstly put five C s on the surface of Number of fullerenes 240 GNR. Then the fullerenes randomly diffuse around and aggre- Fig. 5 – The maximum width of graphene which can be gate into a close-packed hexagonal structure. By analyzing rolled up as a function of the number of fullerenes. (A color the interaction energy (see Fig. 7b), we can find that the inter- version of this figure can be viewed online.) action energy between C240s and itself decreases in this per- iod, and it can be divided into three stages. In detail, the first stage starts immediately after the simulation begins, 384 ps side view of Fig. 6a), which does not occur in the case of which corresponds to the fast aggregation between four single C60. Thus, the aggregation may slightly promote the C240s. The second and third stages stand for the aggregation wrapping of GNR. However, the interaction between C60 and between one last C240 and the four aggregated C240s. After GNR is very small. And since it is the interaction between full- that, the GNR begins to wrap around the fullerenes and we erene and GNR that overcomes the bending energy of GNR, can observe a sharp decrease of interaction energy between this effect is limited. Besides, to quantify the cooperative C240s and GNR. When the GNR reaches a half wrapped state, effect of aggregated C60s, we calculate the interaction it will push one of the fullerenes to the top of other four between C60s and GNR, and compare with five times the inter- fullerenes, which further decreases the interaction energy action between single C60 and GNR. As illustrated in Fig. 6b between C240s (the fourth stage). However, the fullerene on

(a) (b) 1 0 2 3 Total -1 4 C60-GNR 5 C60-C60 -2 -3 -4 -5

Interaction energy (eV) -6 -7 384 ps 0 500 1000 1500 2000 0 ps 49 ps 84 ps 193 ps 384 ps (side view) Time (ps)

Fig. 6 – (a) Snapshots of the self-assembly between five C60s and the graphene with a width of 3:6 nm. (b) Interaction energy between five C60s and GNR, C60s and itself and total interaction energy as a function of time. The five labels from 1 to 5 correspond to the five moments in (a), respectively. The dashed line represents five times the interaction between single C60 and GNR (not the average interaction energy between five C60s and GNR). (A color version of this figure can be viewed online.) CARBON 90 (2015) 34– 43 39

(a) (b) 0 1 Total 2 C240-GNR 3 C -C -5 4 240 240

-10

-15

-20 Interaction energy (eV)

-25 0 500 1000 1500 2000 0 ps 80 ps 400 ps 650 ps Time (ps)

Fig. 7 – (a) Snapshots of the self-assembly between five C240s and the graphene with a width of 3:6 nm. (b) Interaction energy between five C240s and GNR, C240s and itself and total interaction energy as a function of time. The four labels from 1 to 4 correspond to the four snapshots in (a), respectively. The dashed line represents five times the interaction between single

C240 and GNR. (A color version of this figure can be viewed online.) the top will hinder the following wrapping because it prevents keeping its edge-scrolled configuration till the end of the the GNR from contacting with the other four fullerenes and simulation. the GNR itself, and the interaction energy keeps unchanged We can better understand the process by analyzing the after the fourth stage. So we infer that the structure of five total potential energy. As shown in Fig. 8b, the total process fullerenes is quite stable because it maximizes the contact is divided into three stages. The first stage is from 0 to area between fullerenes and minimizes the interaction 200 ps, which mainly represents the reorganization of the energy. Finally, we notice that the interaction between aggre- fullerenes. The fullerenes are found to favor the corners and gated C240s and GNR is larger than five times the interaction edges of the graphene, which is also observed in Fig. 1a. To between single C240 and GNR (see Fig. 7b, green and dashed demonstrate it more clearly, we calculate the potential energy lines). So the aggregated C240s can work cooperatively to roll landscape of one C540 located on the surface of graphene (see up graphene, which is different from the case of multiple Fig. 9a). The position (0,0) represents the corner of graphene.

