Figure 1

Measurements of the lateral force between a tungsten tip with a graphite nanoflake attached [3, 4, 5] and a highly oriented, pyrolytic graphite substrate. Results were obtained with high-resolution FFM [28] at a scan speed of $30\mathrm{nm}/\mathrm{s}$ under a constant positive normal force of 24.3 nN. (a) Friction force (average lateral force) as function of time (scan line number); the arrows indicate the locations of the three individual friction loops in (b)–(d); (b) scan line 1 (green arrow); (c) scan line 45 (red arrow); (d) scan line 195 (blue arrow). One scan line equals to 6 nm (3 nm forward and backward) or 0.2 s. The distance between subsequent scan lines equals 0.024 nm.Reuse & Permissions

Figure 2

The 150-atom symmetric graphite flake on the graphite surface. (a) Schematic view of the system. (b) Time-averaged friction force as a function of the misfit angle $\varphi$ for nonrotating flakes of different sizes. (c),(d) Frictional force in the direction of pulling and the misfit angle as functions of the support displacement, $X$, for the rotating flake. Dash-dotted lines indicate a few instances where the flake enters or leaves commensurate orientations. (e),(f). 2D maps for the potential and torque experienced by the flake as functions of $\varphi$ and the flake displacement in the pulling direction, $L_{\parallel }.f$. Distribution function for the misfit angle $\varphi$ calculated for hundred trajectories, one of which is shown in Figs. 2c, 2d. Parameter values: $F_K=K{\lambda }_1$, $N{U}_0/(F_K{\lambda }_1)=2.5$, $\gamma V/F_K=0.33$, $\Gamma V/(F_K{\lambda }_1^2)=0.13$, $F_0/(F_K{\lambda }_1)=1.25$. Under the experimental conditions, where $K=1.8\mathrm{N}/\mathrm{m}$, ${\lambda }_1=0.246\mathrm{nm}$, $V=30\mathrm{nm}/\mathrm{s}$, we have $F_K=0.44\mathrm{nN}$, $N{V}_0=0.34\mathrm{eV}$, $\gamma =4.8\times {10}^{-3}\mathrm{kg}/\mathrm{s}$, $\Gamma =1.2\times {10}^{-4}\mathrm{kg}{\mathrm{nm}}^2/\mathrm{s}$, $F_0=0.14\mathrm{nN}\mathrm{nm}$. Note that the typical magnitudes of the friction forces obtained in simulations are in agreement with the experimental data presented in Fig. 1. Both experiments and calculations have been performed under overdamped conditions.Reuse & Permissions

Figure 3

An asymmetric graphite flake on a surface of square symmetry. (a)–(d) Schematic view of four configurations corresponding to the most commensurate states of the flake. (e) Frictional force in the direction of pulling as a function of the support displacement, $X$, for the rotating flake. (f) Distribution function for the misfit angle $\varphi$ calculated for hundred trajectories, one of which is shown in Fig. 3e. Parameter values as in Fig. 2, and the period of the surface lattice $\lambda ={\lambda }_1$.Reuse & Permissions