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J. Phys. Chem. B 2000, 104, 7944-7950
Tribology of Shearing Polymer Surfaces. 2. Polymer (PnBMA) Sliding On Mica Gustavo Luengo,† Manfred Heuberger,‡ and Jacob Israelachvili*,§ Department of Applied Physics, L’Oreal Research, 90 rue Ge´ neral Roguet, 92583 Clichy Cedex, France, Materials Department, ETH-Zentrum, 8092 Zu¨ rich, Switzerland, and Department of Chemical Engineering, and Materials Department, UniVersity of California, Santa Barbara, California 93106 ReceiVed: February 14, 2000; In Final Form: May 22, 2000
Quantitative friction force measurements were made using a Surface Forces apparatus (SFA) modified for friction studies of a smooth poly(n-butyl methacrylate) (PnBMA) surface sliding on a stationary mica surface, and the results are compared with those of the complementary system (ref 1) of mica sliding on a stationary polymer surface. The results indicate that qualitatively and quantitatively different tribological behavior may be expectedsas manifested by smooth or stick-slip sliding, high or low steady-state friction stresses, transient effects such as stiction, and surface deformations and wearsfor such “asymmetric” surfaces depending on whether the sliding or stationary surface carries the lubricant or polymer layer, on whether the motion is continuous in one direction or cyclic (back and forth), and on the area of the contacting junctions. None of these effects would arise if the friction forces were determined solely by the instantaneous load (pressure) and velocity (shear rate) of the shearing junctions, which is generally assumed in conventional theories or models of friction.
Introduction Most tribological systems are “asymmetric” in the sense that the two surfaces are either physically and/or chemically different. For example, when a computer head slides on a disk surface or when a piston ring moves inside a cylinder, the moving surface, or SLIDER, remains in constant “sliding contact” with the stationary surface, or SUBSTRATE. Thus, all the molecules on the slider surface experience a shear force at all times during the sliding, but the molecules of the substrate surface experience a shear force only when the slider passes across them at that location. Furthermore, if one or other of the two surfaces is coated with a boundary lubricant layer, different tribological behavior can be expected whenever the properties of the layer depend on the previous sliding history. In Part I of this two-part series1 we reported on the friction forces of a solid surface of mica sliding on a polymer substrate surface of PnBMA (henceforth: PBMA). The adhesion and friction of polymer surfaces, which were briefly reviewed in refs 1 and 2, are quite different from those of hard, elastic surfaces owing to their viscoelastic properties and to their having a glass transition temperature instead of a melting point. These properties give rise to high effective adhesion and complex history-dependent friction.1-4 Our recent SFA experiments1,2 focused on the adhesion and friction of PBMA near its glass transition temperature at Tg ) 25 °C. The results showed that both the adhesion energy hysteresis and frictional energy dissipation are maximum at temperatures close to Tg, and that for mica sliding on PBMA (Figure 1a) the friction is mainly of the stick-slip type at low sliding velocities: the static friction force FS is high and attains its equilibrium steady-state value immediately on commencement of sliding, but the kinetic friction force FKsdefined as the minimum measured value during a stick-slip cyclesdecreases monotonically from an †
L'Oreal Research. ‡ ETH-Zentrum. § University of California.
