Adhesion and friction between individual carbon nanotubes measured using force-versus-distance curves in atomic force microscopy

The adhesion and friction between individual nanotubes was investigated in ambient using a dynamic atomic force microscope (AFM) operating in force-calibration mode to capture force-versus-distance curves. A multiwalled carbon nanotube (MWNT) tip attached to a conventional AFM probe was brought into contact with and then ramped in vertical direction against a single-walled carbon nanotube (SWNT) bridge suspended over a $2\text{−}\mu \text{m}$-wide trench. The interaction between nanotubes altered the oscillation amplitude, phase lag, and average deflection of AFM cantilever, from which the interacting forces between nanotubes are quantitatively derived. During ramping, a stick-slip motion was found to dominate the sliding between the nanotubes. The stick was attributed to the presence of high-energy points, such as structural defects or coating of amorphous carbon, on the surface of the MWNT tip. The coefficients of static friction and shear strength between nanotubes were evaluated to be about 0.2 and 1.4 GPa, respectively. They are about 2 orders of magnitude larger than the kinetic counterparts. The kinetic values are on the same order as that measured previously by sliding a MWNT tip across a SWNT bridge in lateral direction.

Figure 1

The SEM image shows the morphology of the MWNT tip.

Figure 2

Schematic drawing of the experimental setup for nanotribological measurements between individual nanotubes. The double arrow indicates the ramping direction ($z$ direction). $F$ and $N$ indicate the friction and normal force between nanotubes.

Figure 3

(Color online) Typical force-versus-distance curves of the MWNT tip ramping in vertical direction against a SWNT bridge from below. Feature points are labeled in the top plots, and the corresponding contact geometries of nanotubes are illustrated in the bottom schematics. The arrows in the schematics indicate the ramping direction at those points.

Figure 4

(Color online) Typical force-versus-distance curves of the MWNT tip ramping in vertical direction against a SWNT bridge from above. Feature points are labeled in the top plots, and the corresponding contact geometries of nanotubes are illustrated in the bottom schematics. The arrows in the schematics indicate the ramping direction at those points.

Figure 5

Schematic illustration of the contact geometry of nanotubes. The SWNT bridge was displaced by a distance of $d$ and tilted from the vertical direction by an angle of $\alpha$. The angle between the displacement of the SWNT bridge and the MWNT tip is denoted as $\beta$.

Figure 6

(Color online) The interaction between nanotubes is partially detected as vertical deflection of AFM cantilever, from which the vertical force is calculated and plotted against normalized amplitude using (a) 17 force-versus-distance curves with the MWNT tip below the SWNT bridge and (b) 12 force-versus-distance curves with the MWNT tip above the SWNT bridge.

Figure 7

(Color online) The relative magnitude of interaction stiffness and damping coefficient for the interaction between nanotubes are determined by mapping (a) the data in the top figures of Fig. 3 and (b) in the top figures of Fig. 4 into the contour plots of interaction stiffness and damping coefficient against normalized amplitude and phase. The solid lines represent the damping coefficient and the dashed lines represent the interaction stiffness. The data basically follow the zero contour line of damping coefficient highlighted by a thick solid line.

Figure 8

(Color online) Plots of kinetic friction force between nanotubes against normalized amplitude as calculated from the combination of amplitude and phase data using (a) nine force-versus-distance curves with the MWNT tip below the SWNT bridge and (b) 14 force-versus-distance curves with the MWNT tip above the SWNT bridge.

Figure 9

(Color online) The contact geometry between nanotubes is partially determined and the distance (left column) and angle (right column) of the displacement of SWNT bridge are plotted against normalized amplitude. The plots are calculated from (a) Fig. 3 and (b) Fig. 4. The results are used for precise evaluation of the adhesive and friction force between nanotubes.