Transition from Stick-Slip to Continuous Sliding in Atomic Friction: Entering a New Regime of Ultralow Friction

A transition from stick-slip to continuous sliding is observed for atomically modulated friction by means of a friction force microscope. When the stick-slip instabilities cease to exist, a new regime of ultralow friction is encountered. The transition is described in the framework of the Tomlinson model using a parameter $\eta$ which relates the strength of the lateral atomic surface potential and the stiffness of the contact under study. Experimentally, this parameter can be tuned by varying the normal load on the contact. We compare our results to a recently discussed concept called superlubricity.

Figure 1

(a)–(c) Measurements of the lateral force acting on the tip sliding forward and backward in (100) direction over the NaCl(001) surface. The lines are typical cross sections through a two-dimensional scan along the strongest force amplitude. The externally applied load was (a) $F_N=4.7\mathrm{nN}$, (b) $F_N=3.3\mathrm{nN}$, and (c) $F_N=-0.47\mathrm{nN}$. (d)–(f) Corresponding numerical results from the Tomlinson model for (d) $\eta =5$, (e) $\eta =3$, and (f) $\eta =1$ . The stiffness was chosen as $k=1\mathrm{N}/\mathrm{m}$ and the lattice constant as $a=0.5\mathrm{nm}$. Note that for values of $\eta \le$ 1 the hysteresis loop enclosed between the forward and the backward scan vanishes; i.e., there is no more dissipation within this model.

Figure 2

(a) Mean lateral force versus normal load. The experimentally determined adhesion has been added to the externally applied load. The data points represent the average over a two-dimensional scan of $3\times 3{\mathrm{nm}}^2$. (b) Numerical evaluation of the mean lateral force as a function of the parameter $\eta$ in the one-dimensional Tomlinson model. Quantitative difference between experimentally and numerically obtained forces can result from the two-dimensional averaging in the case of experimental results. The numerical results have been calculated for lines with maximal corrugation, like those presented in Fig. 1.

Figure 3

(a) Energy corrugation $E_0$, (b) slope $k_{\exp }$ of the lateral force versus distance in the sticking part, (c) parameter $\eta$, and (d) effective lateral stiffness $k$ of the contact, as a function of the normal load $F_N$ acting on the tip.