Control mechanism of friction by dynamic actuation of nanometer-sized contacts

We studied both the mechanism and the condition of dynamic superlubricity actuated in a dynamic way for the atomic contact of a friction force microscope, using dynamical simulation of the Tomlinson model. The superlubricity was achieved by ac modulation of the normal force acting between two contacting bodies at well-defined frequencies corresponding to normal resonances of the combined system [A. Socoliuc et al., Science 313, 207 (2006)]. The time-averaged friction force depends crucially on the modulation amplitude and the superlubricity occurs above the critical amplitude. The effect on the superlubricity of the corrugation amplitude of surface potential, sliding velocity, a damping coefficient, and temperature are clarified. The superlubricity at zero temperature can be induced by transit of the tip via the “turning point,” the top position of the surface potential without elastic deformation, and it is allowed at low-sliding velocities in the underdamped case. The superlubricity at a room temperature can be actuated efficiently with a much smaller critical amplitude than that at zero temperature and it can be achieved at sufficiently low-sliding velocities in both the underdamped and the overdamped cases, assisted by thermally activated hopping of the tip.

Figure 1

The relation between the time-averaged friction force $⟨F⟩$ and the oscillation amplitude $\alpha$ of ac modulation at four sliding velocities $V$, for $\eta =3$ (a), 5 (b), 6 (c), and 7 (d). Here, $\xi =2$, $T=0.016$, $f=0.05$ are assumed.

Figure 2

The relation between the time-averaged friction force $⟨F⟩$ and the oscillation amplitude $\alpha$ of ac modulation at four sliding velocities $V$, for $\xi =0.4$ (a), 2 (b), 4 (c), and 10 (d). Here, $\eta =6$, $T=0.016$, $f=0.05$ are assumed.

Figure 3

The relation between the time-averaged friction force $⟨F⟩$ and the oscillation amplitude $\alpha$ of ac modulation at four sliding velocities $V$, for $\eta =3$ (a), 5 (b), 6 (c), and 7 (d). Here, $\xi =2$, $T=0$, and $f=0.05$ are assumed.

Figure 4

The relation between the time-averaged friction force $⟨F⟩$ and the oscillation amplitude $\alpha$ of ac modulation at four sliding velocities $V$, for $\xi =0.4$ (a), 2 (b), 4 (c), and 10 (d). Here, $\eta =6$, $T=0$, and $f=0.05$ are assumed.

Figure 5

The relation between the tip coordinate $x$ and the support point $R$ in the dynamical simulation at $T=0$, for $\xi =0.4$ (a) and 4 (b). Here, $\eta =6$, $f=0.05$, and $V=0.001$ are assumed. The turning point and the relation of $x=R$ are also plotted.

Figure 6

The relation between the tip coordinate $x$ and the support point $R$ in the dynamical simulation at $T=0$, for $\xi =0.4$ (a) and 4 (b). Here, $\eta =6$, $f=0.05$, and $V=0.01$ are assumed. In (a), the result of $f=0.02$ is also plotted at $\alpha =0.9$ by a dashed line. The turning point and the relation of $x=R$ are also plotted.

Figure 7

The relation between the tip coordinate $x$ and the support point $R$ in the dynamical simulation at $T=0.016$, for (a) $\xi =0.4$ and $\alpha =0$, (b) $\xi =0.4$ and $\alpha =0.6$, (c) $\xi =4$ and $\alpha =0$, (d) $\xi =4$ and $\alpha =0.6$. Here, $\eta =6$, $f=0.05$, and $V=0.0001$ are assumed. The relation of $x=R$ is also plotted.

Figure 8

The relation between the tip coordinate $x$ and the support point $R$ in a range of $1a\le R\le 1.005a$, for (a) $\xi =0.4$ and (b) $\xi =4$. Here, $T=0.016$, $\alpha =0$, $\eta =6$, and $V=0.0001$ are assumed.

Figure 9

The relation of Eq. (8) between the position of the support point $R$ and the tip coordinate $x$, for $U=U_0\left(1\pm \alpha \right)$. Here, $\eta =6$, $\alpha =0$ (thick solid line), $\alpha =0.6$ (medium solid line), and $\alpha =0.9$ (thin solid line) are assumed.