The Effects of Humidity on the Velocity-Dependence and Frictional Ageing of Nanoscale Silica Contacts

Rate-and-state friction (RSF), like Coulomb and Amontonian friction, consists of a set of empirical laws describing the frictional response of materials [1]. While RSF behavior was discovered and described much later than the other friction laws, it has been found to apply to a broad range of materials [2], from rocks to paper to hydrogels. Within the RSF framework, friction can be described by an equation of the formwhere \(\mu\) is the friction coefficient, \(\mu_{0}\) is the steady-state friction coefficient at a reference velocity \(V_{0}\), V is the current sliding velocity, \(D_{c}\) is the so-called “memory distance” which is the characteristic sliding distance over which transients empirically evolve [3, 4], \(a\) and \(b\) are empirical constants, and \(\theta\) is a state variable which has units of time. Note: for consistency with the RSF literature (“velocity-weakening” etc.), we use the term velocity throughout, but in all cases we are referring to the magnitude of the velocity, i.e., the speed. The second term on the righthand side of Eq. 1 is referred to as the direct effect, since it describes how friction changes in direct response to a change in sliding velocity (for example, friction increases (decreases) abruptly with a step increase (decrease) in sliding velocity); the third term is the evolution effect, so-named because the state variable \(\theta\) in this term evolves over time (or with slip) with a change in sliding velocity. This term also describes static ageing, a characteristic phenomenon in RSF where the magnitude of static friction grows with time due to a time-dependent growth in the magnitude of \(\theta\).

A basic prediction of this law is that during steady-state sliding, \(\mu\) varies linearly with the logarithm of velocity with a slope of \(a - b\). Additionally, the frictional response is invariably mediated via the elastic coupling between the application point of a lateral stress and the sliding interface (e.g., torsion of the atomic force microscope (AFM) cantilever in this study) which can give rise to complex overall behaviors such as stick–slip motion [5‐7]; note that this type of stick–slip is not due to the position-dependent potential energy corrugation that leads to atomic lattice stick–slip motion [8], but rather, is due to an increase in static friction with time in stationary contact (static ageing) [6], and/or a decrease in kinetic friction with slip speed (evolution effect) [5].

A hallmark of RSF is the history dependence of friction, which is described analytically with a state variable. The evolution of state with time is typically described by either of two equations, the slowness law and the slip law. The slowness law, attributed to Dietrich, is given by Ref. [9]:and the slip law, attributed to Rice and Ruina, is given by Ref. [7]

The slowness law differs fundamentally from the slip law in that it allows the state to increase with the time of stationary contact during a hold, whereas the slip law requires slip to increase the state [1].

The physical basis of these and other laws describing RSF behavior is still debated [10‐13], particularly with regard to the physical meaning of state, with multiple mechanisms having different degrees of empirical and theoretical support. Given the complexity of real macroscale and geoscale contacts it is likely that multiple mechanisms contribute [14, 15]. The canonical view in the rock physics community is that the state variable represents the real area of contact at a frictional interface, which increases with the time of stationary contact due to plastic creep of asperities, with a number of macroscale studies demonstrating it’s existence [16, 17]. This mechanism leads to rate-and-state response in other material systems such as polymers [10, 11, 18‐20].

Another proposed mechanism for RSF is one that emerges from the rheology of granular packings [12]. Such an interfacial geometry is ubiquitous in the particulate gouge found at geological faults. The primary prediction is that the coefficient of friction is determined by a dimensionless “inertial number” that depends upon the shear rate and the confining pressure [12]. Despite the absence of time-dependent friction (i.e., RSF response) between contacting grains in the simulations, the authors were able to reproduce many features of the RSF response including time-dependent static strengthening attributed to stronger inter-particle coupling with slow compaction [12]. To date, however, such simulations have not been able to reproduce velocity-weakening friction, which is commonly observed in rock friction experiments and considered to be a necessary condition for earthquake nucleation [5, 7].

