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Effect of Capillary Condensation on Friction Force and Adhesion Adam A. Feiler,†,§ Johanna Stiernstedt,† Katarina Theander,† Paul Jenkins,‡ and Mark W. Rutland*,† Department of Chemistry, Surface Chemistry, Royal Institute of Technology and Institute for Surface Chemistry, Stockholm, Sweden, and UnileVer Research, Port Sunlight, Wirral, UK ReceiVed February 16, 2006. In Final Form: September 15, 2006 Friction force measurements have been conducted with a colloid probe on mica and silica (both hydrophilic and hydrophobized) after long (24 h) exposure to high-humidity air. Adhesion and friction measurements have also been performed on cellulose substrates. The long exposure to high humidity led to a large hysteresis between loading and unloading in the friction measurements with separation occurring at large negative applied loads. The large hysteresis in the friction-load relationship is attributed to a contact area hysteresis of the capillary condensate which built up during loading and did not evaporate during the unloading regime. The magnitude of the friction force varied dramatically between substrates and was lowest on the mica substrate and highest on the hydrophilic silica substrate, with the hydrophobized silica and cellulose being intermediate. The adhesion due to capillary forces on cellulose was small compared to that on the other substrates, due to the greater roughness of these surfaces.
Introduction The behaviors of powders or biofiber networks, for example, paper, cotton, and wool, are crucially dependent upon the friction and adhesion interactions between individual fibers or particles. The influence of capillary condensation is determining for the performance of such materials since they can often be exposed to a large humidity range, and thus an understanding of the dependence of friction and adhesion on capillary condensation in such systems is of immense commercial interest. From a fundamental point of view, most of these questions remain unanswered even for model surfaces. While paper strength can readily be measured macroscopically on test sheets, the effect of capillary condensation on the interactions between individual cellulosic contacts is more challenging, due to the fact that fibers have complicated morphologies and change their material properties in the presence of water. Complementary measurements on model substrates with well-defined surface chemistry and roughness give us an insight into the specific roles of these surface properties on the tribology in the presence of water condensates. The dissipative mechanisms behind interfacial friction remain to a large extent unexplained. Attempts have been made to relate measured frictional behavior to adhesion hysteresis,1-3 adhesion,4 and polar contributions5 to the surface energy. Such studies are complicated by surface roughness effects and by humidity effects which in general are not accounted for. In a related6 article, we showed a relative humidity dependence on adhesion and friction forces between silica surfaces consistent with the idea of an interaction mediated by water, the extent of which depended * Author to whom correspondence should be addressed. E-mail:
[email protected]. † Royal Institute of Technology and Institute for Surface Chemistry. ‡ Unilever Research. § Current address: Centre for Surface Biotechnology, Uppsala Biomedical Centre (BMC), Uppsala, Sweden. (1) Israelachvili, J.; Chen, Y. L.; Yoshizawa, H. J. Adhes. Sci. Technol. 1994, 8, 1231-1249. (2) Homola, A.; Israelachvili, J. N.; McGuiggan, P. M.; Gee, M. L. Wear 1990, 136, 65-83. (3) Yoshizawa, H.; Chen, Y. L.; Israelachvili, J. N. Wear 1993, 168. (4) Bhushan, B. Nanotribology and its Applications; Kluwer: Dordrecht, 1997. (5) Bogdanovic, G.; Tiberg, F.; Rutland, M. W. Langmuir 2001, 17, 59115916. (6) Feiler, A.; Jenkins, P.; Rutland, M. W. J. Adhes. Sci. Technol. 2005, 19, 165-179.
