Theoretical Simulation of Atomic-Scale Peeling of Single-Walled Carbon Nanotube from Graphite Surface

Molecular mechanics simulation of atomic-scale peeling of carbon nanotube (CNT) from the graphite substrate surface is performed. We have first obtained the theoretical 'peeling force curve' of the CNT, where the CNT physically adsorbed on the graphite substrate surface is gradually retracted or peeled. In the simulation the single-walled carbon nanotube (SW-CNT) of the (3, 3) armchair type with a length of 40.3 A comprised of 198 carbon atoms is used. It is clarified that the peeling force curve shows a characteristic behavior mainly dominated by the van der Waals interaction acting between the CNT and the substrate surface. The typical change of the CNT shape during the peeling process, shows a transition from the 'line contact' to the 'point contact', which reflects the covalent bonding interaction. The peeling force curve gives us information of an elementary process of peeling of the CNT. [DOI: 10.1380/ejssnt.2006.133]


I. INTRODUCTION
The promising mechanical and electronic properties of the carbon nanotubes (CNT's) [1] have attracted our attentions in many research-and industrial areas, which have been discussed so far by many researchers. Recently, experimental studies to use CNT as machinery parts such as CNT tip [2], nano-pincette [3], and rotational actuators in microelectromechanical systems [4], have been performed. Therefore importance of the study of the CNT's regarded as machinery parts to build up machines and objects in nano-and micrometer scale, have been rapidly increased. First it is important to consider the CNT interacting with the substrate surface. Then the CNT physically adsorbed on the substrate surface must be retracted or peeled from the surface, and moved to a desired position and attached onto the substrate surface again.
In this paper, the former half of the process, 'peeling' process of the CNT from the substrate surface, is numerically studied. Molecular mechanics simulation of atomic peeling of the CNT from the graphite surface is performed. As an example of the substrate surface, graphite is adopted, which is an inert and standard sample. First, it is clarified what interaction gives significant influences on the behavior of the peeling force curve. Here the van der Waals interaction and covalent bonding interaction are considered. We also found characteristic change of the shape of the CNT during the peeling process, the physical * This paper was presented at International Symposium on Surface Science and Nanotechnology (ISSS-4), Saitama, Japan, 14-17 November, 2005. † Corresponding author: naru@st.seikei.ac.jp ‡ Present address: Institute of Materials Science, University of Tsukuba, Tsukuba 305-8573, Japan origin of which is also discussed by considering the above interactions.