initially high value to a very low value as sliding progresses toward the steady-state. The measured friction forces exhibited complex dependencies on time, temperature, load and velocity, and at least two relaxation or energy-dissipating mechanisms could be identified that involve both submolecular rearrangements at and across the shearing interface and bulk viscous flow effects around it. Here we report on the complementary or inverse geometry of this asymmetric system, viz. polymer sliding across a mica surface (or “polymer on substrate” configuration, Figure 1b). These two geometries (Figure 1a,b) can be very different, both quantitatively and qualitatively, when different surfaces are involved. This is because the same part of the sliding surface remains in contact with the stationary surface during sliding, whereas the contact region of the stationary surface is constantly changing as the slider moves across it. In other words, the two surfaces experience very different shearing right from the start of sliding and during the steady-state. The steady-state itself can also be different depending on the type of shearing cycle. As illustrated in Figure 1c, it can be a single-pass (half a cycle) or repeated cyclic passes, either in the same direction (repetitive cycling) or back and forth (reversible cycling). Other cycling geometries are also possible and important, but are not considered here: these include changes in the sliding direction or angle (other than 180°).6-8 Recent research5-8 and this work suggests that the tribology and wear of asymmetric systems can be quite different both because of the different shearing geometries and the different histories experienced by the moving and stationary surfaces, even when the basic tribological conditions of load and sliding velocity are the same. Experimental Section SFA Friction Apparatus. As described in part 11 we used a friction force-measuring attachment to a Surface Forces apparatus Mk 3. This device has the capability of driving one of
10.1021/jp0005773 CCC: $19.00 © 2000 American Chemical Society Published on Web 07/28/2000
Tribology of Shearing Polymer Surfaces
Figure 1. Schematic of steady-state sliding configuration that can exhibit different tribological behavior (friction forces, stick-slip) when the materials of the two surfaces are exchanged. (a) “substrate sliding on stationary polymer surface” configuration and how this was achieved in the SFA experiments described in ref 1. (b) “Polymer sliding on stationary substrate” configuration and, below, how this was achieved in the SFA experiments described here. Note that the (nominally) “stationary” surface may actually be the moving one during experiments. Further differences can arise even for the same combination of surfaces, load and sliding velocity when one considers different types of steadystate geometries, three of which are shown in (c): “Single-pass” or continuous sliding in one direction only, where the slider passes across the stationary surface once (for example, when rolling a photographic film) or when the shearing surfaces remain in contact at all places at all times (for example, rotating concentric cylinders); “repetitive cycling” where the slider passes repeatedly over the stationary surface in the same direction each time (for example, a pin on disk tribometer or a read-write head sliding on a computer disk), and “reversible cycling” where the slider passes repeatedly over the stationary surface in the opposite direction each time (for example, any vibrating or oscillating mechanism such as a pendulum or piston). The experiments reported here involved reversible cycling as in configuration (b). Typical experimental parameters are given in the figure legends.
the surfaces in any direction and at variable speeds using either a mechanical or piezoelectric drive. The friction force is measured from the deflection of two parallel cantilever springs of stiffness K supporting one of the surfaces, as measured by semiconductor strain gauges attached to the springs. The geometrical arrangement of the two surfaces in the SFA was that of two cylinders crossed at 90° to each other (Figure 1b). During friction experiments, the contacting cylinders were moved relative to each other along a direction parallel to one cylinder’s axis. In the configuration adopted here the lower surface carried the polymer layer while the upper surface was bare mica. The complementary system, shown in Figure 1a, was studied in ref 1. Sample Preparation and Characterization. A 0.4 µm thick layer of PBMA [-CH2C(CH3)(COO(CH2)3CH3)-]n of molecular weight Mw ) 337 000 and glass transition temperature Tg ) 25 °C was deposited by evaporative solvent-casting on a mica surface as previously described.1 The deposited layer was characterized for smoothness and uniformity by atomic force microscopy (Figure 2) and multiple beam interferometry (MBI) using “fringes of equal chromatic order” (FECO). The mechanical and viscoelastic properties of bulk PBMA are well-known.9
J. Phys. Chem. B, Vol. 104, No. 33, 2000 7945
Figure 2. AFM scan of one of the PBMA surfaces obtained by solvent casting. The RMS surface roughness is Tg).
smallsvery much lower than anything previously measured at this temperaturesand more typical of a fluid-lubricated system. Figure 6 shows the effect of speed on the static and kinetic friction forces. As in the case of the minimal effect of load, there is no strong dependence on V although our speed range was somewhat limited to one decade. The large errors are due to the very low friction forces measured at this “high” temperature (T > Tg); however, a weak maximum in the static friction force is indicated at a sliding velocity of about 3 µm/s, which is similar to the maximum observed in the complementary system at 7 µm/s,1 and reinforces the notion that there are at least two different relaxation mechanisms in this system. Further Measurements and Observations of the Transitions to Steady-State Sliding. From the results, it appears that one can distinguish two types of transition: one that depends on the temperature, the other on the sliding time or distance (or cycle number). These two transitions are most likely to be related. They do not appear in the mica on polymer system1 or, if they do, they are much weaker and not as sharp. Temperature Transition. The very different steady-state static friction forces measured at 15 and 20-25 °C (cf. Figure 4) provide insight into the transition that depends on the temperature, especially on going through the glass transition temperature. A large drop in FK was also observed on passing through Tg in the complementary system of mica sliding on polymer [cf. Figure 8 in ref 1]. This transition and its broader implications are discussed in the Discussion.