critically on surface roughness. The results, which were consistent with other AFM studies, showed large adhesion at high humidities but no hysteresis in the friction measurements. It has been shown recently that liquid droplets condensed around an AFM tip can be stable on time scales of hours.7-9 In fact, it has been proposed that capillary condensates can even exist after 24 h baking at 180 °C.10 It appears that both the equilibrium time of the measurement and the contact time of the surfaces are likely to be relevant. However, a variable, which has not yet been fully investigated, is whether the formation of a water film occurs on the same time scale as capillary condensation. Previously,6 the humidity was varied in a humidity chamber by first drying at close to 0% RH and then equilibrating at various relative humidities for 1 h. In other studies, the time allocated for equilibration varies but, in general, the time scales are of the order of minutes to hours, and no investigation has specifically preconditioned the samples at high humidity for a prolonged time. In this work, we exposed the surfaces to high humidity for 24 h prior to measurement in controlled and ambient RH conditions. Experimental Section The hydrophilic silica substrates were polished silicon wafers with a thermally oxidized layer (170 nm) of SiO2 (kindly provided by Dr Stefan Klintstro¨m, University of Linko¨ping, Sweden). AFM imaging revealed an rms roughness of 1-2 nm over a scan size of 1 µm2. The silica substrates were cut to into 1-cm squares and cleaned by thorough rinsing in water followed by ethanol; subsequently they were plasma-treated in an air environment (PDG-32G plasma cleaner Harrick Scientific Corp.) on medium setting for 1 min and placed immediately into the AFM. Hydrophobic silica substrates were prepared by vapor treatment with hexamethyldisilane (HMDS) at 60 °C for 2 h. Contact angle measurements gave a water contact angle of 80° indicating that the surfaces were substantially hydrophobic. Mica (muscovite) substrates were prepared from sheets cut to the appropriate size and cleaved immediately prior to the start of the experiment by means of double-sided adhesive tape. (7) Piner, R. D.; Mirkin, C. A. Langmuir 1997, 13, 6864-6868. (8) Rozhok, S.; Sun, P.; Piner, R.; Lieberman, M.; Mirkin, C. A. J. Phys. Chem. B 2004, 108, 7814-7819. (9) Xu, L.; Lio, A.; Hu, J.; Ogletree, D. F.; Salmeron, M. J. Phys. Chem. B 1998, 102, 540-548. (10) Bhattacharya, S.; Mittal, K. L. Surf. Technol. 1978, 7.
10.1021/la060456f CCC: $37.00 © 2007 American Chemical Society Published on Web 12/08/2006
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Figure 1. Friction behavior of a glass probe sliding on mica in ambient conditions (64% RH, 22 °C) after preconditioning the system for 24 h at 65-70% RH. The lower branch was measured on loading, the upper branch on unloading. AFM friction measurements were carried out using a Nanoscope IIIa multimode (Digital Instruments, Santa Barbara). Colloid probes were functionalized by attaching glass spheres (R ≈ 10 µm) (Duke Scientific Corporation) or cellulose particles (R ≈ 8 µm) to tipless AFM cantilevers. Friction force measurements and calibration were carried out as described previously6 according to the standardized methodology.11 The silica and mica samples were mounted in the AFM and left for 24 h in ambient air which had a relative humidity of 64-70% ( 1% RH prior to measurement. The temperature and relative humidity was continuously measured with a humidity probe (Vaisala, Helsinki, Finland). (Identical friction and adhesion results were observed when the surfaces were preconditioned with the use of saturated K2SO4 solutions.) The cellulose measurements were conducted between two cellulose spheres (Kanebo, Japan, regenerated via the viscose process) of which one was applied as colloidal probe and the other was attached to a mica surface. The rms roughness was typically 13 nm over a scan size of 2 µm. The radius of curvature, R, was calculated as R ) (R1 × R2)/(R1 + R2), where R1 and R2 are the radii of the cellulose spheres. Measurements were made in a humidity cycle from 7 to 80% RH and back again to 7%; at each humidity step the system was equilibrated overnight. There was very good agreement between measurements with low spring constant (0.2 N/m) and higher spring constant (5.3 N/m); however, necessarily, lower loads were applied with the lower spring constant. (The load is applied by pressing the surfaces together, and the load is calculated from the deflection of the spring.) The lower spring constant provides better resolution for the weaker forces observed for the cellulose case. Unless otherwise specified, the values for the pull-off force were taken at contact times of approximately 0.1 s, corresponding to the conventional 1-Hz piezo ramp rate for force measurements.
