Load and Time Dependence of Interfacial Chemical Bond-Induced Friction at the Nanoscale

Rate and state friction (RSF) laws are widely used empirical relationships that describe the macroscale frictional behavior of a broad range of materials, including rocks found in the seismogenic zone of Earth’s crust. A fundamental aspect of the RSF laws is frictional “aging,” where friction increases with the time of stationary contact due to asperity creep and/or interfacial strengthening. Recent atomic force microscope (AFM) experiments and simulations found that nanoscale silica contacts exhibit aging due to the progressive formation of interfacial chemical bonds. The role of normal load (and, thus, normal stress) on this interfacial chemical bond-induced (ICBI) friction is predicted to be significant but has not been examined experimentally. Here, we show using AFM that, for nanoscale ICBI friction of silica-silica interfaces, aging (the difference between the maximum static friction and the kinetic friction) increases approximately linearly with the product of the normal load and the log of the hold time. This behavior is attributed to the approximately linear dependence of the contact area on the load in the positive load regime before significant wear occurs, as inferred from sliding friction measurements. This implies that the average pressure, and thus the average bond formation rate, is load independent within the accessible load range. We also consider a more accurate nonlinear model for the contact area, from which we extract the activation volume and the average stress-free energy barrier to the aging process. Our work provides an approach for studying the load and time dependence of contact aging at the nanoscale and further establishes RSF laws for nanoscale asperity contacts.

Figure 1

Effect of the hold time and applied normal load on static aging. Relative humidity $(\mathrm{RH})=53\%$, temperature $T=24°\mathrm{C}$, and the loading point velocity is $500\mathrm{nm}/\mathrm{s}$. (a) Friction drop vs log of the hold time for different normal loads. The inset shows the lateral force vs lateral displacement curve from the test for 100 s hold time and 23 nN applied load and indicates how we measure the friction drop. The linearity of friction drop vs log of the hold time is seen for all normal loads. (b) The slope of each linear fit in (a) vs the load. The slope varies linearly with the load. (c) Friction drop vs load for different hold times. For a given hold time, the friction drop increases linearly with the load. (d) The slope of the linear fits from (c) vs the log of the hold time. The slope increases linearly with the log of the hold time. Loads and hold times are varied randomly to exclude systematic errors.

Figure 2

Fitting of the friction drop vs load. The data points correspond to a hold time of 0.1 s in Fig. 1. The fitting is according to Eq. (3). It can be extracted from the fitting that $G_0=(1.06\pm 0.21)\mathrm{eV}$ and $V_0=(78\pm 28){\AA }^3$.

Figure 3

Kinetic friction vs normal load. The silica substrate was cleaned with a piranha solution before the experiment. The load is systematically varied from 0 to 325 nN.