Temperature Dependence of Atomic-Scale Stick-Slip Friction

We report experiments of atomic stick-slip friction on graphite as an explicit function of surface temperature between 100 and 300 K under ultrahigh vacuum conditions. A statistical analysis of the individual stick-slip events as a function of the velocity reveals an agreement with the thermally activated Prandtl-Tomlinson model at all temperatures. Taking into account an explicit temperature-dependence of the attempt frequency all data points collapse onto one single master curve.

Figure 1

(a) Atomic stick-slip friction in the thermally activated Prandtl-Tomlinson model can be explained with a mechanical model. An atom attached via a spring to a moving top surface is sliding over the potential energy landscape of the bottom surface (dashed line). (b) If the tip is scanned over the sample surface the spring elongates till its force is large enough to overcome the potential and the tip jumps into the next minimum. Thermal energy induces premature jumps, reducing the average slip-inducing lateral force. (c) Simulation of the stick-slip movement of the tip for different temperatures using the thermally activated PT model [13]. For $T=0\mathrm{K}$ the force $F_c=1.55\mathrm{nN}$ is needed to overcome the potential barrier. With increasing temperature, however, the tip jumps earlier and the lateral forces reduce. The assumed scan velocity of $125\mathrm{nm}/\mathrm{s}$ corresponds to the experimental one in Fig. 3; all other parameters also correspond to the experimental ones described in the text.

Figure 2

Friction force experiments on HOPG showed atomic resolution from (a) 109 K up to (b) 295 K. These two lateral force maps have a size of $3\times 3{\mathrm{nm}}^2$ and were acquired at a sliding velocity of $v=125\mathrm{nm}/\mathrm{s}$. (c) Schematic of the underlying structure of the graphite layer. The spheres indicate the single carbon atoms, arranged in a honeycomb pattern, in which the shaded areas, assigned with $H$, denote the hollow sites. (d) The adhesion (or snap-off) force (closed symbols) and the effective lateral contact stiffness (open symbols) reveal no systematic trend with temperature.

Figure 3

Experimental atomic friction loops for different temperatures reveal the stick-slip movement in forward- (solid lines) and backward-direction (dashed lines), acquired at increasing temperatures: (a) 109, (b) 155, and (c) 295 K, respectively. The scan-velocity was $v=125\mathrm{nm}/\mathrm{s}$. The signals are offset and tilt corrected by an average over the whole friction-loop. The dashed lines indicate a force value of 1 nN for a better comparison between the graphs. The black arrows in (a) indicate the slip-inducing forces ${\tilde{F}}_{\mathrm{l}}^{\exp }$, which were numerically determined for all jumps in the data sets.

Figure 4

(a) The measured slip-inducing forces are plotted by symbols as a function of sliding velocity for different temperatures. The dashed lines represent lines represent a fit to the data using Eq. (1) with $f_0$ fixed to 24 MHz for all temperatures. As described in the text the data fits much better if the temperature dependence is explicitly considered (solid lines). (b) The master curve based on all data sets. Plotting all experimental data in this way all measurements collapse into one linear curve. The inset shows a plot of the attempt rate $\ln \mathbf{(}{f}_0(T)\mathbf{)}$ which is the only parameter varied in the fits shown by solid lines in (a).