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Dynamic Transitions in Molecularly Thin Liquid Films under Frictional Sliding† Shinji Yamada* Tokyo Research Laboratories, Kao Corporation, 2-1-3 Bunka, Sumida-ku, Tokyo 131-8501, Japan ReceiVed June 11, 2007. In Final Form: October 2, 2007 The friction properties of the molecularly thin films of an asymmetric ether, 1,3-dimethylbutyl hexadecyl ether (DBHE), confined between mica surfaces were investigated using the surface forces apparatus. Kinetic friction was measured as a function of normal load and sliding velocity, and the static friction (stiction) was measured as a function of normal load and surface stopping time. Kinetic friction measurements exhibited unstable sliding dynamics: the friction force exhibited cyclic bumps and valleys in the sliding velocity range from about 10-2 to 1 µm/s, but above and below the velocity range, smooth sliding was observed. Stop-start experiments showed a stiction spike when surface stopping time exceeded a characteristic nucleation time, indicative of the static friction state at very low sliding velocity. These results imply that the friction of the confined DBHE film has at least three responsible friction statessstatic friction and two different kinetic friction statessdepending on the sliding velocity. The unstable sliding (bumps and valleys of the friction force) reflects the dynamic transition between two different kinetic states. The different friction states and their transitions are discussed on the basis of the recent experiments and theories of “inverted” stick-slip friction.
Introduction The shear dynamics of molecularly thin lubricant films confined between smooth surfaces exhibits various kinds of friction states or regimes depending on the sliding velocity. At low sliding velocity, the shearing surfaces often exhibit unstable motion such as stick-slip friction (both erratic or periodic), and above some critical sliding velocity, the system shows smooth sliding. Because of academic interest as well as practical importance, a number of experimental and theoretical works have been published on this subject, and these have greatly increased our understanding of the dynamics. The relationship between friction states and sliding velocity is now discussed from the viewpoint of molecular relaxation processes at the sliding interface and their time scales (relaxation times).1 Frictional dissipation often exhibits a maximum when the surfaces are slid at the sliding velocity (time scale) at which specific molecular relaxation appears.2 Below the velocity for the maximum, friction force increases with sliding velocity (dF/dV > 0), and the system exhibits smooth sliding. Above the velocity for the maximum, friction force decreases with sliding velocity (dF/dV < 0). Unstable sliding such as stick-slip motion generally appears in this negative slope regime. Furthermore, when sliding is stopped for a certain time, some static structures or domains may be formed at the contact interface, and their sizes grow with stopping time; the breaking (melting) of the structures by lateral forces produces static friction (stiction spike). Thus, the static friction behavior is a reflection of a molecular relaxation mechanism on an extremely long time scale. Because confined lubricants sometimes have multiple molecular relaxation mechanisms at the sliding interface, friction force versus sliding velocity curves exhibit multiple friction maxima and minima depending on the different friction states or regimes.3-7 †
Part of the Molecular and Surface Forces special issue. * E-mail:
[email protected]. Tel: +81-3-5630-9426. Fax: +81-35630-9330. (1) Israelachvili, J.; Berman, A. D. In CRC Handbook of Micro/Nanotribology, 2nd ed.; CRC Press: Boca Raton, FL, 1999; Chapter 9 and references therein. (2) Yoshizawa, H.; Chen, Y. L.; Israelachvili, J. J. Phys. Chem. 1993, 97, 4128-4140.
The surface forces apparatus (SFA) has proven to be an excellent tool for investigating the tribological behavior of confined liquid lubricants.8-11 It allows the study of single asperity contact, where load, contact area, and sliding velocity between surfaces can be controlled and unambiguously measured with higher accuracy than in any conventional tribometer. Furthermore, the fringes of equal chromatic order (FECO) allows us to monitor the real size and shape of the contact area and the distance of two surfaces (lubricant film thickness) during sliding.12 During the past decade, a number of authors have studied the molecular relaxations of confined lubricant molecules at sliding interfaces and the resulting friction properties using the SFA.1,13,14 Stick-slip friction was observed for many different confined liquids and boundary monolayers in the negative slope regimes (dF/dV < 0), and the molecular mechanisms were interpreted by the transitions between the static state and kinetic state during sliding. 1,15,16 For simple liquid lubricants, the two states were attributed to the solidified structures of confined liquids (static state) and shear-induced melting of the structures (kinetic state).17,18 For more rigid molecules such as fluorocarbon materials, sticking of the sliding surfaces at the (3) Luengo, G.; Israelachvili, J.; Granick, S. Wear 1996, 200, 328-335. (4) Yamada, S.; Israelachvili, J. J. Phys. Chem. B 1998, 102, 234-244. (5) Yamada, S.; Nakamura, G.; Amiya, T. Langmuir 2001, 17, 1693-1699. (6) Yamada, S. Langmuir 2005, 21, 8724-8732. (7) Qian, L.-M.; Luengo, G.; Perez, E. Europhys. Lett. 2003, 61, 268-274. (8) Israelachvili, J. N.; McGuiggan, P. M.; Homola, A. M. Science 1988, 240, 189-191. (9) Granick, S. Science 1991, 253, 1374-1379. (10) Klein, J.; Kumacheva, E. Science 1995, 269, 816-819. (11) Luengo, G.; Schmitt, F. J.; Hill, R.; Israelachvili, J. N. Macromolecules 1997, 30, 2482-2494. (12) Israelachvili, J. J. Colloid Interface Sci. 1973, 44, 259-272. (13) Granick, S. Phys. Today 1999, 52, 26-31 and references therein. (14) Urbakh, M.; Klafter, J.; Gourdon, D.; Israelachvili, J. Nature 2004, 430, 525-528. (15) Berman, A.; Ducker, W. A.; Israelachvili, J. Langmuir 1996, 12, 45594563. (16) Aranson, I. S.; Tsimring, L. S.; Vinokur, V. M. Phys. ReV. B 2002, 65, 125402-1-125402-7. (17) Yoshizawa, H.; Israelachvili, J. J. Phys. Chem. 1993, 97, 11300-11313. (18) Yoshizawa, H.; MuGuiggan, P.; Israelachvili, J. Science 1993, 259, 13051308.
