Atomic-Scale Friction of Monolayer Graphenes with Armchair- and Zigzag-Type Edges During Peeling Process

We numerically studied the atomic-scale friction of the monolayer graphene sheet during the nanoscale peeling process by molecular mechanics simulation. The zigzag behavior appears twice in the force curve during the surface and line contacts between the graphene sheet and the graphite surface. During the surface contact, the graphene sheet takes the atomic-scale sliding motion, which exhibits the transition from the continuous to the stick-slip sliding particularly for the graphene with the armchair-type free edge. The period of the zigzag structures for the stick-slip motion in the peeling force curve nearly corresponds to the lattice period of the graphite depending on the lattice orientation and the edge structure of graphene. During the line contact, the graphene sheet also takes the stick-slip sliding motion. Comparison between armchair- and zigzag-type free edges reveals the diﬀerence of the characteristic atomic-scale sliding of the graphene sheet. These ﬁndings indicate the possibility of not only the direct observation of the atomic-scale friction of the graphene sheet at the tip/surface interface but also the identiﬁcation of the lattice orientation and the edge structure of the graphene sheet. [DOI: 10.1380/ejssnt.2010.105]


I. INTRODUCTION
The carbon nanostructures such as carbon nanotube (CNT) and graphene have recently attracted great interests as the components of the electronic, magnetic and optical devices. We have so far studied the peeling mechanics of the carbon nanotube (CNT) adsorbed onto the graphite surface both theoretically [1][2][3] and experimentally [4,5]. It is clarified that the transition from the line-to the point-contact between the CNT and the graphite surface occurs during the peeling process [1][2][3][4][5]. On the other hand, since the success of its experimental isolation [6], the potential of various application of the graphene has been discussed by many researchers [7,8]. Therefore the peeling mechanics of the graphene sheet is also very important, which can be regarded as the elementary process of the macroscopic sticky tape such as the gecko-foot-mimic adhesives [9][10][11], or that of the microscopic extension of the crack in the fracture process.
In our preliminary experiments, we have already succeeded in peeling the multilayered graphene plate with a thickness of several µm by using atomic-force microscopy tip [12]. Here the two-component epoxy resin adhesive is used to bond the graphene plate to the AFM tip. The junction formed between the AFM tip and the graphene should be mechanically rigid enough to measure the elasticity of the graphene sheet during the peeling process. Ahead of experiment, we have theoretically reported the nanoscale peeling behaviors of the monolayer graphene sheet by lifting the center position based on the molec-ular mechanics simulation [13]. The peeling force curve exhibits the nanoscale change of the graphene shape from the surface to the line contact. However the clear atomicscale behaviors of the graphene sheet have not been found yet during the peeling process. In this paper, the characteristic atomic-scale sliding behaviors of the graphene sheet are found during both the surface and line contacts in the case of lifting the edge of the graphene sheet. It is clarified that effect of the free edge structure gives the marked influences on the atomic-scale peeling process. These simulated results can indicate the possibility of not only the direct observation of the atomic-scale friction of the graphene sheet at the tip/surface interface but also the identification of the lattice orientation and the edge structure of the graphene sheet.

II. MODEL AND METHOD OF SIMULATION
The same model as that used in the previous work [13] is adopted as illustrated in Fig. 1(a): a rectangular-shaped monolayer graphene sheet with each side of 38Å×21Å comprised of 310 carbon atoms, adsorbed onto the rigid rectangular graphene sheet (which is called, the 'graphite surface,' hereafter) with each side of 164Å × 58Å comprised of 3536 carbon atoms. The initial position of the graphene is set so that the AB stacking registry between the graphene sheet and the graphite surface is satisfied as shown in Fig. 1(b). The green-colored outermost atoms at the left edge of the graphene sheet are assumed to be attached to the AFM tip apex [ Fig. 1  scale peeling process for the armchair-type edge is discussed. Then, in Sec. IIIC, the case for zigzag-type edge is also discussed. Effect of the free edge structure gives the marked influences on the atomic-scale peeling process. For each lifting edge height of the graphene sheet z, the total energy V total = V cov + V vdW is minimized using the conjugate gradient (CG) method [14]. Here the covalent bonding V cov [15] and nonbonding energies V vdW [16,17] are considered. Thus the optimized shape of the graphene sheet and the peeling force acting on the lifting left edge, F x and F z , are calculated during the peeling process.

A. Nanoscale peeling behavior within x−z plane
When the left edge of the monolayer graphene sheet is lifted, the shape of the graphene sheet markedly changes during the peeling process within the x − z plane as illustrated in Figs ceives the averaged attractive interaction force per one carbon atom. As illustrated in Fig. 3    B. Atomic-scale sliding within x−y plane Fig. 3(a) shows the atomic-scale zigzag structures within the surface-and line-contact regions, which can be explained by the following atomic-scale sliding motions of the graphene sheet within the x−y plane.

