Nonmonotonic Friction due to Water Capillary Adhesion and Hydrogen Bonding at Multiasperity Interfaces

Capillary adhesion due to water adsorption from the air can contribute to friction, especially for smooth interfaces in humid environments. We show that for multiasperity (naturally oxidized) Si-on-Si interfaces, the friction coefficient goes through a maximum as a function of relative humidity. An adhesion model based on the boundary element method that takes the roughness of the interfaces into account reproduces this nonmonotonic behavior very well. Remarkably, we find the dry friction to be significantly lower than the lubricated friction with macroscopic amounts of water present. The difference is attributed to the hydrogen-bonding network across the interface. Accordingly, the lubricated friction increases significantly if the water is replaced by heavy water (${\mathrm{D}}_2\mathrm{O}$) with stronger hydrogen bonding.

Figure 1

Experimental setup (a). A silicon ball inside a humidity-controlled chamber is clamped to the geometry of a rheometer which is used to measure normal and frictional forces between the silicon ball and the silicon wafer. The known distance between the rotation axis and the sphere, $r=10\mathrm{mm}$, is used to translate the imposed rotation speed $\omega$ into a sliding speed and to translate the imposed torque into a friction force. AFM images of the wafer (b) and silicon ball (c) are shown. The root-mean-squared roughness of the surfaces was 0.5 nm (wafer) and 40.5 nm (sphere), measured over an area of $\mathrm{31.1331.13}\mathrm{\mu }{\mathrm{m}}^2$. Scale bar, $10\mathrm{\mu }\mathrm{m}$.

Figure 2

Friction as a function of relative humidity (RH) and partial pressure of hexane (a). Measurements were performed with increasing (black squares) and decreasing (red squares) relative humidity to rule out significant hysteresis (more experiments are reported in Fig. S4 [26]). The corresponding simulation result is represented by the solid green circles. The olive triangles in (a) display the evolution of the friction coefficient with the partial pressure of hexane at a sliding velocity of $1\mathrm{\mu }\mathrm{m}/\mathrm{s}$. The hexane gas was introduced into the system after several sliding strokes were performed in the dry environment (leftmost data point). The relative humidity level for all hexane measurements was around 1%. Lines through the data points are drawn to guide the eye. (b) and (c) are two simulated contact maps under 20% RH (b) and 80% RH (c). The red, white, and black regions in the contact map correspond to the contact area, capillary area, and noncontact area without water bridges, respectively. Scale bar: $10\mathrm{\mu }\mathrm{m}$.

Figure 3

Dependence of the friction coefficient on sliding velocity. The red, black, and green data correspond to the friction coefficient measured at increasing (squares) and decreasing (solid circles) velocities ranging from 0.1 to $100\mathrm{\mu }\mathrm{m}/\mathrm{s}$ in the dry case (relative $\text{humidity}=0.6\%$), the water-immersed case, and hexane-immersed case, respectively. The inset displays the change in friction coefficient as a function of time, measured as the ${\mathrm{D}}_2\mathrm{O}$ immersed contact evolves into an ${\mathrm{H}}_2\mathrm{O}$ immersed contact. In the inset, the red and black colored data points (squares) correspond to two independent experiments.