Atomic-Resolution Dynamic Force Microscopy and Spectroscopy of a Single-Walled Carbon Nanotube: Characterization of Interatomic van der Waals Forces

We report atomic-resolution imaging and site-specific quantitative force measurements on a single-walled carbon nanotube by dynamic force microscopy and three-dimensional force field spectroscopy at low temperatures. The topography imaged in the attractive force regime reflects the trigonal arrangement of the hollow sites as maxima. Individual force curves were unambiguously assigned to carbon atoms and hollow sites, respectively. Site-specific quantitative evaluation revealed that the short-range interatomic van der Waals forces are responsible for the atomic-scale contrast.

Figure 1

A three-dimensional view of the atomically-resolved carbon nanotube image acquired under constant frequency shift feedback control in the noncontact regime; $\Delta f=-65.3\mathrm{H}\mathrm{z}$, $A=2.4\mathrm{n}\mathrm{m}$, image size $3\mathrm{n}\mathrm{m}\times 3\mathrm{n}\mathrm{m}$. The atomic-scale features are clearly observed around the elevated topmost area and are still slightly observed on the sloping sides. The maximum corrugation amplitude is about 40 pm.

Figure 2

(a) Constant frequency shift image with atomic-scale features; $\Delta f=-69.6\mathrm{H}\mathrm{z}$, $A=2.3\mathrm{n}\mathrm{m}$, image size $1\mathrm{n}\mathrm{m}\times 1\mathrm{n}\mathrm{m}$. For better visualization of the atomic-scale features, a parabolic curvature has been subtracted from the raw data. (b) Contour plot of the $z$ values recorded at the stabilizing points during capturing the 3D-FFS. Note that the $20\times 20$ data points have been extrapolated to $400\times 400$ image points for better visualization. The individual $\Delta f(z)$ curves acquired at the positions labeled C1, C2, and H are shown in Fig. 3. The slightly distorted corresponding carbon lattice is depicted on the image.

Figure 3

Analysis of individual spectroscopy curves above the specific atomic sites of the hexagonal carbon lattice. (a) $\Delta f(z)$ curves measured above the positions C1, C2, and H in Fig. 2b. The close proximity regime is magnified in the inset. (b) The total interaction forces $F(z)$ (lower curves) have been directly converted from $\Delta f(z)$ curves in (a). The blue line has been fitted to the long-range force data from 3.2 to 1 nm using a $1/z$ force law. The short-range forces $F_{\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}}$ (upper curves) are obtained by subtracting the long-range fit from the total forces. The inset displays the close proximity regime (symbols) together with the corresponding L-J force fits (lines). The starting poins were adjusted for the L-J fittings.