Sliding Time or Distance-Dependent Transition (at Constant Temperature). The time-evolving shapes of the friction traces at 15 °C provide insight into the smooth to stick-slip sliding transition that takes place soon after the commencement of sliding, i.e., the transition that depends on some characteristic sliding time (τtr), sliding distance (Dtr), or cycle number (ntr). Figure 7 shows actual friction traces of the first seven cycles. The transition from smooth to stick-slip sliding starts at the second cycle (i.e., after one pass) and is complete by the fifth or sixth cycle. There are more cycles corresponding to n > 7 in which there is only stick-slip (not shown). In comparison, the friction traces at the higher temperatures (20-25 °C) show stick-slip motion right from the start of the first cycle but of much smaller amplitude (cf. Figure 3). Comparison of these results with those obtained on the complementary system1 reveal that in these two very different geometries this transition was complete after the same number of cycles n have been passed (typically between 1 and 5, depending on the temperature), rather than the sliding time or sliding distance: the sliding “time”, τtr, was already rejected as the characteristic parameter in ref 1, and the sliding distances needed to reach steady-state conditions, Dtr, differ by factors of 20-50 in the two complementary systems. We have also checked that the energy inputted into the system, defined by ∫F dx integrated over the transition, is not constant at different sliding velocities, for example. Our results therefore indicate that the crucial parameter that characterizes the transition from smooth to stick-slip sliding is the number of sliding cycles or passes, ntr. The FECO fringes were monitored during this transition, giving information about the surface shape as the sliding progresses. Figure 8 shows the fringes as observed at 15 °C and their interpretation. Panel (a) shows the fringe pattern during the first cycle when the friction is high but smooth. Panel (b) shows the fringe pattern in the stick-slip regime. When sliding in the stick-slip regime, small amplitude long-wavelength ripples or undulations of approximate height 10 nm develop on the polymer surface as well as on the mica surface, probably due to transfer of polymer material. These ripples may be related to the “Schallamach waves’ that have been previously seen to develop on viscoelastic polymer surfaces during sliding,13 although these Schallamach waves have been of much larger wavelength. At the end of a stick-slip cycle, when the mica surface was viewed under on ordinary optical microscope, discrete spots of transferred polymer could be seen on the sliding path (Figure 8, panel (c)). The distance between these spots
7948 J. Phys. Chem. B, Vol. 104, No. 33, 2000
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Figure 9. Friction trace showing consecutive cycles in an experiment with PBMA sliding on mica in the steady-state at 20 and 25 °C. The top and bottom parts of each trace represent forward and backward motions along the same path. Note that (a) all the forward traces are similar to each other, and all the backward traces are similar to each other, but not to the forward traces. On the other hand, the forward and backward traces are roughly mirror images of each other (in time).
Figure 8. Fringes of equal chromatic order observed when the surfaces at T ) 15 °C are sliding smoothly (a), and in the stick-slip regime (b) where small ripples or undulations (Schallamach waves?13) develop of approximate height 10 nm. (c) Optical microscope photo of mica surface just after a stick-slip cycle showing locations of adhesion sites that must be due to polymer transfer during the first few cycles. The number and distance between spotssabout 8-10 spots separated by about 100 µmscorrespond approximately to the number of stick-slip spikes and their separation (slip distances) measured during the friction cycle.
