Origin of Friction in Superlubric Graphite Contacts

More than thirty years ago, it was theoretically predicted that friction for incommensurate contacts between atomically smooth, infinite, crystalline materials (e.g., graphite, ${\mathrm{MoS}}_2$) is vanishing in the low speed limit, and this corresponding state was called structural superlubricity (SSL). However, experimental validation of this prediction has met challenges, since real contacts always have a finite size, and the overall friction arises not only from the atoms located within the contact area, but also from those at the contact edges which can contribute a finite amount of friction even when the incommensurate area does not. Here, we report, using a novel method, the decoupling of these contributions for the first time. The results obtained from nanoscale to microscale incommensurate contacts of graphite under ambient conditions verify that the average frictional contribution of an inner atom is no more than ${10}^{-4}$ that of an atom at the edge. Correspondingly, the total friction force is dominated by friction between the contact edges for contacts up to $10\mu \mathrm{m}$ in lateral size. We discuss the physical mechanisms of friction observed in SSL contacts, and provide guidelines for the rational design of large-scale SSL contacts.

Figure 1

Schematic setup and typical friction force vs displacement curve. (a) An AFM cantilever tip shears a graphite mesa due to slip at a preexisting twist boundary (the red dotted interface) away from its original position by a distance $x$, and then slides the mesa forward and backward around $x$ by a small displacement amplitude $\mathrm{\Delta }x$. (b) A typical measured friction force vs displacement relation (triangles), showing a linear dependence on $x$ (dashed line shows a linear fit). Results are repeatable for stepwise increasing (solid triangles) and decreasing (open triangles) values of $x$. Inset: The friction force is calculated as the area enclosed in the friction loop (in the dashed rectangle) divided by the distance traveled.

Figure 2

(a) Friction force as function of $x$ measured for 7 runs with 6 different mesas having the same size $L=5.7\mu \mathrm{m}$ and $B=3.5\mu \mathrm{m}$. Data are well fit linearly (dashed lines). Notably, certain mesas (e.g., mesa 1 and mesa 4) show nearly constant friction, indicating that the friction in the contact area and along the parallel edges is unmeasurable. (b) $f(L)$ extracted from the linear fits of the friction force vs $x$, which were measured for mesas of four different sizes, as a function of the mesa width $B$ [including all the data from (a), where $B=3.5\mu \mathrm{m}$]. Each data point represents a friction vs $x$ measurement on one mesa. A linear fit of $f(L)$ with respect to $B$ (red line) yields an average value of $⟨f_{\perp }⟩=0.53\pm 0.07\mathrm{pN}/\mathrm{atom}$. (c) The slope $-df/dx$ obtained from the linear fit of the friction force vs $x$, which were measured for mesas of four different sizes, as a function of the mesa width, $B$. The linear fit of $-df/dx$ as a function of $B$ (dashed line) yields an average slope of $⟨f_A⟩=-0.02\pm 0.02\mathrm{fN}/\mathrm{atom}$ and the intercept of the fit at $B=0$ gives $⟨f_{\parallel }⟩=0.81\pm 0.15\mathrm{pN}/\mathrm{atom}$. These results show that the average friction contribution of atoms located in the contact area $⟨f_A⟩$ is at least four orders of magnitude smaller than the average contribution of edge atoms $⟨f_{\perp }⟩$ and $⟨f_{\parallel }⟩$.

Figure 3

Dependence of friction force on the contact size $D$ for square graphite mesas with side length ranging from 800 nm to $10\mu \mathrm{m}$. Our results and those from literature [4, 15, 25, 26] are presented. The gray line shows the fit of Eq. (4), yielding $f_A=-0.02\pm 0.01\mathrm{fN}/\mathrm{atom}$, $\xi f_E=0.73\pm 0.04\mathrm{pN}/\mathrm{atom}$. (A portion of this figure is adapted from [27, 28] ].)

Figure 4

(a) AFM height image of the interface of the exposed surface of the bottom section of a graphite mesa, showing steps and bumps buried under the smooth topmost graphene layer. The section shows the height profile at the position indicated by the blue line, as well as the corresponding friction profile. (b) SEM image shows that nanoscale corrugations are found at the mesa edge.