Results The frictional force as a function of load for a silica particle sliding against a mica surface after 24 h conditioning at high relative humidity is shown in Figure 1. The friction forces measured as the load is stepwise increased constitute the lower half of the friction curve. The friction is approximately linear with increasing applied load, as predicted by Amontons’ law, but does not go through the origin. From zero load (non contact) the friction force jumps straight to the intercept value of 95 nN. This indicates that there is an adhesive contact between the surfaces, and the intersect of the projected continuation of the line of best fit with the load-axis is a measure of the adhesion between the surfaces. Thus, the frictional force depends both on the externally applied load, plus an additional “intrinsic” load (11) Ralston, J.; Larson, I.; Rutland, M. W.; Feiler, A. A.; Kleijn, M. Pure Appl. Chem. 2005, 77, 2149-2170.
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Figure 2. Friction behavior of a glass probe sliding on silica (squares) and hydrophobized silica (triangles) and mica (filled circles) in ambient conditions (64% RH, 22 °C) after preconditioning the system for 24 h at 65-70% RH. The friction coefficients obtained from the linear slopes yielded the following: µmica ) 0.02, µsilicahydrophobic ) 0.15, and µsilicahydrophilic ) 0.13.
due to the adhesion. At an externally applied load of 2700 nN, the loading cycle is reversed and the friction is measured as the load is stepwise reduced. Significant hysteresis is observed. Hysteresis has been observed before in experiments where the area of contact of two spherical or cylindrical surfaces is measured as a function of applied load.12,13 Such “adhesion hysteresis” has also been correlated with changes in the frictional behavior. The dependence of friction force on contact area now being well established,1-3,5 it would at first sight seem reasonable to assume that the hysteresis in the frictional behavior observed here is also due to some sort of hysteretic behavior in the true area of contact as the load is varied. However, the situation is more complicated, and we devote extensive discussion to this point later. In Figure 2, friction-load relationships are displayed for the case of the silica colloidal probe interacting with a hydrophilic silica surface and a hydrophobized silica surface, with the mica result from Figure 1 shown for comparison. The two silica samples exhibit the same behavior as with the mica substrate, with a jump into a frictional force at zero load and a hysteretic friction trace leading to large negative applied loads before separation. The pull-off force implied from the figure is approximately the same for both mica and hydrophilic silica (∼3 µN), whereas for hydrophobized silica the adhesion is considerably smaller (∼1.9 µN). Since the adhesion is due to capillary condensation, this seems reasonable. Mica and silica have similar contact angles (silica 0°, 0° < mica < 7°), and in all these cases the same probe was used which is expected to have a contact angle of 0° also. Thus the mature capillary condensate would be expected to be very similar in the probe-mica and probe-silica cases. Hydrophobized silica on the other hand has a contact angle of the order of 80°, and thus a smaller adhesion would be expected for the case of the hydrophobic surface. The driving force for capillary condensation is reduced and the geometry of the resulting condensate will lead to a smaller area covered by the drop, and thus a smaller adhesive force. (Note that hydrophobizing one of the surfaces is not sufficient to prevent capillary condensation, particularly if the contact angle is 90° or less.) The inferred adhesion from the friction traces is borne out by the pull-off force measurements (not shown) which gave large and similar values for mica and silica surfaces with lower values in the case of hydrophobic silica. (12) Schmitt, F. J.; Yoshizawa, H.; Schmidt, A.; Duda, G.; Knoll, W.; Wegner, G.; Isrealachvili, J. N. Macromolecules 1995, 28, 3401-3410. (13) Chen, Y. L.; Helm, C. A.; Isrealachvili, J. N. Langmuir 1991, 7.
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Figure 3. The frictional behavior of silica (squares) (from Figure 2) and mica (filled circles) (from Figure 1) plotted together. Note the different scales on the axis for the data. The data taken on mica coincides rather well with the data taken on silica by multiplication by a constant factor of ∼11.3. (There is no theoretical significance to this number, and the value was chosen to make the zero applied load data coincide).