was found to be the same as (or a simple fraction of) the distance between ripples seen on the FECO fringes and the slip length deduced from the friction traces, indicating that these were the points at which the surfaces became stuck during the stick part of each cycle. In other words, at each slip the polymer surface jumps from one spot to the next, sometimes skipping one. While the spots of transferred polymer on the mica surface remain there after the surfaces are separated, the ripples on the polymer surface quickly disappear on separation or stopping, bringing the polymer surface back to its native smooth state (cf. Figure 2c in ref 2). The precise shape and topography of the ripples, undulations and spots that develop on the two surfaces appear to determine the subtle features of the stickslip friction traces: whenever the steady-state stick-slip was not perfectly regular but “erratic” or exhibited a variation in amplitude and/or frequency during a cycle, the same friction pattern repeated itself almost exactly on each path. This is illustrated in Figure 9. Discussion Transitions to Steady-State Sliding. Below the glass transition temperature (T e Tg) the results show a transition in the friction soon after commencement of sliding from smooth sliding (where FK ) FS) to stick-slip sliding characterized by a high static friction force and a low (underdamped) kinetic friction force (FK , FS). This transition is complete after the slider is cycled about 6 times; this corresponds to a total sliding distance Dtr of about 5 mm which is much larger than a molecular dimension or even the contact diameter of the slider or “asperity”. These findings are similar to those reported in ref 1
for the complementary system of mica sliding on PBMA at T < Tg, but there are also important differences, discussed below. Our cumulative results of this and the previous paper1 indicate that the crucial parameter that characterizes the transition from smooth to steady-state stick-slip sliding (at constant temperature) is the number of sliding cycles or passes, ntr, rather than the total sliding distance Dtr, the sliding time τtr, or the frictional energy input ∫F dx. This does not mean that the system has no characteristic time, length or energy scales, it does, but these are associated with other tribological relaxations.1,14 For example, the relaxation of the molecules back to their resting state once they move out of the shearing contact zone, or when sliding is stopped, are characterized by (different) relaxation times, τo.15 Another example arises in “continuous sliding” where two shearing surfaces remain in contact at all places at all times (cf. Figure 1c). This occurs when the contact areas of both surfaces are effectively infinite, as in the case of a rotating shaft in a cylindrical bearing. For such geometries the number of cycles or passes has no meaning and the attainment of steadystate conditions appears to depend on the total distance sheared: the “critical”, “massaging” or “memory” distance, Dc.1,14,16 However, it could be that even in such situations the number of passes per molecule or asperity is the important parameter. Thus, if the molecular dimension is δ, we would have
Dc ) ntrδ
(1)
and for constant δ it then becomes difficult to experimentally distinguish between a characteristic memory length and the cycle number or number of passes. The difference between Dc and Dtr is also worth mentioning: Dtr is the total sliding distance of the transition (as observed experimentally), and Dc is the characteristic length scale of the system (an intrinsic property). These two quantities differ when the diameter of the contact 2r is less than Dc, for then the distance sheared during each pass (2r) is not sufficient to reorder all the molecules into their steady-state configuration (see Figure 10 later). Our findings show that for polymer surfaces the magnitude of Dc can be very largesmuch larger than typical asperity contact diameters, 2r. In such cases, the concept of the
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J. Phys. Chem. B, Vol. 104, No. 33, 2000 7949
Figure 11. Schematic stick-slip friction envelopes (solid curves enclosing shaded regions) above and below Tg for “PBMA sliding on mica”, as studied here. Dotted curves: Corresponding envelope for “mica sliding on PBMA” which did not change dramatically on heating through the glass transition.1
Figure 10. (a) Suggested sliding mechanism for PBMA sliding on mica or, more generally, for any polymer sliding on a solid substrate at temperatures just below Tg. (b) Sliding mechanism for mica sliding on PBMA (polymer sliding on substrate) studied previously.1 In case (a) all the polymer molecules in the contact zone will be fully shearaligned soon after the commencement of sliding. In case (b) the molecules at the front will not be aligned while those at the back will be partially or fully aligned, depending on the characteristic “massaging” distance Dc relative to the contact diameter, 2r.