The evolution of state may also be due to increases in the frictional strength (i.e., in the shear strength) of the contacts, instead of increases in contact area as described above. In particular, silica-silica interfaces are known to form bonds, including covalent siloxane (Si–O–Si) bonds [21, 22]. At the nanoscale, this has been shown to result in a corresponding increase in static friction [21, 23‐26]. This is referred to as interfacial chemical bond-induced (ICBI) friction at the nanoscale. In the case of nanoscale silica-silica contacts, ICBI has been shown to be due to the formation of strong siloxane bonds between hydrated silica surfaces. Our earlier work employed AFM to examine this phenomenon for nanoscale silica contacts wherein plastic deformation and creep of the contacts were negligible [21, 23‐26]. The frictional strength of these contacts increases with the logarithm of the hold time, consistent with the slowness law, and complementary simulations demonstrate how this logarithmic rate of chemical bonding arises from a combination of a distribution of activation barriers to bonding and an antagonistic interaction effect between bonding at neighboring sites [23]. Since then, we and others have shown how the slowness law can be derived from the ICBI mechanism [24, 27], demonstrated how this mechanism can lead to stick–slip friction, another hallmark of RSF [25], and examined how this nanoscale phenomenon can manifest in more complex macroscale contacts [28, 29]. Finally, it was also shown that ICBI mechanism can in fact lead to increase not only of the shear strength, but also of the real contact area, both contributing to the logarithmic increase of static friction with time [30].

An important aspect of the RSF response is the role of water, especially in the case of interfacial chemical bonding. The presence of ambient water is known to control the density of thermodynamically favored hydroxyl terminated sites on the surface of silica, as well as other geologically relevant minerals [31‐33]. Hydroxyl groups participate directly in the interfacial bonding reactions responsible for ICBI [21, 23, 34]. Empirically, it is known that humidity has a strong effect on the frictional behavior of rocks, and is necessary for the evolution of state [35, 36]. Trends in the frictional response of materials with changing humidity are not universal, and depend on the specific material system, interface morphology, and testing protocol. For macroscale experiments, steady-state friction has been found to either decrease [35, 37‐39] or remain static [36, 38] with increasing humidity. Additionally, increasing humidity often leads to enhancements in static ageing [21, 35, 36] and unstable sliding [35, 36], as characterized by velocity-weakening or the observation of stick–slip. Intriguingly, macroscale experiments on quartz rocks [35] at RH < 1% and quartz powders [36] at RH < 5% show an absence of state evolution in slide-hold-slide experiments. These results were attributed to a humidity dependence of the mechanical creep of quartz. However, some of the present authors recently showed using nanoindentation that a quartz sample does not show any humidity-dependent mechanical creep up to 50% RH [40]. This demonstrates that the humidity dependence of the frictional ageing of quartz cannot be explained by asperity creep, and instead indicates that other humidity-dependent mechanisms, including time-dependent chemical bond formation or slip-induced strengthening, are at play.

Theoretical examination of the relevant chemistry between SiO₂ interfaces has revealed that water can play an important role. First principles molecular dynamics (FPMD) calculations which were based on density functional theory (DFT) and therefore captured electronic interactions, were utilized to study the role of water during wear of sliding quartz slabs by Ootani et al. [34] This study showed that the activation energy for interfacial bonding is reduced by 72% when water molecules participate in the reaction, as shown in Fig. 1, adapted from Ootani et al. [34] In these simulations, nearby water molecules facilitated the reaction by functioning as proton receptors, forming H₃O⁺ and leaving a reactive SiO⁻ ion termination at the silica surface, which subsequently could form an interfacial covalent bond. The scheme in the lower panel of Fig. 1 is one example of such a water-facilitated reaction, but the water-mediated proton transfer was a common feature in the formation of all interfacial bonds observed in the aforementioned simulations. The much lower activation energy for interfacial bond formation when water was present to act as a proton acceptor suggests that water allows for much more rapid interfacial bonding kinetics. The same H₂O proton acceptor mechanism for the formation of interfacial Si–O–Si bonds was found to be operative in another study using classical MD with the ReaxFF force field [41], and in the Si₃N₄ and SiC material systems [42]. Experimental studies of nanoscale wear in silica systems have found accelerated wear with increasing humidity, which is consistent with an increased rate of interfacial bonding due to elevated humidity [43, 44].