C60s. However, the graphene is not completely scrolled It is found that if the fullerene locates at the corner and edge because the interaction between C240 and graphene is not of graphene, the system will have a relatively lower potential large enough, which is also different from the case of giant energy. This is because the corner of graphene can bend to fullerenes (see below). the surface of fullerene (see Fig. 9b), which decreases the total energy of about 2:5 eV. If the fullerene locates at the center of

3.3.3. Self-assembly of multiple C320s/C540s and GNR graphene surface, it will not interact with the corner. In this

Multiple C320s and C540s show dramatically different behav- sense, this interaction is short-ranged. As shown in Fig. 9c, iors from the smaller fullerenes. As shown in Fig. 5, when once C540 diffuses to the corner, it will bind to it till the end we use three C540s or four C320s, they can even roll up gra- of simulation. We also find that the total energy decreases 2 phene flake as large as 16:0 16:0nm. Taking C540s for by about 8 eV after three fullerenes bind to the corner of gra- example (Fig. 8a), we firstly put four C540s on the surface of phene (see the left inset of Fig. 8b). It is also observed that the a large graphene with size of 16:0 16:0nm2. Then, it is potential energy landscape is symmetric with respect to the observed that one of the fullerenes diffuses to the corner of diagonal line (X ¼ Y). Notice that the edge geometries along graphene (61 ps), similar to the self-assembly between one X and Y directions are armchair and zigzag, respectively. We fullerene and GNR. At 110 ps, the left top corner of graphene can infer that the edge geometry does not affect the interac- is bound with three fullerenes. And then the three fullerenes tion between fullerene and graphene. Interestingly, the can roll up the graphene from the corner to a partially potential landscape of smaller fullerene C180 is completely wrapped state (157 ps). At the same time, the other fullerene different from that of C540. As shown in Fig. 9d, the potential in the middle part also diffuses to the boundaries of the gra- energy at the corner is larger because the interaction between phene, and it further adsorbs to the three fullerenes after the C180 and graphene is small and the corner of graphene will graphene is partially wrapped. After that, the four fullerenes not bend to the surface of C180 (Fig. 9e). As a result, multiple can drive the scrolling of the graphene from the corner in less small fullerenes will diffuse for the whole time (Fig. 9f) and than 50 ps and the system reaches a fully wrapped state. For not aggregate at the corner, and that is the reason why they the sake of convenience, we name this configuration ‘‘corner- cannot roll up large graphene flake. Once fullerenes bind to scrolled’’. After scrolling (263 ps), the graphene further the corner, the graphene will form a cave-like structure, changes its configuration to minimize the potential energy. which is easier for the remaining fullerenes to bind to the cor- At 295 ps, the graphene adopts the configuration that seems ner (see 157 to 209 ps in Fig. 8a). In this sense, the first stage is to be scrolled from the edge. So we name this configuration a positive feedback process. The second stage is the scrolling ‘‘edge-scrolled’’. Then, the graphene changes its configuration of the graphene. After enough fullerenes bind to the corner, between corner-scrolled and edge-scrolled back and forth they can drive the scrolling of the graphene. This is driven (320 ps and 345 ps), and is finally equilibrated after 600 ps, by the interaction between fullerenes and graphene, which 40 CARBON 90 (2015) 34– 43

(a)

0 ps 61 ps 110 ps 157 ps 209 ps

247 ps 263 ps 295 ps 320 ps 345 ps (b) (cross section) (cross section)

-8.845 -8.85 -8.86 -8.846 -8.864 -8.847 -8.868 -8.86 30 60 90 120 150 280 320 360 Potential energy (10^4 eV) 0 200 400 600 800 1000 (c) Time (ps) -200 -8.815

-300 -8.82

-400 -8.825 vdW interaction (eV) -500 -8.83 0 200 400 600 800 1000 Bonded interaction (10^4 eV) Time (ps)

2 Fig. 8 – (a) The wrapping process of four C540s on the surface of graphene with a size of 16:0 16:0nm . (b) Potential energy of the system as a function of time. The two insets show close views of the potential energy function. (c) vdW interaction and bonded interaction of the system as a function of time. (A color version of this figure can be viewed online.)