total number of cycles or passes becomes the characterizing parameter of the transition to steady-state sliding. One logical conclusion of the above argument is that the transition should also depend on the contact diameter or area, i.e., that ntr is also a function of r. The results and conclusions of our two studies are based on a limited range of contact diameters, typically from 20 to 40 µm, which does not allow us to unambiguously establish the effect of the contact diameter on the transition. The characteristic cycle number may well also depend on the diameter or area of the slider, most likely increasing as the area decreases. In addition to the transition that depends on the cycle number or distance sheared, there is also one associated with the temperature, defined by Ttr, where a large drop in the friction force occurs on heating the system through Ttr, which was found to be very close to Tg. A large drop in FK on passing through Tg was also observed in the complementary system of mica sliding on polymer [cf. Figure 8 in ref 1]. Our combined results therefore indicate that the transition temperature is the same as, or very close to, Tg, i.e., that Ttr ) Tg. But it may not be exactly the same as same as Tg, which may anyway be different at a surface compared to the bulk.11 These temperature transitions depend on the Deborah number(s) of the molecular relaxation mechanisms responsible for the frictional energy dissipation which are related to the sliding velocity via the timetemperature superposition principle.17 As already noted, the results of both studies show that at least two molecular relaxation mechanisms are involved in PBMA,18 and we further suspect that these two different processes are activated at different temperatures, but each within 10 °C of Tg. Thus, FK appears to be activated around 20-25 °C, and FS at 15-20 °C, but we cannot be certain of this difference. An important difference was found concerning the temperature dependence of the static friction in the two geometries.
In the present geometry (Figure 1b), on heating the surfaces by 5 °C to the glass transition temperature and above, a transition to very low static (and kinetic) friction was observed. The very low static friction FS was not observed in the complementary system, and is discussed in the following section. The very low kinetic friction FK, which was also observed in the complementary system, suggests one of two possible mechanisms: (a) The surfaces may not be touching during the slip but jumping from spot to spot on the mica surface over a thin cushion of air, which is unlikely: the FECO fringes show that the surfaces remain in intimate contact during the slips, and this explanation would not account for the low kinetic friction observed in the complementary system, (b) The polymer chains at the surface have adopted a highly mobile transient “superkinetic” configuration (the explanation used in the first paper1), or (c) A combination of the above occurs, except that the surfaces slip from spot to spot while remaining in contact. Scenario c appears to be consistent with all of the observations, and is shown in Figure 10a. Differences between Polymer-on-Substrate and Substrateon-Polymer Configurations. Figure 11 shows the main differences in the friction between the two geometries. The main differences are (a) a larger and more abrupt transition from totally smooth to large-amplitude stick-slip sliding for PBMAon-mica (in contrast, for mica-on-PBMA, there was always a finite stick-slip right from the start) and (b) very low steadystate friction above Tg for PBMA-on-mica, whereas the behavior of mica-on-PBMA was not very different above and below Tg. A likely explanation for the very different friction forces exhibited by these two configurations, especially at and above Tg, is as follows: for mica sliding on PBMA (Figure 10b), at any instant all parts of the polymer surface that are in contact with the mica surface will have a different configuration because each part has a different shearing history; for example, the polymer at the front end has only recently come into contact with the shearing mica surface while the polymer at the back end has been sheared for some time. Thus, the transition to steady-state conditions must occur at different times in different regions of the contact zone, thereby causing a weak and more gradual transition in the friction from rest to steady-state sliding, as observed. In contrast, for the case of PBMA sliding on mica (Figure 10a), all parts of the polymer surface remain in constant contact with the shearing mica surface and therefore experience the same “history” at all times. Thus, if there is a transition from smooth to stick-slip sliding (triggered by some confor-
