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.

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.

Nano-rheology of hydrogels using direct drive force modulation atomic force microscopy.

We present a magnetic force-based direct drive modulation method to measure local nano-rheological properties of soft materials across a broad frequency range (10 Hz to 2 kHz) using colloid-attached atomic force microscope (AFM) probes in liquid. The direct drive method enables artefact-free measurements over several decades of excitation frequency, and avoids the need to evaluate medium-induced hydrodynamic drag effects. The method was applied to measure the local mechanical properties of polyacrylamide hydrogels. The frequency-dependent storage stiffness, loss stiffness, and loss tangent (tan δ) were quantified for hydrogels having high and low crosslinking densities by measuring the amplitude and the phase response of the cantilever while the colloid was in contact with the hydrogel. The frequency bandwidth was further expanded to lower effective frequencies (0.1 Hz to 10 Hz) by obtaining force-displacement (FD) curves. Slow FD measurements showed a recoverable but highly hysteretic response, with the contact mechanical behaviour dependent on the loading direction: approach curves showed Hertzian behaviour while retraction curves fit the JKR contact mechanics model well into the adhesive regime, after which multiple detachment instabilities occurred. Using small amplitude dynamic modulation to explore faster rates, the load dependence of the storage stiffness transitioned from Hertzian to a dynamic punch-type (constant contact area) model, indicating significant influence of material dissipation coupled with adhesion. Using the appropriate contact model across the full frequency range measured, the storage moduli were found to remain nearly constant until an increase began near ∼100 Hz. The softer gels' storage modulus increased from 7.9 ± 0.4 to 14.5 ± 2.1 kPa (∼85%), and the stiffer gels' storage modulus increased from 16.3 ± 1.1 to 31.7 ± 5.0 kPa (∼95%). This increase at high frequencies may be attributed to a contribution from solvent confinement in the hydrogel (poroelasticity). The storage moduli measured by both macro-rheometry and AFM FD curves were comparable to those measured using the modulation method at their overlapping frequencies (10-25 Hz). In all cases, care was taken to ensure the contact mechanics models were applied within the important limit of small relative deformations. This study thus highlights possible transitions in the probe-material contact mechanical behaviour for soft matter, especially when the applied strain rates and the material relaxation rates become comparable. In particular, at low frequencies, the modulus follows Hertzian contact mechanics, while at high frequencies adhesive contact is well represented by punch-like behaviour. More generally, use of the Hertz model on hydrogels at high loading rates, at high strains, or during the retraction portion of FD curves, leads to significant errors in the calculated moduli.

Atomic force microscopy on plasma membranes from Xenopus laevis oocytes containing human aquaporin 4.

Atomic force microscopy (AFM) is a unique tool for imaging membrane proteins in near-native environment (embedded in a membrane and in buffer solution) at ~1 nm spatial resolution. It has been most successful on membrane proteins reconstituted in 2D crystals and on some specialized and densely packed native membranes. Here, we report on AFM imaging of purified plasma membranes from Xenopus laevis oocytes, a commonly used system for the heterologous expression of membrane proteins. Isoform M23 of human aquaporin 4 (AQP4-M23) was expressed in the X. laevis oocytes following their injection with AQP4-M23 cRNA. AQP4-M23 expression and incorporation in the plasma membrane were confirmed by the changes in oocyte volume in response to applied osmotic gradients. Oocyte plasma membranes were then purified by ultracentrifugation on a discontinuous sucrose gradient, and the presence of AQP4-M23 proteins in the purified membranes was established by Western blotting analysis. Compared with membranes without over-expressed AQP4-M23, the membranes from AQP4-M23 cRNA injected oocytes showed clusters of structures with lateral size of about 10 nm in the AFM topography images, with a tendency to a fourfold symmetry as may be expected for higher-order arrays of AQP4-M23. In addition, but only infrequently, AQP4-M23 tetramers could be resolved in 2D arrays on top of the plasma membrane, in good quantitative agreement with transmission electron microscopy analysis and the current model of AQP4. Our results show the potential and the difficulties of AFM studies on cloned membrane proteins in native eukaryotic membranes.

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.

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.

Template-assisted patterning of nanoscale self-assembled monolayer arrays on surfaces.

We report a general, simple, and inexpensive approach to pattern features of self-assembled monolayers (SAMs) on silicon and gold surfaces using porous anodic alumina films as templates. The SAM patterns, with feature sizes down to 30 nm and densities higher than 10(10)/cm(2), can be prepared over large areas (>5 cm(2)). The feature dimensions can be tuned by controlling the alumina template structure. These SAM patterns have been successfully used as resists for fabricating gold and silicon nanoparticle arrays on substrates by wet-chemical etching. In addition, we show that arrays of gold features can be patterned with 10-nm gaps between the dots.