Surface-contact region
During the surface contact region between C and E in Fig. 3(a), z − F z curve takes the atomic-scale zigzag structures from I to VII.   Fig. 4(c)10. The period of the zigzag behavior of the F z curve decreases from 3.7Å to 2.5Å as shown in Fig. 4(a) as the peeling proceeds. The lattice spacing of the graphite surface, 2.5Å, appears in the peeling force curve particularly for the stick-slip region.

Line-contact region
During the line contact region between G and H in Fig. 3(a), z − F z curve takes another atomic-scale zigzag structures as shown in Fig. 5(a). One of the zigzag behaviors in the force curve

C. Edge effect
The free edge of the graphene sheet discussed in the previous section is 'armchair type.' However, it is well known that the edge structure plays quite an important role in electronic properties of graphene, which can be also expected to give influences on the mechanical properties such as the peeling process. Therefore, in this section, the peeling process of the graphene sheet with the 'zigzagtype' free edge is discussed. In the simulation, the model obtained by rotating Fig. 1(b) by 30 • is used [Fig. 6(a)], and the left zigzag edge is lifted to simulate the peeling process, while the right free edge is zigzag type. As a result, the nanoscale peeling process within the x−z plane and the global shape of the force curve [ Fig. 6(b)] is similar to that of Figs   During the line contact, the difference between the armchair-and zigzag-type edge is enhanced. Fig. 8(a) reflects the zigzag stick-slip motion of the graphene sheet

IV. DISCUSSIONS AND CONCLUSIONS
In this paper the atomic-scale sliding motion of the monolayer graphene sheet during the peeling process is found by molecular mechanics simulation. For the graphene sheet with armchair-type free edge, the transition from the continuous to the stick-slip motion of the graphene sheet is also found, which can be explained as follows: The peeling process induces the increase of the peeled area of the graphene sheet, and the decrease of the surface contact area. Considering the peeled area of the graphene sheet acts as an effective spring as shown in Fig. 9(a), the increase of the peeled area makes the effective spring softer, and the decrease of the surface contact area decreases the energy barrier to slide the graphene sheet. Finally the peeling process induces the transition from the continuous to the stick-slip sliding motion of the graphene sheet, together with the decrease of the period and amplitude of the z −F z curve. Here the period of the zigzag structures of the peeling force curve particularly for the stick-slip region corresponds to the lattice spacing of the graphite surface along [1230] direction, 2.5Å. For the graphene sheet with zigzag-type free edge, the period becomes the lattice spacing along [1010] direc-tion, 2.9Å. This means the sliding length of the graphene sheet along x direction becomes nearly equal to the peeled length along z direction. The zigzag structures of the peeling force curve with the same period of about sev-eralÅ have been also observed by our preliminary experiments using the multilayered graphene, which will be reported elsewhere [12]. Of course, if the number of the peeled graphene sheets is reduced, the direct comparison between the present simulation and the experiment will become possible. Another interesting point is that the behavior of the lateral force curve (F x (z)) is qualitatively the same as that of the vertical force curve (F z (z)) during the surface contact as shown in Fig. 9(b). Therefore it can be said that the peeling force curve, F z (z), directly reflects the atomic-scale friction force, F x (z), which decreases to 0.019 eV/Å 30 pN for z = 27.8Å [ Fig. 9(b)]. This ultralow friction force, F x , is derived from the superlubricity at the interface between the graphene sheet and the graphite surface [18][19][20]. Furthermore effect of the edge structure on the peeling process is clarified by comparison of the free edge between the armchair-and zigzag-types. The atomic-scale structure of the force curve during the surface contact reflects the lattice spacing of the graphite surface. So the period of the atomic-scale structure of the force curve can tell us the atomic-scale lattice orientation and structure of the free edge of graphene. Such information can be used for the control of the electronic properties of the graphene sheet adsorbed onto the substrate. Therefore this paper indicates the possibility of the identification of the lattice orientation and the edge structure of the graphene sheet.
The peeling process discussed in this paper is closely related to the atomic-scale wear of the graphite and the graphene tip formation in the friction force microscopy [21]. When the tip is pushed onto the surface for less than the critical tip height, the outermost graphene layer is attached to the FFM tip, which results in the formation of the graphene tip. In that case, the graphene sheet takes the surface contact with the second layer graphene, and it takes the two-dimensional stickslip motion. However it is difficult to observe directly the stick-slip motion during the scan process, due to the very small gap between the FFM tip and the graphite surface. On the other hand, if the peeling process is used, it can be expected that the contact at the AFM tip/graphite interface has a wider space to be observed directly by ex. Transmission Electron Microscopy (TEM). This paper indicates the possibility of a direct observation of the stick-slip motion of the graphene sheet, that's to say, the elementary process of the atomic-scale friction or superlubricity which occurs at the tip/graphite surface interface.