Rate and State Friction Laws for Interfacial Chemical Bond-Induced Friction at the Nanoscale

Rate and state friction (RSF) laws are widely-used empirical relationships that describe macroscale frictional behavior of a broad range of materials, including rocks. Conventional RSF laws entail a linear combination of the direct effect (friction increasing with sliding velocity) and evolution effect (evolution of the state of the contact). One manifestation of evolution effect is ageing , where static friction increases logarithmically with contact time. In order to understand the physical origins of RSF laws, we use atomic force microscope (AFM) to study nanoscale friction of silica, which is one important component of rocks. Overall, we observe RSF behavior, due to interfacial chemical bond-induced (ICBI) friction, which is manifested in several ways. The first aspect is the load and time dependence of ageing, whereby ageing magnitude increases approximately linearly with the product of the normal load and the log of the hold time. The second aspect is a physically-based RSF law we establish for single asperity contact, which we call the Prandtl-Tomlinson with temperature and evolution effect (PTTE) model. In PTTE model, the velocity for the direct effect is loading point velocity rather than tip velocity. Also, the combination of direct effect and evolution effect is nonlinear. The third aspect is the velocity dependence of kinetic friction, which reflects the competition of direct effect and evolution effect. Kinetic friction first decreases and then increases logarithmically with sliding velocity (the increase corroborates PTTE model). We explain the logarithmic decreasing by assuming that during low-velocity sliding, after an interfacial bond breaks, the resulting dangling bond can easily bond with other dangling bonds on the opposing surface. The fourth aspect is stick-slip, which could be better understood with PTTE model. We observe quasi-periodic stick-slip at lower velocities and uncover the velocity dependence of stick-slip. We also observe partial dropping of lateral force in some slip events in the transition regime between quasi-periodic stick-slip and smooth sliding, which corroborates the physical picture of dangling bonds forming interfacial bonds. In conclusion, these four aspects together demonstrate the nature of RSF behavior for nanoscale single-asperity contacts, and establish new, physically-based frictional laws for nanoscale contacts