Friction and Capillary Forces at the Nanometer Scale∗

Frictional behaviors between mica surfaces have been investigated with the Surface Force Apparatus under various relative vapor pressures (rvp) of both water and cyclohexane. Stick-slip frictional behaviors were observed only under cyclohexane vapor. At rvp of 20%, stick-slip appeared but faded out with sliding time. At a rvp greater than 50%, the stick-slip pattern was stable without fading. Dependence of sliding velocity and applied load on stick-slip motions indicated that the mechanism of the stick-slips in the high rvp (stable stick-slip) region differs from that of the region of fading stick-slip. In the rvp range between 20% and 50%, where the fading stick-slip is observed, the condensate liquid seeps into the contact area under the influence of the applied tangential force and thus triggers the slip motion. Due to the small condensation volume, the liquid condensed around the contact area is exhausted in the process of repeating stick-slip. At a rvp greater than 50%, where stable sick-slip is observed, the stick-slip caused by essentially the same origin as that observed with mica surfaces sliding in bulk cyclohexane liquid. In vapor, the stick-slip is enhanced by the increase of the negative Laplace pressure in the capillary condensed liquid, thereby forcing the surfaces toward each other more strongly with decreasing rvp. [DOI: 10.1380/ejssnt.2009.137]


I. INTRODUCTION
Reducing friction forces is important for improving the performance of moving components in devices.In ambient conditions, confined liquids have a great influence on friction forces since an attractive force is induced by capillary condensation and adsorption between the surfaces.For example, adsorbed water films with a thickness of only a few molecules can dramatically influence the wear properties of surfaces.However, there is a lack of research into how (and how much) capillary forces influence frictional behaviors.
We investigated frictional behaviors between molecularly flat mica surfaces under various relative vapor pressures (rvp) of both water and cyclohexane (the saturated vapor pressure of cyclohexane is much higher than that of water) with Surface Forces Apparatus.The dependence of frictional forces on rvp, particularly in the low rvp range, has been studied because the embryo of liquefaction and layering of molecules occurs in these conditions.
The results of the measurements of kinetic shear stress as a function of sliding velocity at different rvp reveal the role of liquid condensed around the contact zone.A mechanism based on capillary condensation is proposed to explain the role of rvp on friction by adsorption of liquid layers on free mica surfaces and at contact.

II. EXPERIMENTAL
Friction Force Measurements.Friction force measurements were carried out with the Surface Force Apparatus (SFA, Mark IV, Australian National University) with the friction attachment (Fig. 1), which has been described in detail previously [1,2].Some measurements on adsorbed film thickness between mica surfaces and the height of capillary condensation were carried out with the SFA Mark π (Ian Wark Research Institute, University of South Australia) [3].Thin mica sheets for interferometry were prepared by cleaving and silvering the back sides of the mica surfaces and then gluing them with sym-diphenylcarbazide (Aldrich Chemical Co.) onto supporting silica disks installed in the usual geometrical configuration of the SFA.The lower surface is mounted horizontally on a double cantilever spring of 250 N/m stiffness.The other end of the spring is connected to a base which can be moved vertically; in this way, the normal load can be controlled, and the pull-off force can be measured.The upper mica surface is attached via another cantilever, a double stainless steel spring of 1000 N/m stiffness, to a horizontal translation stage driven by a motor at a constant speed of 0.2 µm/s except for measurements with a changing sliding velocity.Four strain gauges, each of 350 Ω resistance, are glued to the beams of the friction spring and are electrically connected in the form of a Wheatstone bridge.The bridge is driven by a voltage source at a frequency of 260 Hz, and the out-of-balance voltage is detected with a PAR 5210 lock-in amplifier (EC&G Princeton Applied Research).Any shear force that results from friction between the surfaces gives rise to a bending of the spring attached to the translation stage and thence to an out-of-balance electrical signal from the bridge which is proportional to the force.The horizontal position of the translation stage is measured with an electrical encoder, and the data are recorded as frictional force against stage position.The fringe pattern arising from the interference of white light between the silvered mica surfaces was continuously monitored, with the setup ensuring that the pattern remains stationary (with stickslip motion in some cases) in the field of view while the upper surface moves.In this way, the radius (typically 25 µm) of the contact spot between the surfaces could be measured at any time, and any change or damage to the mica could be identified immediately.The shear stress acting during the sliding was calculated by dividing the measured frictional forces by the measured contact area, using the contact radius observed by interferometry.All measurements, unless particularly described, were carried out on mica surfaces at zero external normal load at a temperature of 25±0.2˚C.
Materials.Cleaved sheets of 2-4 µm thickness Brown muscovite mica (Brown Mica Co., Sydney Australia) were prepared in a laminar flow cabinet (humidity, 30-40%; temperature, 23 (±2˚C) in the standard manner [4] and then stored adhesion-sealed in a desiccator under a vacuum of 10-2 Torr with silica gel.All the mica surfaces were used for measurements within 2 weeks of preparation.The mica surfaces used in a particular series of experiments were cut out of the same cleavage mica sheet.New pairs of mica surfaces were used for measurements at each rvp.
The water was distilled and processed through a Millipore UHQ unit.Cyclohexane (Fluka, analytical grade) was stored to remove trace water, with 4A molecular sieves under dry filtered nitrogen.
Relative Vapor Pressure Control.The humidity in the SFA chamber (rvp of water) was controlled by introducing solutions of known concentrations of LiCl (AJAX Chemicals Ltd., Sydney) or MgCl 2 (J.T. Baker) at the bottom of the chamber.Humidity was monitored with a hygrometer (RS 212-124).Errors in the humidity determination are ±5%.
The relative vapor pressure of cyclohexane in the SFA chamber was changed by vaporizing measured amounts of cyclohexane into the sealed chamber.High rvps of cyclohexane in the SFA chamber were monitored by measuring the condensation height detected with the interference fringes [5], while low rvps were estimated from the introduced amount of cyclohexane.Errors in the rvp determination are (5-10% as confirmed with the interference fringes measurements at higher rvp.The inside of the chamber was dried by purging nitrogen, dried beforehand with calcium hydride (CaH 2 , Fluka AG) and phosphorus pentoxide (P 2 O 5 , Aldrich).

