Tuning Diffusion and Friction in Microscopic Contacts By Mechanical Excitations

We demonstrate that lateral vibrations of a substrate can dramatically increase surface diffusivity and mobility and reduce friction at the nanoscale. Dilatancy is shown to play an essential role in the dynamics of a nanometer-size tip which interacts with a vibrating surface. We find an abrupt dilatancy transition from the state with a small tip-surface separation to the state with a large separation as the vibration frequency increases. Atomic force microscopy experiments are suggested which can test the predicted effects.

Figure 1

Frequency dependence of the relative diffusion coefficient (top panel, $F_x\equiv 0$), the time-averaged tip velocity (middle panel, $F_x=F_{\mathrm{dc}}=0.01F_0$) and the friction force [bottom panel, $F_x=K_x(vt-x)$] calculated for a fixed tip-surface separation (solid curves) and including the normal motion (dashed curves); (a) $A=1$ and (b) $A=2$. Parameter values: $\lambda /b=1$, $\sigma =1$, ${\eta }_{x,z}/M{\omega }_0=3.2$, $k_{B}T/U_0=0.01$, $K_x{b}^2/(4{\pi }^2{U}_0\sigma )=3.2\times {10}^{-3}$, $K_z{\lambda }^2/U_0=0.63$, $F_{\mathrm{dc}}/F_0=0.01$, $v/V_0=0.16$, where $F_0=2\pi U_0/b$ and $V_0={\omega }_{0}b$.

Figure 2

Frequency dependence of the rmsd of the tip. Solid curve—numerical simulations, dashed curve—calculation according to the equation $\Delta L(\Omega )=\sqrt{D(\Omega ){\eta }_x/K_x}$. Parameter values: $A=1$, $K_x{b}^2/[(2\pi {)}^2{U}_0\sigma ]=3.2\times {10}^{-4}$, $K_z\to \infty$, other parameters as in Fig. 1.

Figure 3

Frequency dependence of the time-averaged tip-surface separation; solid curve—$A=1$, dashed curve—$A=2$. Parameters’ values as in Fig. 1.

Figure 4

Time dependencies of the relative friction force, $F_x/F_0$, the tip-surface separation, $z/b$, and the lateral displacement of the tip, $x/b$ calculated for $A=1$ and three frequencies: $\Omega =0.26$ (a), 0.29 (b), and 0.32 (c). Parameters value as in Fig. 1.