We have previously demonstrated that the interfacial chemical bonding mechanism can provide a physical basis for friction behavior that follows the slowness law in nanoscale silica-silica contacts [15, 21, 23‐26, 28, 29], just as mechanical creep did before it. Further investigations of this mechanism are warranted. In particular, the influence of humidity on interfacial bonding and the resulting RSF effects in nanoscale silica-silica contacts, the subjects of this study, have not been established. We are further motivated by the fact that a nanoscale system remains the best way experimentally to test whether RSF behavior can occur in the absence of significant plastic deformation and granular dynamics effects (as opposed to larger length scales where these effects, and others, typically are present), i.e., to show that chemical bonding alone can lead to RSF-like behavior.

All experiments were performed in an RHK350 AFM mounted in a vacuum chamber (RHK Technologies, Troy, MI), but with pressures ranging from 1 atm to 0.09 mbar. In experiments at atmospheric pressure, humidity was controlled by mixing clean, dry N₂ gas from the boiloff of a liquid nitrogen Dewar with moist N₂ gas that had been directed through a deionized water-filled bubbler. Relative humidity was monitored via a hygrometer (FisherBrand traceable hygrometer/thermometer/dew point meter, Fisher Scientific, Pittsburgh, PA) with its probe located inside the vacuum chamber. In the experiments under vacuum, the chamber was exposed to ambient air conditions overnight then sealed and pumped with a scroll pump until the desired pressure was achieved. The pump was deenergized and the chamber isolated prior to the AFM measurements. For the slide-hold-slide experiments under reduced pressure, the pressure was progressively lowered while measuring the ageing response at particular pressures; a final test was performed again after venting to atmospheric pressure to confirm the ageing response did not change significantly during the testing due to tip wear or sample reactivity changes.

All experiments were performed with commercial Si AFM probes (PPP-FM, Nanosensors, Neuchatel, Switzerland) and polished Si wafer samples (El-Cat, Ridgefield Park, NJ) which were both subjected to annealing in a quartz tube furnace at 1000°C for 20 min in ambient air, 30–50% RH, to grow an oxide coating with a thickness > 20 nm, confirmed with post-annealing TEM imaging of the AFM probes. Dedicated quartz tubes were used for all annealing runs to ensure no contaminants from the furnace annealing of other samples was present. The probes and samples remained in the furnace during heatup and cooldown. This temperature led to little blunting of the probes with post-annealing tip radii of 15–25 nm based on blind tip reconstruction and TEM imaging (see SI), whereas we found empirically that similar annealing times at 1100°C led to final tip radii larger than 100 nm. Prior to each experiment, the silica sample was cleaned via O₂ plasma for 5 min, both to remove hydrocarbon contamination and maximize the density of hydroxyl group terminations on the silica surface [45]. We note that the wafers are phosphorous-doped at a level of 1 × 10¹⁵ cm⁻³ because they are produced for semiconductor applications; at this doping level a concentration of only 1 P dopant per 1 × 10⁶ nm² is expected even before the surface is oxidized. Thus, the dopants play no role in the experimental behavior. The AFM probes were calibrated for normal forces using the Sader method [46], and for lateral forces using the diamagnetic lateral force calibration technique [47].

Slide-hold-slide experiments were performed by laterally translating the probes in a reciprocating path on the substrate across a 500-nm track at 50 nm/s and zero applied load (maintained using the AFM’s normal force feedback control). Zero applied load was used to ensure contact pressures remained well below the hardness value of the silica counterfaces, as confirmed in a prior study with similarly prepared probes and substrates [21]. Kinetic friction values were stable at steady-state, without any evidence of a stick–slip response that would necessitate stability analysis [48]. Holds were performed by stopping the lateral translation at the center of the track for the specified hold time, then continuing in the same direction at 50 nm/s. Values for the friction drop, from peak static friction after the holds to lower friction when sliding begins, were measured from the lateral force vs. lateral translation data, as demonstrated in the inset of Fig. 2a. The friction drop is a common measure used to quantify the ageing magnitude [21, 23]. Hereafter, the ageing response will be referred to as “ageing response ΔF”. Each reported average value and standard deviation were calculated from at least 8 slide-hold-slide cycles. The order in which holds of different times were performed was randomized to prevent the possibility of a systematically changing tip geometry and thereby affecting the results. The lack of such a sequence-dependence in the slide-hold-slide ageing response also provides further reassurance that plastic creep of the asperity could be effectively excluded as a physical mechanism for ageing in these experiments. Adhesion was also periodically measured via the maximal adhesion force during force-distance curves where the probe approached the surface at a rate of 100 nm/s up to a maximum load of ~ 20 nN, then retracted at the same rate.