Figure 4. Adhesion as a function of relative humidity between two cellulose particles. The arrow indicates changes with increased conditioning time. At 55% RH, the adhesion increased somewhat after a friction measurement had been performed.
The absolute values of the friction are very different for the three curves, with the atomically smooth mica surface having the lowest friction. The highest friction is observed for the silicasilica case, which is also the case with the highest surface roughness, so this is ascribed to a mechanical interlock mechanism since both surfaces have approximately the same roughness. Often it is difficult to compare friction values for different substrates directly, since the adhesion values can vary significantly, which effectively alters the applied load. In this case, the adhesion values are the same (because the capillary condensate dimensions are essentially the same) so direct comparison is possible, and the difference can consequently be ascribed to the roughness. In Figure 3 the friction curves for silica and mica curves are plotted on the same graph with different scales, and it can be observed that they are qualitatively almost identical, despite their quantitative difference. The friction data obtained on the mica can be made to match that obtained on the silica by multiplication with a constant factor of 11.3. It is much easier to see in this figure that the adhesion values indicated by the negative load values are close to identical. The implications of this rather extraordinary observation are discussed later. The results for the adhesion as a function of relative humidity between two cellulose surfaces conditioned overnight are shown in Figure 4. At lower humidities the adhesion is rather low, but it increases significantly above a threshold value which is around 55% relative humidity. While the theory for adhesion between two smooth surfaces predicts an adhesion independent of the relative
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Figure 5. Friction-load traces between two cellulose spheres performed at 7% RH (triangles), 55% (filled circles), 80% (squares), 55% after being at higher humidity (filled triangles), and 7% after being at higher humidity (crosses). The friction coefficients obtained from the linear slopes yielded the following: µ7% ) 0.26, µ55% ) 0.51, µ80% ) 0.25, µ55%afterhigherhumidity ) 0.64, and µ7%afterhigherhumidity ) 0.22.
humidity,14,15 the observation of an adhesion threshold has been made earlier for nonideal surfaces.6,16,17 In this case it is held that at lower humidities the Kelvin radius of the condensate is smaller than the surface asperities and thus any condensates can occur only between contacting asperities. At higher humidities the Kelvin radius exceeds the roughness and the entire contact is flooded, leading to a considerably enhanced adhesion. (For reference, the Kelvin radii for a spherical concave meniscus vary from 10 nm at RH ) 90% to 1.6 nm at RH ) 50% and approximately 0.5 nm for RH ) 10%,14 which is approaching the size of a water molecule and thus the lower boundary of the validity of the theory.) Note that the values of the adhesion are much lower for cellulose than observed for mica and silica surfaces, even above the threshold, probably revealing that the roughness of cellulose is too large for a full condensate to form. Not only is the adhesion behavior analogous to that of oxide surfaces, even the friction behavior is similar. The friction traces for cellulose surfaces for a few humidities are shown in Figure 5. The uppermost curve is taken at 80% RH, well above the threshold, and it is this curve in particular which is reminiscent of those in Figure 2.The applied load range is much more compressed due to the weaker spring constant employed for the cellulose measurements. (A lower spring constant was used due to the much smaller forces observed in this system.) Note that the friction-load traces performed at lower humidities generate friction and adhesion (the lowest measurable load) which are rather similar, as would be expected from the adhesion measurements alluded to above. Importantly, the same frictional force was measured again at low humidities after the measurements equilibriated at the high RH indicating that the state of the surfaces and the water condensate is reversible with long enough equilibration. What is noticeable is that the hysteresissthe separation between the loading and unloading arms of the curvesincreases as the humidity increases. For the “higher” 55% curve this hysteresis is maximized. The fact that in some of the loops the friction actually increases with decreasing load is disconcerting; a possible explanation is that the adhesion is actually increasing with time, (14) Israelachvili, J. Intermolecular and Surface Forces; Academic Press: London, 1991. (15) Fisher, L. R.; Israelachvili, J. N. Nature (London, United Kingdom) 1979, 277, 548-549. (16) Ata, A.; Rabinovich, Y. I.; Singh, R. K. J. Adhes. Sci. Technol. 2002, 16, 337-346. (17) Rabinovich, Y. I.; Adler, J. J.; Ata, A.; Singh, R. K.; Moudgil, B. M. J. Colloid Interface Sci. 2000, 232, 17-24.