is similar to the case in Fig. 1a. After the C540s are totally bonded interaction. As shown in Fig. 8c, the vibration of wrapped, the corner of graphene will contact with itself and potential energy mainly arises from the vdW interaction, the interaction between itself further drives the scrolling. It which infers that the change of configurations is dominated should be pointed out that single fullerene or two fullerenes by surface energy between graphene and itself rather than cannot be fully wrapped, and the corner of graphene won’t the bending energy. Besides, it is also observed that the local contact with itself if we only use one or two C540s. So the minimal energies of vdW interaction are almost the same aggregation of fullerenes is very important. Because of the during the vibration, corresponding to the same structure large contact area between graphene itself, the potential (see Fig. 8a, 295 and 345 ps). Likely, there exist some local decreases by as large as 200 eV, and it happens very quickly minimums in the bonded interaction (e.g., 259 and 295 ps). (in less than 50 ps). The third stage is the configuration However, these are caused by the known artifacts (called change of graphene from corner-scrolled to edge-scrolled. the flying ice cube) introduced by the thermostat [46], but it Since the contact area can be enlarged by adopting the will not affect the overall mechanism, because at most time, edge-scrolled configuration, the graphene favor this config- the translational and rotational kinetic energies are close to uration to minimize the potential energy. However, due to zero. It should be noticed here that the graphene is located the low friction of graphene surface, the graphene vibrates in vacuum, and the resistance force can be much larger in between the two configurations like a spring for as long as aqueous solution. So the vibration will be weakened in real 400 ps (see the right inset of Fig. 8b). Such oscillation has also applications. been observed in previous reports [44,45]. To better under- Generally, the graphene flake can be rolled up after at least stand this phenomenon, we divide the potential energy into three C540s located at one corner. So if the initial structure is two parts, i.e., the van der Waals (vdW) interaction and the different from that in Fig. 8a, four C540s may diffuse to CARBON 90 (2015) 34– 43 41

(a) (b) (c) 5 0

4 -0.5 -1 3 -1.5

Y (nm) 2 -2 Potential (eV) 1 -2.5 0 -3 0 1 2 3 4 5 (d) X (nm) (e) (f) 3 0 -0.5 2 -1 -1.5 Y (nm) 1 -2 Potential (eV) -2.5 0 -3 0 1 2 3 X (nm)

Fig. 9 – (a) Potential energy landscape as a function of X and Y when one C540 binds to the surface of graphene. The point (0,0) represents the corner of graphene. (b) Snapshot of one C540 binds to the corner of graphene. (c) Trajectory of one C540 diffusing 2 on the surface of graphene with a size of 16:0 16:0nm . The red point represents initial position of C540. (d–f) Potential energy landscape, snapshot and trajectory in the case of C180, respectively. (A color version of this figure can be viewed online.) different corners and the fully wrapping may not happen. To study the effect of initial structure, we use ten different struc- 0 tures and find that only two of them form core–shell structure finally. However, we should point out that the number of C540-GNR GNR-Substrate nanoparticles on graphene may be much larger than four in -10 real experiments. Thus we also use ten fullerenes and con- duct ten independent simulations. It is found that core–shell structure occurs in eight simulations, indicating that the -20 probability of fully wrapping increases with the increase of Interaction energy (eV) fullerene number. Finally, to see whether the size of graphene influence the mechanism, we further carry out extra sim- -30 ulations using a large graphene (32 32 nm2). It is observed 0 500 1000 1500 2000 that the graphene can also be scrolled from the corner (see Time (ps) Video S1 in the Supplementary data), which implies that the Fig. 10 – Interaction energies between C and GNR and mechanism is independent of the dimensions as long as the 540 between GNR and the substrate as a function of time. The graphene flake has finite size. However, fullerenes will not roll width and length of GNR are chosen as 1:7 nm and 8:5nm, up a graphene sheet with infinite size, since an infinite two respectively. The inset shows final structure of the system. dimensional layer has no edge or corner. Similarly, we also (A color version of this figure can be viewed online.) investigated the influence of thermostat by using the V- rescale method, and it makes no difference to our results.

Our observations can well explain the previous experimental substrate, and find that the interaction energy between C540 report, where it is found that the Cu nanoparticles guide the and GNR is far less than that of GNR and the substrate (see curls of graphene [30,31]. Fig. 10). As a result, the wrapping is hindered under this situa- tion, which is in accordance with previous simulation result 3.4. Fullerene on supported graphene flake [29]. Actually, some experiments have also revealed that nanoparticle alone cannot roll up graphene oxide (GO) sheets Experimentally, graphene flakes are usually deposited on sub- from substrate [31]. So external energy (e.g., sonication [31]) strates such as SiO2/Si, h-BN. However, there is no standard must be provided to overcome the interaction energy, or we force parameter for SiO2/Si or h-BN in AIREBO potential func- can simply disperse GO into suspensions [30]. tion, so we use the graphene plane to mimic the substrate in the simulations. As shown in Fig. 10,C540 is unable to roll up 4. Conclusions the supported GNR in 2000 ps, while free GNR is found to wrap around C540 in less than 100 ps (see Fig. 1). We also We have investigated the self-assembly of graphene and analyze the interaction energies between C540, GNR and fullerenes with different sizes by using molecular dynamics 42 CARBON 90 (2015) 34– 43

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