Controlling Macroscopic Friction through Interfacial Siloxane Bonding

Controlling macroscopic friction is crucial for numerous natural and industrial applications, ranging from forecasting earthquakes to miniaturizing semiconductor devices, but predicting and manipulating friction phenomena remains a challenge due to the unknown relationship between nanoscale and macroscopic friction. Here, we show experimentally that dry friction at multiasperity Si-on-Si interfaces is dominated by the formation of interfacial siloxane ($\mathrm{Si}─\mathrm{O}─\mathrm{Si}$) bonds, the density of which can be precisely regulated by exposing plasma-cleaned silicon surfaces to dry nitrogen. Our results show how the bond density can be used to quantitatively understand and control the macroscopic friction. Our findings establish a unique connection between the molecular scale at which adhesion occurs, and the friction coefficient that is the key macroscopic parameter for industrial and natural tribology challenges.

Figure 1

Experimental system (a) and enhanced friction upon plasma cleaning of silicon surfaces (b). (a) Top: a 3-mm-diameter silicon ball inside a humidity-controlled chamber is clamped to the geometry of a rheometer and brought into contact with a silicon wafer. The distance ($r$) between the rotation axis and the silicon ball is 10 mm. By lowering and rotating the rheometer tool at a constant angular velocity ($\omega$), the normal force ($F_n$) and friction force ($F_f$) on the contact can be measured simultaneously at an imposed sliding speed ($\omega r$) . Bottom: AFM images of the silicon ball (bottom left) and silicon wafer (bottom right). The rms roughness of the surfaces is 40.5 nm (ball) and 0.5 nm (wafer), measured over an area of $31.13\times 31.13\mathrm{\mu }{\mathrm{m}}^2$, corresponding to the average roughness (Ra) of 26 and 0.6 nm, respectively. The small changes in surface roughness induced by the plasma treatment are reported in Fig. S3. Scale bar, $10\mathrm{\mu }\mathrm{m}$. (b) Friction force ($F_f$) as a function of normal load ($F_n$), measured in the dry nitrogen environment ($\mathrm{RH}=0.8\%$). The ratio of these two forces gives the coefficient of friction (CoF), $\mu =F_f/F_n$. The red and black data correspond to the friction force measured with pristine and with oxygen plasma-cleaned silicon surfaces, respectively. Insets display water contact angle ($\theta$) images on wafer surfaces in the dry nitrogen environment ($\mathrm{RH}=0.8\%$) before (bottom) and after (top) plasma cleaning, in which the average measured $\theta$ are 32° and 5°, respectively. All the reported water contact angles represent the average of three measurements.

Figure 2

Friction force as a function of the time during which the surfaces were in contact with dry nitrogen ($<0.8\%$ relative humidity). Friction measurements were performed on the plasma-cleaned silicon surfaces at a normal load of 40 mN after different nitrogen drying times (see also Fig. S1). The water contact angles corresponding to the nitrogen drying times are indicated by the red data points.

Figure 3

Modeling and measurement of the surface OH density. The surface OH density (red data) is calculated using the Cassie-Baxter model (black solid line) and the measured water contact angles. The OH density was also measured through fluorescence labeling (dark yellow circles). The upper right inset shows the linear relationship between the measured fluorescence intensity and the modeled OH density.

Figure 4

Frictional shear stress as a function of the interfacial siloxane density. The slope of the solid line represents the bond rupture force of a single interfacial $\mathrm{Si}─\mathrm{O}─\mathrm{Si}$ bond. The black area in the upper circular inset displays the area of real contact calculated using the boundary element method at a load of 40 mN. Scale bar, $10\mathrm{\mu }\mathrm{m}$.

Figure 5

Dependence of the frictional shear stress on sliding velocity. The friction force was measured at increasing (squares) and decreasing (solid circles) velocities ranging from 0.1 to $10\mathrm{\mu }\mathrm{m}/\mathrm{s}$ at a load of 40 mN. The frictional shear stress is defined as the measured friction force divided by the calculated area of real contact. The surfaces were plasma-cleaned silicon surfaces after drying for 1 h at a relative humidity of 0.8% (black data symbols), after drying for 6 h (dark yellow), and with a monolayer of hydrophobic CVD coating (red, see main text for details), respectively. The nonbonding frictional shear stress (0.4 GPa) observed at the hydrophobically coated interfaces is small compared to the bonding-induced shear stress (3 GPa) and therefore only has a minor impact on our bonding analysis. The inset displays the water contact angle ($\theta$) image on the hydrophobically coated wafer, in which the measured $\theta$ is around 114°.