7950 J. Phys. Chem. B, Vol. 104, No. 33, 2000 mational transition of the polymer chains at the surface18), this will occur at the same time throughout the whole contact and, therefore, be seen as a sharp transition, as observed. More importantly, in the case of Figure 10b, since polymer molecules at the surface are continually coming in to and out of contact with the shearing mica surface and only remain in contact with it for a small fraction of the time during any one cycle, its shear-induced low-friction state will be quickly lost after each pass. The situation is quite different in the case of Figure 10a where the polymer in the contact zone is being continuously shear-aligned and, therefore, can quickly adopt and then keep its low friction conformation so long as the sliding continues. This would account for the much lower friction observed at and above Tg only in the case of polymer sliding on mica. These effects, which are likely to arise in other polymer systems, are ultimately due to the existence of history-dependent relaxation times and memory distances in these kinds of systems. Implications for Fundamental and Practical Understanding of Tribological Systems The effective characteristic distance Dc over which the surfaces have to be sheared before they attain their steady-state configuration is surprisingly largesmuch larger than any molecular dimension, grain size or even the diameter of the contact zone. This latter fact has important implications when interpreting experimental data obtained on a particular tribological system, however idealized, because it implies that there can be no simple scaling of the contact area or junction geometry. For example, for the simple planar geometry of Figure 10b, a flat slider having half or twice the area or diameter may experience very different steady-state friction forces or stresses: in the former the majority of the polymer molecules in the contact zone are always in the nonaligned, high-friction state, while in the latter most of them are in the aligned, lowfriction state. Other tribological differences may also occur in consequence, such as different local temperatures, track geometry and wear rates. This may explain why apparently similar tribological experiments on similar systems and conditions often produce very different results. In view of the results presented here and elsewhere,1,14 it appears that the previous historysmanifested by the number of passes, memory distances and timessplays a major role in determining the steady-state friction forces of any asymmetric system that is lubricated by complex polymer-like molecules. This implies that different system geometries and cycling procedures, some of which are illustrated in Figure 1, may exhibit very different tribological properties depending also on factors such as the location of the lubricating surface or boundary layer. For example, for an asperity or tip moving across a flat surface in the “repetitive cycling” mode of Figure 1c, the location of the lubricant layer on the asperity or surface could make a large difference to the resulting friction and initial wear: lubricant molecules on the surface are only in periodic contact with the asperity, while those on the asperity are in continual shearing contact with the surface. As already mentioned, such differences do not arise when the friction forces are determined solely by the instantaneous load (pressure) and velocity (shear rate) of the shearing junction which is often assumed in conventional theories or models of friction,16 but they become crucial when the previous history plays a role. Acknowledgment. We would like to thank Dr. Yuval Golan for his invaluable help and expertise in AFM microscopy. This work was supported by the Department of Energy under grant