Using blind tip reconstruction [49] before and after experiments, the wear rates of the AFM probes in the SiO₂ system were found to be excessive at intermediate humidity levels. For context, a probe with an initial radius of 63 nm was slid for 32 µm at zero applied load at 10% RH during conventional speed-dependence testing and experienced 4 nm of vertical wear resulting in a punch shape with a 50 nm diameter. To give a sense of how little sliding this is, a single 100 × 100 nm² image with 256 lines experiences 51 µm of sliding; a well-functioning AFM tip should be able to acquire many such images without appreciable wear [43]. This led to difficulty in extracting repeatable trends for the velocity-dependence of friction across multiple humidity levels when measured in the typical way of performing contact mode imaging at each sliding velocity.

To deal with this difficulty, a new protocol was developed which involved continuously varying the sliding velocity across the entire velocity range in a single scan line. This technique and the associated analysis are detailed in the Supplemental Information. To ensure that the track length was long enough to maintain steady-state conditions at all velocities (i.e., negligible transient history effects on kinetic friction due to RSF behavior), the protocol was performed on 1 and 2-μm long tracks, and equivalent results were obtained for the two track lengths. All velocity-dependent friction results reported from this are the average values and standard deviations obtained from at least three sliding cycles. The only exception is where individual cycles are reported to demonstrate a repeatable evolution effect across the test. This protocol minimized the amount of sliding required to capture each velocity-dependence curve and therefore minimized cumulative tip wear, allowing for repeatable results across a succession of humidity levels. This also allowed for a high density of data in each curve (e.g., the 1013 mbar trace in Fig. 2b), which is composed of 50 data points, each of which is an average across a 40 nm track length and a small range of velocity). For the load-dependent kinetic friction tests discussed later, the load was progressively increased to the maximum load while measuring the speed-dependence of kinetic friction at select loads, and then lowered progressively back to zero applied load while repeating the kinetic friction tests at the same loads to confirm a similar response was achieved.

Figure 2a shows the trends in ageing response ΔF from slide-hold-slide measurements under varying total pressure of ambient air for hold times of 0.1, 1, 10, and 100 s, with a partial pressure of water corresponding to 16 ± 2% RH at ambient pressure (1013 mbar). In this nanoscale silica system, the ageing response ΔF increases approximately linearly with the logarithm of the hold time for hold times between 1 and 100 s. The increasing slope of the curves in Fig. 2a with increasing total pressure can be attributed to an increase in the availability of water to participate in the interfacial bonding reaction (other constituents of the ambient environment such as nitrogen and argon are not expected to participate). The decline of static ageing on timescales above several seconds in highly inert, UHV environments has been reported in other AFM studies [50, 51].

Figure 2b shows velocity-dependence of the kinetic friction at the two extremes of pressure in Fig. 2a, across sliding velocities from 10 nm/s to 10 μm/s. The overall shapes of the curves are similar to what has been seen in macroscale rock friction experiments [1], with a near-linear dependence on the logarithm of the sliding velocity (V). At the lowest total pressure (1 mbar), we observed mildly velocity-strengthening behavior, whereas at the highest total pressure (1013 mbar) we observe a strong velocity-weakening trend. The observed change in the velocity-dependence can again be attributed to the availability of water molecules to participate in the interfacial bonding reaction. At low pressure, water is unavailable, so interfacial bonding is largely precluded. This in turn results in low overall friction and a velocity-dependence of friction that is dominated by the direct effect in the framework of RSF. Specifically, the increase of kinetic friction with log V in a non-bonding nanoscale system is well understood to be due to thermally activated jumps between adjacent energy minima in the potential energy landscape, with thermal activation becoming less effective with increasing load-point velocity [52, 53]. In contrast, at the highest total pressure, water is readily available to participate in interfacial bonding, which results in higher overall friction due to the presence of many interfacial bonds. The velocity-weakening behavior can be rationalized in simple fashion under the assumption of a constant bond formation rate for these short-lived contact sites [54]: each possible bonding site on the tip traverses more of the sample surface in an unbonded state at higher sliding velocities, thereby lowering the average friction with increasing sliding velocity. The approximately linear dependence on the logarithm of velocity is typical of RSF behavior [27].