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Figure 6. Pull-off force as a function of time in contact for two cellulose spheres at 75% RH.
which may be due either to growth of the condensate or to plastic deformation of the spheres leading to larger contact areas. Pulloff force measurements between two cellulose surfaces were independent of the applied load indicating that plasticity is likely not the reason for the anomalous increase in friction with decreasing load. However, the pull-off force obtained from surface force measurements did show a dependence on time in contact, supporting the view that the condensate may grow with time. These results are shown in Figure 6.
Discussion We stress that the equilibration time referred to in this work is not the equilibration time of the condensate itself, but of the surfaces. The fact that the same result is achieved irrespective of whether the surfaces were pre-equilibrated at 90% RH or at around 65% RH seems to indicate that the longer equilibration time gives a good representation of “equilibrium”. Thus the results indicate that the adhesion and the maturity of the condensate are strongly dependent on the state of the water film on the surfaces prior to contact and that the RH of the gaseous phase is not the only determining parameter. Exactly why this is the case is unclear at this stage, and we will pursue this issue in the future. At this point, we can only state that it is so and speculate as to the cause. The water film on the surfaces has a thickness which is significant on the scale of the Kelvin radius. As discussed in an earlier article6 (e.g., Figure 1 in that paper), the area of the condensate (and thus the area over which the Laplace pressure operates) is determined by the Kelvin radius (as well as the surface roughness). In the derivation of the adhesion due to capillary condensation, no account is taken of the presence of adsorbed water films. It is thus not entirely clear whether the water film should be treated as part of the surface and thus ignored, or whether when contained within the condensate it can be treated as part of the condensate. In the latter case, the thickness of the water film should be added to the diameter of the meniscus to determine the “height” of the condensate; this will significantly increase the area occupied by the condensate while preserving the same Laplace pressure. Thus, the adhesion would be expected to be significantly larger for a thicker adsorbed film. Another possibility is that the flooding of the contact zone referred to in the preceding paper is incomplete without a mature surface film. Why the surface film should require a longer equilibration time is less clear. Early indications (unpublished data) are that this effect is less significant for mica, suggesting that surface roughness may play a role here, too. Possibly the high local curvature of the film adsorbing to nanometer scale asperities means that there is a kinetic hinder to full film adsorption.
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Figure 7. Left panel: A schematic which may explain the hysteresis in Figures 1, 2, 3, and 5. The top image represents contact without an external applied load. On compression (middle figure), the condensate preserves its Kelvin radius, but on unloading (bottom) does not retreat and instead swells, leading to a larger condensate. a is the radius of the condensate such that a1 < a2 ≈ a3.. Right panel: Upper, both surfaces have a low contact angle. Lower, the lower surface has a contact angle of 90°.
