How square ice helps lubrication

In the context of friction we use atomistic molecular-dynamics simulations to investigate water confined between graphene sheets over a wide range of pressures. We find that thermal equilibration of the confined water is hindered at high pressures. We demonstrate that, under the right conditions, square ice can form in an asperity, and that it is similar to cubic ice VII and ice X. We simulate sliding of atomically flat graphite on the square ice and find extremely low friction due to structural superlubricity. The conditions needed for square ice to form correspond to low sliding speeds, and we suggest that the ice observed in experiments of friction on wet graphite is of this type.

Figure 1

A sketch of our simulation box. Carbon atoms are shown in gray, oxygen in blue, and hydrogen in white. The topmost and bottommost graphene sheets are rigid. The topmost sheet is attached with a spring to a support that moves at constant velocity during sliding runs.

Figure 2

The oxygens in the bottom layer of the water (filled symbols) together with the carbons in the top layer of the bottom graphene slab (open symbols) for three different cases: icelike obtained by slowly reducing the temperature at high pressure (temperature-scan, top), liquidlike obtained by rapidly increasing the FIG. 2. (Continued) pressure at constant temperature (load-scan, middle), and liquidlike at lower pressure (bottom). At low loads the system equilibrates more easily. Icelike structures appear at sufficiently high pressures, after careful equilibration, as expected from the phase diagram of bulk water. In these simulations $N_{\mathrm{O}}/N_{\mathrm{C}}=1.33$ and the loads were (ramped up to) 1.0 nN/atom for (a) and (b), and 0.1 nN/atom for (c).

Figure 3

Oxygen-oxygen radial distribution functions obtained from the temperature-scan method (a) and from the load-scan method (b). The temperature-scan method results in more icelike structures with rather well-defined peaks in the RDF while the load-scan method results in significantly more disordered, liquidlike environments. In both these simulations $N_{\mathrm{O}}/N_{\mathrm{C}}=1.33$.

Figure 4

Thickness-pressure plot of the average local structure index (LSI), $\overline{q}4$, and $\overline{q}6$. For comparison, 1 nN/atom of load corresponds to a pressure of 38 GPa.

Figure 5

Force traces for identical parameters (boundary layer thickness, sliding velocity, etc.) but different initial conditions, liquidlike (a) and ice VII-like (b). Due to the incommensurate lattice parameters of ice VII and graphite, there is in this case superlubric sliding. The liquidlike water rearranges in a configuration that is strongly commensurate with the graphite and thus has higher friction. The stick-slip period is consistent with the graphite substrate. In these simulations $N_{\mathrm{O}}/N_{\mathrm{C}}=1.33$ and the load was (ramped up to) 0.5 nN/atom. The average lateral forces were $0.29\pm 0.02$ pN/atom for the liquidlike water and $0.027\pm 0.007$ pN/atom for the ice VII-like water. The errors were estimated using block averaging. The plotted forces were averaged over short intervals of 5 ps to eliminate thermal fluctuations.