To access higher humidity levels, similar experiments were performed at varying % RH at ambient pressure in N₂. The ageing and velocity-dependent behavior show non-monotonicity at these higher humidity levels. Figure 3a shows the ageing response ΔF for 1–60 ± 2% RH. The arrows are added to emphasize the non-monotonicity. At the lowest humidity, the ageing response ΔF is weak, consistent with data shown in Fig. 2a. For humidities in the range 10–40 ± 2% RH, the ageing response ΔF is approximately constant, and at 60 ± 2% RH the ageing response ΔF is again subdued. The inset of Fig. 3a shows the trend in adhesion across the same humidity range. The adhesion varies substantially across this range. This variation can be attributed primarily to capillary formation between the tip and the sample and is consistent with previous literature [55‐57]. The non-monotonic change in adhesion with %RH is typical in the literature [58, 59], and has often been attributed to the formation of a load-bearing ice-like water layer at the sample surface which causes a reduction of adhesion at high humidity. This phenomenon can also rationalize the friction and ageing seen in Fig. 3. Separation of the two silica surfaces by an ice-like layer would prevent the formation of interfacial chemical bonds. This prevents ageing (Fig. 3a) and chemical bonding during sliding (Fig. 3b), which leaves only a velocity-strengthening Prandtl-Tomlinson type friction response.

Figure 3b shows the velocity-dependence of kinetic friction. Similar to the trend shown in Fig. 3a, the trend in kinetic friction is also nonmonotonic with humidity (as indicated by the arrows). At 1 ± 2% RH, friction is relatively low and independent of velocity. When the humidity increased to 10 ± 2% RH, the overall friction became high and strongly velocity-weakening across the entire velocity range, which extends to 100 μm/s. As the % RH is raised further, the overall friction decreased and velocity-weakening became less and less pronounced until velocity-strengthening (and low friction) was observed again at 60 ± 2% RH. It should be noted at this point that while these qualitative trends were easily reproducible, the % RH corresponding to the maximum friction and to the regime of velocity-weakening could vary from 5 to 20% RH between experiments [21, 60, 61]. This variation can be attributed to the difficulty of maintaining a perfectly reproducible SiO₂ surface chemistry and thus sample reactivity. After plasma cleaning, the surface hydroxyl density decreases substantially on the timescale of hours due to adsorption of hydrocarbon molecules present in ambient air, which reduces the density of hydroxyl sites available for interfacial bonding [45, 62].

To better understand the transition from velocity-strengthening to velocity-weakening friction at low % RH, velocity-dependence testing was performed at a succession of closely spaced humidity levels. The results are shown in Fig. 4. At each humidity level there is a transition velocity where the trend switches from velocity-weakening to velocity-strengthening. This effect has been observed in other studies [63, 64] but is inconsistent with the most common forms of the RSF laws [5, 65, 66]. Such a transition velocity could have important effects in earthquake mechanics, such as promoting stable slip and limiting the magnitude of slip events [5, 63, 67, 68]. As the humidity level rises, this transition velocity shifts to higher and higher values, as highlighted by the black dashed arrow. The velocity-dependence testing protocol (see SI for more details) involved traversing the entire velocity range during each sliding cycle, with eight cycles performed sequentially in a reciprocating fashion on the same, initially unworn wear track. The test at 1 ± 2% RH, unlike the data shown for the other humidities where data from all cycles were averaged, is subdivided into averages of cycles 1 and 2, 3 and 4, and 5 through 8. The data were subdivided in this way because we typically observed an evolution of the friction at this % RH during the test, with friction decreasing at the lowest sliding velocities during the test. This effect was not observed at higher humidities. Another example of the cycle dependence at low % RH is shown in the SI. We hypothesize that as the test proceeds, adsorbed water molecules are progressively removed from the wear track, leading to a reduced inventory of water that can participate in interfacial chemical bonding.