III. RESULTS AND DISCUSSIONS
The dependence of the dynamic shear stress on the rvp of water and cyclohexane is shown in Fig. 2. As the shear stress in sliding decreases as the rvp increases under either vapor, it is suggested that both water and cyclohexane molecules adsorbed on the mica surfaces effectively work as a lubricant.Both in water and cyclohexane vapor with a rvp below 5%, the mica surfaces did not slide, and they were scratched after the static shear stress reached around 100 MPa.At 5% and up to 20% rvp, the surfaces slid continuously with a shear stress decreasing in increase of rvp.At rvp of 20% and higher, stick-slip frictional patterns were observed only in cyclohexane vapor.Figure 3 shows typical shear stress-displacement curves for mica surfaces in cyclohexane vapor at rvp of 30% and 60%.The fading stick-slip region, a transitional state from the continuous, wearfree sliding to full stick-slip, occurs in the region of 20% < rvp < 50% (Fig. 3(a)).It appears that the shear stress in this region decreases linearly with increasing rvp.The stick-slip pattern stabilizes at a rvp higher than 50% (Fig. 3(b)).Although the shear stress also decreases with increasing rvp in the higher rvp conditions, the stable stick-slips never disappeared even in saturated vapor.The shear stress under saturated conditions is of the same magnitude as the reported values of shear stress of mica surfaces separated by 5-6 cyclohexane molecular layers [6].
Dependence of sliding velocity on stick-slip motion in cyclohexane vapor is shown in Fig. 4. Up to a rvp of 20%, the dependence of shear stress on sliding velocity showed the same tendency as that observed in water vapor [1].The surfaces slid with a constant shear stress at speeds of 0.2-1.0µm/s, while the surfaces were damaged by sliding at a velocity greater than 1 µm/s.Since the amount of cyclohexane between the sliding surfaces decreases with increasing sliding velocity, the surfaces cannot retain enough cyclohexane to lubricate the surfaces at high sliding velocities, resulting in the damage of mica surfaces due to direct contact (same as that observed in dry conditions).
In the fading stick-slip region, the number of times of http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) e-Journal of Surface Science and Nanotechnology stick-slip motion was gradually decreased with increasing sliding velocity, and the surfaces started sliding without stick-slip eventually (Fig. 4(a)).The shear stress started increasing when the stick-slips disappeared.Once the stick-slips disappeared, the stick-slip motion did not reappear with decreasing sliding velocity.
In the stable stick-slip region, the shear stress and stickslip amplitude were not changed by increasing the sliding velocity up to the certain point.Figure 4(b) shows that stick-slip patterns suddenly disappeared at sliding velocities greater than 1.2 µm/s.The transition velocity from the stick-slip sliding to the continuous sliding did not depend on the rvp.The stick-slip reappeared when the sliding velocity was decreased to <1 µm/s.The same effect of the sliding velocity on the stick-slip motion was reported on the friction of a two-layer film of octamethylcyclotetrasiloxane (OMCTS) between mica surfaces [7].It was also reported that the amplitude of stick-slip motion of a five-layer of cyclohexane between mica surfaces decreases with increasing sliding velocity, but the decrease of the stick-slip amplitude at speeds higher than 1 µm/s is much smaller than that at speeds lower than 1 µm/s [6].Our observation of the dependence of stick-slip motion on sliding velocity shows similar behavior to that observed in bulk liquid.
The deferent dependency of sliding velocity between the fading stick-slip region and the stable stick-slip region implies that the stick-slip motion in the two regions is caused by different mechanisms.Figure 5 shows the dependence of applied load on stickslip motion at rvps of 30% and 85%.At a rvp of 30% (Fig. 5(a)), the stick-slip motion disappeared with increasing applied load while the shear stress remained the same (24±1 MPa).In contrast, at a rvp of 85% (Fig. 5(b)), the stick-slip motion was amplified with increasing applied load.The increase of slip length (2.3, 7.0, 13.4 µm at 0, 33, 120mN of applied load) was proportional to the increase of contact area (contact radius 30, 51, 75 µm).By applying a load of up to 120 mN, a visible increase of the shear stress from 2 to 3.6 MPa was observed.
It appears that the meniscus around the contact area has considerable influence on the fading stick-slip motion.If the surface slip is limited to the meniscus width, the surface slip inside the meniscus is terminated at the boundary of the meniscus.Consequently, the slip length should equal approximately the meniscus width as long as the meniscus width is smaller than the maximum mechanical slip length defined by the ratio of the yield force to the spring constant.The calculated menisci widths for a sphere-on-a-flat surface at a rvp of 60±10% (at the boundary between the fading and stable stick-slip regions) are approximately 10 µm (contact radius 25 µm).In Fig. 3, the observed shear stress is about 10 MPa at a rvp of 60±10%, and the stick-slip peak amplitudes are 7.5-10µm.The observed stick-slip peak amplitudes suggest that the liquid condensed around the contact penetrates into the contact area given that the stress intensity is relieved by interfacial microslip [8].The entire meniscus liquid in this condition would spread over the area of contact with the volume of the liquid condensate.
The stable stick-slip motion appeared to be dominantly influenced by another mechanism rather than the influence of the meniscus around the contact area.It may be the process of shear-induced melting and freezing of molecular thin films [9,10] or energy dissipation at the molecular layer interface [11,12], as has been suggested in explaining the observed friction between mica surfaces in bulk cyclohexane liquid [6,7].The contact surrounded by a liquid condensate is similar to the surface contact in the bulk liquid.However, the hydrostatic pressure in the condensate is lower than that in the bulk liquid by the value of the Laplace pressure [13], and the pressure difference increases with decreasing rvp.
Under conditions when the contact radius a ≪ meniscus width l ≪ surface radius R, the capillary force close to the value of 6.07 mN (=4πRγ, γ=24.16mN/m at 25 • C,  R=2cm) acts as an extra external force applied to the surfaces contacted in the bulk liquid.Generally, for a meniscus of principal radii r 1 and r 2 (Fig. 6), the capillary force, F , is [14] For a small wetting meniscus r 2 ≫ r 1 ≈ h/2, the Laplace pressure P = γ(r −1 1 + r −1 2 ) ≈ 2γ/h.For a point contact, the capillary force is constant, independent of the meniscus size.However, for a truncated sphere the capillary force changes by changing the meniscus size.The capillary force can be estimated using Eq. ( 1) with the parameters taken from the interference fringe images observed at each condition (Fig. 6).
We have compared the influence of capillary pressure and the externally applied pressure on the shear stress.From Fig. 5(b), we have estimated the total pressure (capillary pressure + externally applied pressure) applied on the contact area and plotted it against the shear stress (Fig. 7).The points of shear stress against externally applied pressure (filled tilted squares) appear to be on the same line of a linear function as the relation between shear stress and capillary pressure (open circles).This result demonstrates that the capillary pressure acts as the applied load to the sliding surfaces.

