Linear Aging Behavior at Short Timescales in Nanoscale Contacts.

Nanoscale silica-silica contacts were recently found to exhibit logarithmic aging for times ranging from 0.1 to 100 s, consistent with the macroscopic rate and state friction laws and several other aging processes. Nanoscale aging in this system is attributed to progressive formation of interfacial siloxane bonds between surface silanol groups. However, understanding or even data for contact behavior for aging times <0.1 s, before the onset of logarithmic aging, is limited. Using a combination of atomic force microscopy experiments and kinetic Monte Carlo simulations, we find that aging is nearly linear with aging time at short timescales between ∼ 5 and 90 ms. We demonstrate that aging at these timescales requires the existence of a particular range of reaction energy barriers for interfacial bonding. Specifically, linear aging behavior consistent with experiments requires a narrow peak close to the upper bound of this range of barriers. These new insights into the reaction kinetics of interfacial bonding in nanoscale aging advance the development of physically based rate and state friction laws for nanoscale contacts.

Memory Distance for Interfacial Chemical Bond-Induced Friction at the Nanoscale.

Macroscale rate and state friction (RSF) laws include a memory distance, Dc, which is considered to be the distance required for a population of frictional contacts to renew itself via slip, counteracting the effects of aging in slow or static contact. This concept connects static friction and kinetic friction. Here, we use atomic force microscopy to study interfacial chemical bond-induced kinetic friction and the memory distance at the nanoscale for single silica-silica nanocontacts. We observe a logarithmic trend of decreasing friction with sliding velocity (i.e., velocity-weakening) at low velocities and a transition to increasing friction with velocity at higher velocities (i.e., velocity-strengthening). We propose a physically based kinetic model for the nanoscale memory effect, the "activation-passivation loop" model, which accounts for the activation and passivation of chemical reaction sites and the formation of new chemical bonds from dangling bonds during sliding. In the model, we define the memory distance to be the average sliding distance that accrues before an activated reaction site becomes passivated. Results from numerical simulations based on this model match experimental friction data well in the velocity-weakening regime and show that Dc is sensitive to the surface chemistry, and nearly independent of sliding velocity. The simulations also show values of Dc that are consistent with those obtained from the experiments. We propose a semiquantitative physical explanation of the observed logarithmic velocity-weakening behavior based on the conservation of the number of interfacial bonds during sliding. We also extract from the experimental data physically reasonable values of the energy barriers to the activation of reaction sites. Our results provide one possible physical mechanism for the nanoscale memory distance.

Rate and State Friction Relation for Nanoscale Contacts: Thermally Activated Prandtl-Tomlinson Model with Chemical Aging.

Rate and state friction (RSF) laws are widely used empirical relationships that describe macroscale to microscale frictional behavior. They entail a linear combination of the direct effect (the increase of friction with sliding velocity due to the reduced influence of thermal excitations) and the evolution effect (the change in friction with changes in contact "state," such as the real contact area or the degree of interfacial chemical bonds). Recent atomic force microscope (AFM) experiments and simulations found that nanoscale single-asperity amorphous silica-silica contacts exhibit logarithmic aging (increasing friction with time) over several decades of contact time, due to the formation of interfacial chemical bonds. Here we establish a physically based RSF relation for such contacts by combining the thermally activated Prandtl-Tomlinson (PTT) model with an evolution effect based on the physics of chemical aging. This thermally activated Prandtl-Tomlinson model with chemical aging (PTTCA), like the PTT model, uses the loading point velocity for describing the direct effect, not the tip velocity (as in conventional RSF laws). Also, in the PTTCA model, the combination of the evolution and direct effects may be nonlinear. We present AFM data consistent with the PTTCA model whereby in aging tests, for a given hold time, static friction increases with the logarithm of the loading point velocity. Kinetic friction also increases with the logarithm of the loading point velocity at sufficiently high velocities, but at a different increasing rate. The discrepancy between the rates of increase of static and kinetic friction with velocity arises from the fact that appreciable aging during static contact changes the energy landscape. Our approach extends the PTT model, originally used for crystalline substrates, to amorphous materials. It also establishes how conventional RSF laws can be modified for nanoscale single-asperity contacts to provide a physically based friction relation for nanoscale contacts that exhibit chemical bond-induced aging, as well as other aging mechanisms with similar physical characteristics.