We hypothesized that the shift to lower, velocity-strengthening kinetic friction and a weaker ageing response at high % RH (e.g., 60% RH in Fig. 3a, b) was due to a water layer that separates the counterfaces and precludes interfacial bonding; such a trend was recently found in AFM measurements on highly oriented pyrolytic graphite samples [69] and an ice-like layer is expected to form on hydrophilic silica [58]. If this hypothesis is valid, there must be some normal pressure that displaces this water and reimposes velocity-weakening friction. A simple test of this would be to measure the velocity-dependence at a succession of increasing normal loads, where the reappearance of velocity-weakening behavior would indicate that interfacial bonds are again forming between the counterfaces. An example of such a test, performed at 60 ± 2% RH, is shown in Fig. 5. At zero applied load, friction is velocity-strengthening, but as the applied load is increased, the behavior becomes velocity-weakening, consistent with a mechanism of interfacial water preventing covalent bond formation between the counterfaces. Our results are consistent with a previous experimental result obtained for a silica-silica interface immersed in an ionic liquid (IL) [70], where the authors observed that the velocity-weakening trend is obtained only at a relatively high contact pressure range (> 1.1 GPa). This phenomenon was attributed to the expulsion of the confined IL film from the contact, which exposes the surface silanol groups and facilitates the formation of interfacial siloxane bonds. Blind tip reconstruction [49] of the tip after this high-load testing revealed a blunted but still hemispherical geometry (see SI). From this final geometry, the DMT model [71] was used to estimate the nominal contact pressure at each load, the highest and lowest of which are annotated in Fig. 5. These contact pressures are likely underestimated, however, since while the tip apex geometry was approximately spherical, we show next that friction vs. load scaling is linear, which implies that the contact involves multiple asperities. The finding that it requires > 1 GPa of contact pressure to reimpose velocity-weakening friction shows that the water layer between the counterfaces possesses a substantial load-bearing capacity. Similar load-dependencies have been observed previously [72].

We also considered stress enhancement of the interfacial bonding rate as an explanation for the transition from velocity-strengthening to velocity-weakening friction in Fig. 5. If such an effect was significant, at low contact pressures where interfacial bonding is slow, velocity-weakening friction would be observed as a consequence of dominant Prandtl-Tomlinson friction, but at higher contact pressures interfacial bonding would be dominant, leading to a velocity-weakening response. This is what we see in Fig. 5. To examine this possibility, we can use the insights from the load-dependence of friction on load. If the rate of bonding was sensitive to the contact stress in the relevant load range, one would expect a supralinear scaling of friction vs. load. This is because more bonds would form within each unit of real contact area, thereby increasing friction. An earlier study examined the load-dependence of friction in the same material system and found a linear scaling of friction with load [24], suggesting that there is a constant interfacial shear strength with increasing contact pressure [20]. We confirmed the linear scaling of friction with load from Ref. [24] in the current study. Figure 6a shows friction vs. load curves in two different environments. The first environment is 10%RH air. Unlike the results of Fig. 5, velocity-weakening is observed at all normal loads, suggesting the interfacial bonding has a dominant effect on the friction response. The second environment is a reduced pressure of 1 mbar. We expect, based on our results thus far, that interfacial bonding is greatly reduced in this low humidity environment, so Prandtl–Tomlinson velocity-strengthening dominates the friction magnitude and any effect of stress enhancement should be minimal. Similar to Fig. 2b at the same chamber pressure, velocity-strengthening is experimentally observed in Fig. 6a. The data in Fig. 6a is used to generate the friction vs. load curves shown in Fig. 6b. For each environment, we show data corresponding to three different sliding speeds. In all cases, reasonably good linear fits confirm approximately linear friction scaling with load. This suggests that any stress enhancement of interfacial bonding does not have a large effect in the load range of the study.