Recently, Salmeron and others7-9 have shown that capillary condensates can exist as adsorbed drops on a surface for considerable periods after removal of one of the surfaces which induced condensation (i.e., an AFM tip). Thus, while condensation appears to occur rapidly on experimental time scales, evaporation occurs extremely slowly. Thus, the hysteresis on unloading may be due to the fact that the capillary condensate is larger at the same load on the retreating cycle, leading to an effective higher load and thus higher friction. A possible mechanism for this process is depicted in Figure 7. It should be remembered that during a measurement such as that in, for example, Figure 1, the probe never leaves the surface. Thus, if liquid is deposited from the condensate as the surface is scanned underneath the probe, during the loading regime for example, then it is conceivable that harvesting of this water may occur with time. Further evidence for the argument that the capillary condensate is responsible for the hysteresis rather than viscoelastic contact mechanical pinning comes from the remarkable observation in Figure 2. Despite there being a factor ∼11 difference in the frictional forces, the shapes of the curves are identical. Since the adhesion values are the same, it seems reasonable to assume that the capillary condensates surrounding the contact are also the same. Since the contact angle is about zero in both cases, this is to be expected. Thus, it seems probable that the hysteresis is also due to some property of the capillary condensate which is also then hysteretic with loading direction. Since the loading regime is linear, it is implicit that the condensate is not causing any variation in the adhesive force during loading. However, on unloading, the initially lower gradient implies a larger adhesion, which in turn implies that the Laplace pressure is acting over a larger area, commensurate with the idea of a swollen condensate. The fact that there is a reduced adhesion when one of the surfaces is hydrophobized is reasonable. It might be thought that there should be no capillary condensation at all on a hydrophobic surface, but if one of the surfaces has a low contact angle then the driving force for condensation remains (and is driven in part by both surfaces for angles of less than 90°). The only difference is then in the geometry of the condensate and the commensurate reduction in the area over which the Laplace pressure can be said to act. If one surface has a contact angle of 90° and the other has a contact angle of 0°, then the calculated adhesion between them (for the case of ideal spheres in contact) should be a factor
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of 2 smaller than for the case of two surfaces of contact angle 0°. In the second panel of Figure 7, the two cases are depicted and the capillary condensates have the same (spherical) curvature (i.e., the case of same relative humidity and Kelvin radius). The area over which the Laplace pressure acts is given by πa2; in the θ ) 0° case a2 is equal to first order to 4RrK, in the second case 2RrK. Thus the adhesion predicted from capillary condensation for this case of contact angles of 0° and 90°, respectively, is
Fc ) 2πRγ
(1)
where γ is the water surface tension (assumed to be equal to the bulk value even for small radii), and R is the sphere radius. Thus, the fact that a lower absolute friction for the hydrophobized silica is observed is due to the fact that the effective load (arising from the adhesion and any applied load) is smaller by a factor of roughly two (at least for low loads). Interestingly, cellulose displays an adhesion threshold at a very similar value of the relative humidity as silica.6,16 The implication of this is that there is a roughness scale on the cellulose that is similar to that on silica (i.e., of the order of a nanometer or less) which may be flooded by an increase in the Kelvin radius. The smaller values of the adhesion and consequently the friction compared to silica in Figures 4 and 5 are due to a number of factors. First, the contact angle of water on cellulose is about 30° (as measured on single viscose fibers), which will reduce the adhesion by approximately 15% (cos 30°). Second, the “overall” roughness of the cellulose surfaces is much larger, and importantly there is roughness at different scales (rms 13 nm). When the larger scale roughness is greater than the largest values of the Kelvin radius, as in this case, complete flooding of the contact zone is impossible, and thus the contact should be regarded as a series of smaller contacts, each of which may be flooded as the capillary radius surpasses the local roughness superimposed on the larger asperities. The “true contact area” could thus be approximated by comparing the normalized pull-off forces for the rougher surfaces (about 30 mN/m) with that for the smoother surfaces found earlier6 and taking into account the different contact angle. This would suggest that the larger scale roughness reduces the effective contact area by about a factor of 7, which is of the expected order. Garoff and Zauscher18 have measured the interaction of functionalized tips with regenerated cellulose films at two different humidities (8 and 40%) and for the case of hydrophilic and hydrophobic tips. They also observed that adhesion was smaller for the hydrophobic case and the low humidity case and explained the higher humidity adhesion in terms of competing capillary condensation and repulsive van der Waals forcessthe origin of the latter is not completely clear. The lateral force was also higher in the presence of the higher humidity but there was no evidence for hysteresissconsistent with the humidity being below the threshold found here. It is interesting to note that while both adhesion and friction increase for the model cellulose surfaces found here, paper strength actually reduces at higher humidities (corresponding to above the threshold). Clearly the strength of paper cannot be simply treated in terms of the individual adhesional components at the contacts. The effect of the capillary condensation will be to partially solubilize and hydrate the polymeric material at the fiber joints (for example, strength additives as well as natural wood polymers), as well as to swell the cellulose, all of which may well have the effect of actually weakening the joint. Paper strength, for example measured through the so called “burst (18) Garoff, N.; Zauscher, S. Langmuir 2002, 18, 6921-6927.
