Speed Dependence of Atomic Stick-Slip Friction in Optimally Matched Experiments and Molecular Dynamics Simulations

The atomic stick-slip behavior of a Pt tip sliding on a Au(111) surface is studied with atomic force microscopy (AFM) experiments and accelerated (i.e., reduced sliding speed) molecular dynamics (MD) simulations. The MD and AFM conditions are controlled to match, as closely as possible, the geometry and orientation, load, temperature, and compliance. We observe clear stick-slip without any damage. Comparison of both MD and AFM results with the thermally activated Prandtl-Tomlinson model shows that MD results at the highest speeds are not in the thermally activated regime. At lower speeds, within the thermally activated regime, AFM and MD provide consistent energetics, but attempt frequencies differ by orders of magnitude. Because this discrepancy lies in attempt frequencies and not energetics, atomistic details in MD simulations can be reliably used in interpreting AFM data if the MD speeds are slow enough.

Figure 1

(a) Schematic of the AFM experiment, and a $100\times 100{\mathrm{nm}}^2$ topographic AFM image of the Au(111) surface showing large terraces separated by monatomic steps. Inset above: TEM image of the Pt-coated probe. Scale bar is 20 nm. (b) Snapshot of the atomistic tip-substrate model. (c) Lateral force image on Au(111) at 0.6 nN load with a speed of $149\mathrm{nm}/\mathrm{s}$. Inset: Fourier low-pass filtered image. (d) Top view of the simulated Au(111) substrate. White arrows in (c),(d) denote the fast scanning direction. Scale bars are 1 nm. (e),(f) Variation of the experimental (e) and simulated (f) lateral force along the black horizontal line shown in (c) and (d), respectively. The simulation results in (f) are obtained for a relative surface orientation of 30° and a contact area of $7.32{\mathrm{nm}}^2$ (91 atoms) under same normal load as in (c), and sliding speed $1\mathrm{m}/\mathrm{s}$.

Figure 2

(a) Peak friction vs contact area in the simulations for different relative orientations. In all cases, friction increases with contact area. (b) Mean friction force as a function of tip-substrate orientation for a load of 0.6 nN with a tip apex 91 atoms in size.

Figure 3

Mean friction measured experimentally in two different runs (black squares, black circles) for speeds between 1 and $1000\mathrm{nm}/\mathrm{s}$, and predicted via accelerated MD (blue stars) for speeds between $0.005\mathrm{m}/\mathrm{s}$ to $2\mathrm{m}/\mathrm{s}$. The black dashed curve and blue dash-dotted curve are fittings with the PTT model [6, 7] for experimental and simulation data, respectively. The fit to the MD data uses $F_c=0.85\mathrm{nN}$ as obtained from molecular statics, and is only fit to data at speeds below $0.1\mathrm{m}/\mathrm{s}$; higher speeds cannot be fit to the curve due to athermal dissipative contributions to friction.