IV. CONCLUSIONS
The relationship between the capillary force and the shear stress has revealed that the capillary force acts as a load applied to the contact area.From the fading stickslip region to the beginning of the stable stick-slip region, the meniscus size around the contact area contributes the slip length.In the stable stick-slip region, the shear stress and stick-slip amplitude decrease to the level observed under equivalent loads in bulk liquid experiments on approaching saturation since the capillary force acting as a load decreases.

FIG. 1 :
FIG.1: Schematic diagram of the surface force apparatus with the friction attachment.The lower silica disk is held on a double cantilever spring.The translation stage is driven in a horizontal direction at constant speed.If a tangential frictional force is present, the two thin leaf springs deflect and the strain gauges that are glued to them change their resistance, giving rise to an electrical signal proportional to the friction force.

FIG. 6 :
FIG. 6: Interference fringes showing the meniscus and the schematic cross section of the surface.The fringe image (rotate 90 • ) shows a capillary condensate with height h ≈40 nm, contact radius a ≈25µm, meniscus width l ≈25µm, and r2 ≈50µm.

FIG. 7 :
FIG. 7: Relationship between shear stress and applied pressure.The capillary pressures (open circles) were calculated from the data in Fig. 2. The externally applied pressures (filled tilted squares) were estimated by adding the externally applied pressure to the capillary pressure at 85% rvp based on data in Fig. 5(b).