The variation of friction response with relative humidity on hydrophilic surfaces like the plasma-cleaned SiO₂ examined here has had a substantial history of study. In many cases [58, 96, 102, 103], the response has been attributed to the dynamics of capillary formation and motion, rather than the interfacial bonding mechanism proposed here and in earlier work. In Chen et al. [96], for instance, a similar trend of velocity-weakening friction with increasing humidity in an SiO₂–SiO₂ contact is observed. This is attributed to the influence of a capillary whose inferred size varies with the sliding speed. Szoszkiewicz and Riedo [102] reach similar conclusions in the context of a multi-asperity context, but in that case the speed-dependence was attributed to the number of capillaries formed at nanoasperities within the nominal contact area. Such nanocapillaries are assumed to be immobile and break after some small translation of the contact; hence new capillaries must be formed continuously, leading to a speed-dependent steady-state population. Empirical measurements of the size behavior of capillaries via adhesion reach different conclusions, however. In Cassin et al. [104], an AFM tip hovering over an SiO₂ sample surface could detect the formation of a capillary via a change in normal force on the tip. It was found that, indeed, capillary formation was a thermally activated Arrhenius process, but that after the size of the capillary grew from the initial nucleation volume to the equilibrium volume, this volume remained constant for all speeds below 100 um/s. It also showed that, once formed, the capillaries were persistent and could translate with the tip. Noel et al.[105], by measuring the pulloff force of an AFM probe while sliding, found a maximum speed of at least 10 um/s before capillary size (or in the multi-asperity picture, the nanocapillary population) began to vary. At higher speeds, Noel et al. attributed the size variation to an activation barrier for capillary growth, rather than nucleation as Chen et al. concluded, which was influenced by local surface inhomogeneities in chemistry and morphology. Inhomogeneities that raise this local activation barrier were expected to be encountered more frequently at higher sliding speeds. Since our results show strong velocity-weakening at speeds as slow as 3 nm/s, variation in capillary size cannot explain the velocity-weakening. Additionally, the load-dependent friction in Fig. 5 shows a change from velocity-strengthening to velocity-weakening with increasing load. In the context of the capillary explanations, the capillary size dependence on the load should be small and velocity-weakening should be observed at all loads. Our ageing trends in Figs. 2a and 3a cannot be due to capillary growth since in Cassin et al. it was found this process was complete within 10 ms, much faster than ageing times as long as 100 s used in this study. Nucleation times were similarly short in Cassin et al.’s study.

Additionally, a different study with heated AFM probes in similar nanoscale SiO₂–SiO₂ contacts observed strong velocity-weakening even at high temperatures that preclude the presence of a capillary meniscus [61].

In Chen et al. [96], they also observe a monotonic increase in kinetic friction with increasing %RH while the present study shows non-monotonic friction. This can be rationalized by noting that Chen et al., among other differences, performed their experiments at a higher average contact pressure of 1 GPa than the present study with zero applied load and an average contact pressure at high %RH in the range of 700 MPa (although there is uncertainty in this value given the apparent multi-asperity friction-load scaling discussed earlier). Therefore, it is possible the local pressures were sufficient in Chen et al. to displace the ice-like water layer and eliminate the non-monoticity in friction vs. %RH seen in the current study.

We have shown that amorphous SiO₂–SiO₂ contacts can exhibit a prototypical RSF response in ageing as well as velocity-dependent kinetic friction. This response is modulated profoundly by the environmental humidity level. At the lowest humidities, ageing was nearly non-existent and the velocity-dependence was velocity-strengthening, which we attribute to a lack of interfacial bonding. At intermediate humidities, ageing was significant, and the velocity-dependence was velocity-weakening across the entire velocity range examined. Both of these effects are attributed to water-assisted interfacial chemical bonding across the interface. At the highest humidities, the amount of ageing was again reduced, and the velocity-dependence became velocity-strengthening again. This was attributed to a water layer separating the two counterfaces, which was supported by experiments showing that increasing the applied normal load could squeeze water out of the contact and reimpose a velocity-weakening regime.

Multi-bond simulations were performed to test scientific hypotheses regarding physical phenomena responsible for the friction trends observed in our experiments. Simulations incorporated humidity-dependent activation barriers for interfacial chemical bonds and an intrinsic surface energy corrugation. These simulations reproduced the general trends in humidity- and velocity-dependent friction observed in the experiments. These trends include the non-monotonic humidity dependence of kinetic friction at a given sliding velocity, and the transition from velocity-strengthening to velocity-weakening friction, and then back to velocity-strengthening friction, as humidity increases. The experimental agreement supports the validity of hypotheses that underly the physics of these simulations, namely (1) the catalytic effect of water molecules on interfacial chemical bonding reactions, and (2) a lubrication effect from a thick interfacial water layer at high humidities that prevents interfacial chemical reactions and reduces intrinsic non-bonding friction.

Our results demonstrate the importance of water to the friction response at the asperity level in the silica-silica system, and as such are relevant to understanding the tribological response of systems ranging from earthquake faults to microelectromechanical systems.