Luengo et al. number DE -FG-03-87ER45331, though this support does not constitute an endorsement by DOE of the views expressed in this article. References and Notes (1) Heuberger, M.; Luengo, G.; Israelachvili, J. N. J. Phys. Chem. B 1999, 103, 10127. (2) Luengo, G.; Pan, J.-M.; Heuberger, M.; Israelachvili, J. N. Langmuir 1998, 14, 3873. (3) Berthoud, P.; Baumberger, T.; G’Sell, C.; Hiver, J.-M. Phys ReV. B 1999, 59, 14313. (4) Baumberger, T.; Berthoud, P.; Caroli, C. Phys. ReV. B 1999, 50, 3928. (5) Israelachvili, J. N.; Drummond, C. Tribology on the 300th AnniVersary of Amontons' Law, 1999 MRS Workshop Series, San Jose; MRS: Warrendale, PA, 1999; p 63. (6) Wang, A.; Sun, D. C.; Yau, S. S.; Edwards, B.; Sokol, M.; Essner, A.; Polineni, V. K.; Stark, C.; Dumbleton, J. H. Wear 1997, 203, 230. (7) Bragdon, C. R.; O’Connor, D. O.; Lowenstein, J. D., Jr.; Syniuta, W. D. Paper presented at the World Tribology Congress, 1997, 735. (8) Tyfour, W. R.; Beynon, J. H. Tribology International 1994, 27, 401. (9) Hrouz, J.; Hanacek, J. J. Macromol. Sci.sPhys. B5 1971, 2, 245. (10) Berman, A.; Ducker, W.; Israelachvili, J. N. Langmuir 1996, 12, 4559. Berman, A. D.; Ducker, W. A.; Israelachvili, J. N. In Physics of Sliding Friction; Persson, B., Tosati, E., Eds.; NATO Advanced Science Institute Series; Kluwer Academic Publishers: Dordrecht, 1996; Chapter 3, p 51. Negative friction forces can be measured even when the real interfacial friction forcesthe one acting between the two surfacessis always positive. This effect arises from having “underdamped” conditions when the moving surface overshoots after a rapid slip, just as a weight that is attached to the end of a stretched elastic band or spring will move beyond the equilibrium position when it is suddenly released (if the damping is below critical). It is possible to extract the real friction force from the measured force by a deconvolution of the data, as described in the above two references, but this requires a complex, model-dependent theoretical analysis whenever there is stick-slip. (11) The results of measurements of Tg in thin films have been confusing and contradictory. Some show no effect: Xie, L.; DeMaggio, G. B.; Frieze, W. E.; DeVries, J.; Gidley, D. W.; Hristov, H. A.; Yee, A. F. Phys. ReV. Lett., 1995; 75, 4947. Hall, D. B.; Hooker, J. C.; Torkelson, J. M. Macromolecules 1997, 30, 667. Some show a higher Tg: Schu¨ller, J.; Mel’nichenko, Yu. B.; Richert, R.; Fischer, E. W. Phys. ReV. Lett. 1994, 73, 2224. Wallace, W. E.; van Zanten, J. H.; Wu, W. L. Phys. ReV. E 1995, 52 , R3329. van Zanten, J. H.; Wallace, W. E.; Wu, W. L. Phys. ReV. E 1996, 53, R2053. Some show a lower Tg: Jackson, C. L.; McKenna, G. B. J. Non-Cryst. Solids 1991, 221, 131. DeMaggio, G. V.; Frieze, W. E.; Gidley, D. W.; Zhu, M.; Hristov, H. A.; Yee, A. F. Phys. ReV. Lett. 1997, 78, 1524. Some show an increase or decrease that depends on strength of the interaction of the polymer and confining surfaces: Keddie, J. L.; Jones, A. L.; Cory, R. A. Faraday Discuss. Chem. Soc. 1994; 98, 219. Idem. Europhys. Lett. 1994, 27, 59. (12) Berman, A.; Israelachvili, J. N. CRC Handbook of Micro/Nanotribology, 2nd ed.; Bhushan, B., Ed.; CRC Press: Boca Raton & New York, 1999; Chapter 9, p 371. Berman, A. D.; Israelachvili, J. N. In Micro/ Nanotribology and its Applications; NATO Advanced Science Institute Series; Bhushan, B., Ed.; Kluwer Academic Publishers: Dordrecht, 1997; p 317. Campbell, S.; Ulman, A.;. Israelachvili, J. Tribol. Lett. 4 1998, 43. (13) Schallamach, A. Wear 1971, 17, 301. (14) Drummond, C.; Israelachvili, J. N. Macromolecules, in press. Israelachvili, J.; Giasson, S.; Kuhl, T.; Drummond, C.; Berman, A.; Luengo, G.; Pan, J.-M.; Heuberger, M.; Ducker, W.; Alcantar. N.; Proceedings of the 1999 Leeds-Lyon Conference, in press. (15) Yoshizawa, H.; Isrealachvili, J. J. Phys. Chem. 1993, 97, 11300. (16) The exceptions are the “rate-and-state” models which appear to capture the flavor of complex tribological systems, both lubricated or “wet” and unlubricated or “dry”: Ruina, A. J. Geophys. Res. 1983, 88, 10359. Baumberger and co-workers, Ibid. refs 3 and 4. Dieterich, J. H.; Kilgore, D. Pure Appl. Geophys. 1984, 43, 28. Carlson, J. M.; Batista, A. A. Phys. ReV. E 1996, 53, 4153. (17) Reiner, M. Phys. Today 1964, January, 62. Israelachvili, J. N.; Berman. A. Isr. J. Chem. 1995, 35, 85. (18) The molecular models of the two relaxation processes were described in ref 1. Polymers with large side chains such as PBMA are known to shear align (in the bulk) with their backbone perpendicular to, and their side chains parallel to, the shear direction: Kaito, A.; Yatabe, T.; Ohnishi, S.; Tanigaki, N.; Yase, K. Macromolecules 1999, 32, 5647. The molecular model proposed in ref 1 suggested that similar backbone and side-chain orientations occur at the PBMA-substrate interface during sliding, and that these define the two main energy dissipating processes of the system.