Stick-Slip Instabilities for Interfacial Chemical Bond-Induced Friction at the Nanoscale.

Earthquakes are generally caused by unstable stick-slip motion of faults. This stick-slip phenomenon, along with other frictional properties of materials at the macroscale, is well-described by empirical rate and state friction (RSF) laws. Here we study stick-slip behavior for nanoscale single-asperity silica-silica contacts in atomic force microscopy experiments. The stick-slip is quasiperiodic, and both the amplitude and spatial period of stick-slip increase with normal load and decrease with the loading point (i.e., scanning) velocity. The peak force prior to each slip increases with the temporal period logarithmically, and decreases with velocity logarithmically, consistent with stick-slip behavior at the macroscale. However, unlike macroscale behavior, the minimum force after each slip is independent of velocity. The temporal period scales with velocity in a nearly power law fashion with an exponent between -1 and -2, similar to macroscale behavior. With increasing velocity, stick-slip behavior transitions into steady sliding. In the transition regime between stick-slip and smooth sliding, some slip events exhibit only partial force drops. The results are interpreted in the context of interfacial chemical bond formation and rate effects previously identified for nanoscale contacts. These results contribute to a physical picture of interfacial chemical bond-induced stick-slip, and further establish RSF laws at the nanoscale.

Size effects resolve discrepancies in 40 years of work on low-temperature plasticity in olivine.

The strength of olivine at low temperatures and high stresses in Earth's lithospheric mantle exerts a critical control on many geodynamic processes, including lithospheric flexure and the formation of plate boundaries. Unfortunately, laboratory-derived values of the strength of olivine at lithospheric conditions are highly variable and significantly disagree with those inferred from geophysical observations. We demonstrate via nanoindentation that the strength of olivine depends on the length scale of deformation, with experiments on smaller volumes of material exhibiting larger yield stresses. This "size effect" resolves discrepancies among previous measurements of olivine strength using other techniques. It also corroborates the most recent flow law for olivine, which proposes a much weaker lithospheric mantle than previously estimated, thus bringing experimental measurements into closer alignment with geophysical constraints. Further implications include an increased difficulty of activating plasticity in cold, fine-grained shear zones and an impact on the evolution of fault surface roughness due to the size-dependent deformation of nanometer- to micrometer-sized asperities.

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.

Flash heating leads to low frictional strength of crustal rocks at earthquake slip rates.

The sliding resistance of faults during earthquakes is a critical unknown in earthquake physics. The friction coefficient of rocks at slow slip rates in the laboratory ranges from 0.6 to 0.85, consistent with measurements of high stresses in Earth's crust. Here, we demonstrate that at fast, seismic slip rates, an extraordinary reduction in the friction coefficient of crustal silicate rocks results from intense "flash" heating of microscopic asperity contacts and the resulting degradation of their shear strengths. Values of the friction coefficient due to flash heating could explain the lack of an observed heat flow anomaly along some active faults such as the San Andreas Fault. Nearly pure velocity-weakening friction due to flash heating could explain how earthquake ruptures propagate as self-healing slip pulses.

Friction falls towards zero in quartz rock as slip velocity approaches seismic rates.

An important unsolved problem in earthquake mechanics is to determine the resistance to slip on faults in the Earth's crust during earthquakes. Knowledge of coseismic slip resistance is critical for understanding the magnitude of shear-stress reduction and hence the near-fault acceleration that can occur during earthquakes, which affects the amount of damage that earthquakes are capable of causing. In particular, a long-unresolved problem is the apparently low strength of major faults, which may be caused by low coseismic frictional resistance. The frictional properties of rocks at slip velocities up to 3 mm s(-1) and for slip displacements characteristic of large earthquakes have been recently simulated under laboratory conditions. Here we report data on quartz rocks that indicate an extraordinary progressive decrease in frictional resistance with increasing slip velocity above 1 mm s(-1). This reduction extrapolates to zero friction at seismic slip rates of approximately 1 m s(-1), and appears to be due to the formation of a thin layer of silica gel on the fault surface: it may explain the low strength of major faults during earthquakes.