Nonmonotonic Velocity Dependence of Atomic Friction

We propose a theoretical model for friction force microscopy experiments with special emphasis on the realistic description of dissipation and inertia effects. Its main prediction is a nonmonotonic dependence of the friction force upon the sliding velocity of the atomic force microscope tip relative to an atomically flat surface. The region around the force maximum can be approximately described by a universal scaling law and should be observable under experimentally realistic conditions.

Figure 1

Schematic illustration of a friction force microscopy experiment [18].

Figure 2

The average lateral force (1) versus sliding velocity $v$ for the model (3, 4) with $L=0.52\mathrm{n}\mathrm{m}$, $E_0=2.5\times {10}^{-19}\mathrm{J}$, $\kappa =1.2\mathrm{N}/\mathrm{m}$, $\eta ={10}^{-5}\mathrm{k}\mathrm{g}/\mathrm{s}$, $T=293°\mathrm{K}$. Stars: numerical simulations for $m=3\times {10}^{-12}\mathrm{k}\mathrm{g}$ and $\vartheta =0$. Lines: numerical solutions of the Fokker-Planck equation [15] equivalent to (3) for $m=0$ and (from above) $\vartheta =0$, 0.25, 0.5, 0.75, 1. The numerical uncertainty is comparable to the symbol size and linewidth, respectively.

Figure 3

The average lateral force (1) versus sliding velocity $v$ for different values of $\kappa$ in the overdamped limit $m\to 0$. Lower bold line: same as solid line for $\vartheta =1$ in Fig. 2. Dotted line: same but for the $\kappa$ values (from below) $2.4\mathrm{N}/\mathrm{m}$, $0.6\mathrm{N}/\mathrm{m}$, and $0.3\mathrm{N}/\mathrm{m}$. Upper bold line: analytical $\kappa \to 0$ asymptotics (6). Dashed line: analytical approximation (8). Dash-dotted line: analytical approximation (10), valid for $R:=(f_c-f)/{\mu }^{1/3}(kT{)}^{2/3}\gg 1$ (see main text). Plotted is the regime $R>2.5$ (i.e., $v<10\mu \mathrm{m}/\mathrm{s}$).