II. MODEL AND METHOD OF SIMULATION
The model used in the simulation is as follows. As a model of the CNT, a single-walled carbon nanotube (SW-CNT) of the (3, 3) armchair type with a length of 40.3 A and a radius of 2.1Å, comprised of 198 carbon atoms, is adopted [ Fig. 1(a)]. This SW-CNT with open edges is constructed by repeated structures of α and β rings comprised of six carbon atoms as shown in Figs. 1(a) and 1(b). As a model of the substrate surface, the graphene whose shape is an equilateral hexagon with a length of 21.5Å of each side, comprised of 1176 carbon atoms, is used [ Fig. 1(c)].
First covalent bonding structures of both the CNT and graphene are separately optimized by minimizing the total energy described by the Tersoff potential [5], using the Polak-Rebiere-type conjugate gradient (CG) method [6]. Here the convergence criterion is set that the maximum of absolute value of all the forces acting on the movable atoms, is lower than 10 −4 eV/Å, i.e., where N is the total number of movable atoms, and F i is a force acting on the ith movable atom.
Next the CNT is located on the rigid graphene [ Fig.  1(d)], so that the AB stacking registry between the bottom part of the CNT and the graphene is conserved [ Fig.  2(a)]. Then the optimized structure of the CNT physically adsorbed on the graphene is obtained by minimizing the total energy V total = V vdW + V Tersoff , using the CG method. Here, as the interaction potential between the CNT and the graphene, V vdW , the L-J type potential  obtained by Lu, Li and Martin [7], is used, which was parameterized in order to reproduce the interlayer distance 3.354Å and elastic modulus c 33 = 4.08 Gpa of AB stacking graphite crystal structure.
As shown in Fig. 2(a), there are two series of arrays of carbon atoms at the bottom part of the CNT. All carbon atoms of one array surrounded by blue-lined box are located on A sites below which graphene atoms exist, and those of the other array are located on B sites below which graphene atoms do not exist. Since A-site atoms receive larger repulsive forces than B-site ones, vertical z position of A site atoms becomes a little higher than that of B site ones after the structural optimization as shown in Fig. 2(b). Thus the averaged optimized distance between the bottom of the CNT and the graphene sheet is 3.2Å. This structure where the CNT is slightly pushed onto the graphene, is used as an initial structure of atomic peeling [ Fig. 1(d) and Fig. 2(b)].
During the peeling process, the red-colored α and β rings on the left edge [ Fig. 1(a)] are lifted along the z direction, parallel to [0001] axis, by 0.1Å [ Fig. 1(d)].
Here, for each fixed lifting edge, the total energy V total is minimized using the CG method. Therefore the simulation corresponds to the limit of adiabatic approximation of lifting velocity ν → 0 for T = 0 K. Thus the optimized positions of the carbon atoms of the CNT, (x, y, z), the vertical force F z , and the lateral force F x and F y , acting on the fixed position, are obtained. ∆z − F z plot is called the 'peeling force curve', and is mainly discussed in this paper. Here ∆z is assumed to be the displacement of the lifting edge from the initial position along z direction. Figures 3A-3F show the shapes of CNT on the graphene during the peeling process seen from the y axis. The colors allotted to each atom correspond to the van der Waals interaction energies, V vdW , where blue and red colors correspond to the low and high energies, respectively. First the CNT takes an initial structure parallel to the substrate surface just before the peeling starts [ Fig. 3A:

A. Peeling process of CNT
Here the blue region where the effect of the van der Waals interaction energy is the largest, covers all the bottom parts of CNT, that's to say, the 'line contact' between the CNT and graphene occurs. However, as the CNT is peeled from the surface little by little, the line contact gradually vanishes, the bending of the CNT increases more [ Fig

C. Discussion
The physical origin of the shape of the peeling force curve [ Fig. 4 and V Tersoff , respectively, where V total = V vdW + V Tersoff . Both V total and V Tersoff increase just before the complete peeling of the CNT. Then they discretely change at the complete peeling position (∆z = 7.6Å). Then calculated F vdW (∆z) = −dV vdW /d(∆z) and F Tersoff (∆z) = −dV Tersoff /d(∆z), are plotted as shown in Fig. 6. It is clearly shown that the attractive van der Waals interaction force F vdW (∆z) [green curve in Fig. 6] plays a dominant role in the shape of the peeling force curve F z (∆z) [ Fig. 4] including the minimum position around ∆z = 1.2Å. However, as the CNT is gradually peeled, the magnitude of attractive force | F vdW (∆z) | gradually decreases, and finally F vdW (∆z) and F Tersoff (∆z) [blue curve in Fig. 6] become approximately equal to each other, around the position just before the complete peeling (∆z = 6.8Å), which means the relative increase of the effect of the covalent bonding interaction force F Tersoff (∆z). F Tersoff (∆z) reflects the change of the shape of the CNT during the peeling process. The schematic illustrations of the typical CNT shape are shown in the insets (1)-(4) of Fig. 6. First | F Tersoff | increases to a maximum value around ∆z = 0.8Å, where the CNT shape opens upwards [inset (1) of Fig. 6]. Next | F Tersoff | reduces to a minimum value about zero around ∆z = 3.0Å, where the CNT shape takes a 'reverse S character' [inset (2) of Fig. 6]. Then | F Tersoff | increases to a maximum value again around ∆z = 6.8Å, where the CNT shape opens downwards [inset (3) of Fig. 6]. Finally, when | F Tersoff | reduces to nearly zero after the complete peeling, the CNT