strength”, is usually considered in terms of tensile strength and stretch. Different regimes have been identified, but above 55% RH the decrease in tensile strength is greater than the increase in stretch, and bursting strength decreases continuously.19-21 It seems likely from these measurements that the mechanism for water uptake which causes the strength failure is driven by the growth of capillary condensates, which may even act as a reservoir for absorption. It is also worth noting that in the case of cellulose, the hysteresis actually goes through a maximum at the intermediate humidities after being esentially nonexistent at low humidity. This observation further strengthens the argument that the hysteresis has to do with the capillary condensatesthe more mature the condensate (i.e., at high humidities in Figure 5) the less hysteresis might be expected, whereas for an incomplete condensate (e.g., 55% after conditioning) there will be time-dependent issues if nothing else. In all cases the nonlinear response of the friction with load is consistent with the idea that the friction is proportional to the contact area, which changes nonlinearly with load as discussed earlier.3,5,12 It should be noted though that the adhesion due to the condensate operates around the contact zone rather than at the contact zone, so it is difficult to know whether to ascribe the nonlinearity to contact area variation or to some property of the condensate.
Conclusions Conditioning of silica and mica surfaces by long (24 h) exposure to high relative humidities (above the critical threshold of 60% RH) leads to significantly larger adhesion compared to measurements carried out after short (1 h) conditioning for hydrophilic oxide materials such as mica and silica. Implicit in this result is that thickness of the surface water film contributes to the adhesion and that the formation of equilibrium film thickness is slow on the time scale of the experiments. The adhesion and the shape of the friction-load hysteresis were identical for mica and hydrophilic silica, indicating that the capillary growth thought to be responsible for this effect operates equally for both substrates. However, the magnitude of the friction was over an order of magnitude higher in the case of the silica due to the increased roughness of the silica surface. The magnitude of the friction on the hydrophobized silica was intermediate between mica and hydrophilic silica. This was due to a decreased adhesion on the hydrophobic substrate which, in turn, led to a lower effective applied load. The friction coefficient obtained from the linear regions of the friction-load traces were the same for the hydrophilic and hydrophobic silica. Since the surface roughness of the silica was similar on both cases, this is a very clear indication that the surface roughness is a critical determinant of the friction coefficient. The increase in the friction coefficient with increased relative humidity for cellulose shows that a capillary condensate is operative. However, the low adhesion values indicate that the formation of the capillary condensate is restricted and that even at the highest relative humidity conditions measured (90% RH) the system is below the critical threshold regime of complete contact flooding, which was previously observed to occur at ∼60% RH on silica. Thus, it seems that the higher roughness of the cellulose has the effect of “asperities on asperities” and that if the roughness is larger than the Kelvin radius at, for example, 90% humidity the contact as a whole cannot be flooded. (19) Benson, R. E. Tappi 1971, 54, 699-703. (20) Scott, W. E. Properties of Paper: An Introduction; TAPPI Press: Atlanta, 1989. (21) Fellers, C.; Norman, B. Pappersteknik; Avdelningen fo¨r Pappersteknik, KTH: Stockholm, 1998.
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Surface chemistry affects friction significantly, but on this roughness scale the net friction is determined by the magnitude of the capillary adhesion rather than by specific surface chemical effects on the mechanisms of friction. Finally, there is strong evidence that the threshold correlates well with the onset of weakening for paper, implying that water deposited on the surface of fibers via capillary condensates is ultimately responsible for this phenomenon.
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Acknowledgment. A.A.F. gratefully acknowledges Unilever Research, Port Sunlight, U.K., for partial funding during 20012002 when parts of this work were conducted. M.W.R. and J.S. acknowledge support from BiMaC, the Biofibre Materials Centre at KTH and M.W.R. thanks VR, the Swedish Research Council. K.T. acknowledges support from the Bo Rydin Foundation. LA060456F