10.1021/la701714g CCC: $40.75 © 2008 American Chemical Society Published on Web 11/30/2007
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Figure 1. Molecular structure of 1,3-dimethylbutyl hexadecyl ether (DBHE).
molecular-scale bumpiness and slipping over the bumpiness produce stick-slip friction.4,6 Recently, a new type of stick-slip friction, termed “inverted” stick-slip, has been reported for the sliding between boundary surfactant monolayers in water.19-22 Unlike common stick-slip behaviors, inverted stick-slip appears above some critical sliding velocities Vc1, and the stick-slip spikes point down rather than up. Above the second critical sliding velocity Vc2 (> Vc1), smooth sliding was again observed. The molecular mechanism of this new unstable sliding was interpreted not by the transition between static state and kinetic state like common stick-slip friction but by the transition between two different kinetic states. For the friction of the boundary monolayer system, the kinetic state at low sliding velocity is attributed to the formation and rupture of adhesive bonds between the surfactant layers (elastic-adhesive friction model), and that at high sliding velocity is attributed to the viscous contribution.21 In this article, we report a new example of unstable friction (dynamic transition) of a molecularly thin film of liquid lubricant during sliding. The friction properties of an asymmetric ether, 1,3-dimethylbutyl hexadecyl ether (DBHE), confined between mica surfaces were investigated using the SFA. The kinetic friction exhibited unstable sliding motions at some sliding velocity regime, and below and above the regime, smooth sliding was observed that was similar to the inverted stick-slip behavior of the boundary monolayer system. In addition, static friction behavior, which was not seen in the boundary monolayer system, was observed for the confined ether system at very low sliding velocity. The obtained results represent the friction behavior of the confined liquid ether over a broad range of sliding velocity, including a new mechanism of a kinetic-kinetic dynamic transition during frictional sliding. Experimental Methods The liquid lubricant investigated in this study is an asymmetric ether, 1,3-dimethylbutyl hexadecyl ether (DBHE), synthesized via catalytic etherification of alcohols with ketones under a hydrogen atmosphere by the use of a Pd/C catalyst.6,23,24 The molecular structure (shape) of the DBHE is shown in Figure 1. The molecular length is about 2.7 nm, and the bulk viscosity is 7 cP. The purity of the sample is 97.3%, as measured by gas chromatography analysis. The surface forces apparatus used in this study was an SFA3 (SurForce Corp.)25 modified for sliding experiments, which has been described in previous publications.4,11 Briefly, two cylindrical mica surfaces were positioned in a crossed-cylinder configuration and were used to confine a liquid sample. When the mica substrates (19) Richetti, P.; Drummond, C.; Israelachvili, J.; In, M.; Zana, R. Europhys. Lett. 2001, 55, 653-659. (20) Drummond, C.; Elezgaray, J.; Richetti, P. Europhys. Lett. 2002, 58, 503509. (21) Drummond, C.; Israelachvili, J.; Richetti, P. Phys. ReV. E 2003, 67, 0661101-066110-16. (22) Filippov, A. E.; Klafter, J.; Urbakh, M. J. Chem. Phys. 2002, 116, 68716874. (23) Fujii, Y.; Furugaki, H.; Yano, S.; Kita, K. Chem. Lett. 2000, 926-927. (24) Fujii, Y.; Furugaki, H.; Tamura, E.; Yano, S.; Kita, K. Bull. Chem. Soc. Jpn. 2005, 78, 456-463. (25) Israelachvili, J. N.; McGuiggan, P. M. J. Mater. Res. 1990, 5, 22232231.
Figure 2. Schematic drawing of the contact region in the SFA friction experiments. The liquid lubricant is confined between molecularly smooth mica surfaces under a normal load L (pressure P). Lateral sliding motion (sliding velocity V) is applied to the lower surface, and the resulting friction force F is measured by the deflection of friction-measuring springs that support the upper surface. The thickness of the sliding film D and the real contact area A are measured from an optical technique using FECO fringes. were installed in the apparatus, the chamber was purged with dry nitrogen gas. Some P2O5 was also placed inside the sealed chamber to keep the internal atmosphere completely dry at all times. A droplet of a liquid (∼0.1 mL) was injected between the mica surfaces. When brought together under an external load L (pressure P), the surfaces became flat because of the elastic deformation of the glue layer under each mica substrate, as shown in Figure 2. The liquid molecules were squeezed out from the contact interface under compression and finally formed a molecularly confined film. Lateral motions (reversible cycling) at constant sliding velocity V (0.0007 to 1.4 µm/s) were applied to the lower surface using a bimorph slider, and the resulting friction force F was measured by a friction device that supports the upper surface.8,11 The applied load L (pressure P in the range of ∼9 MPa) was controlled by the normal force spring of the bimorph slider (spring constant K ) 9300 N/m) that supports the lower surface. Using multiple beam interferometry (MBI),12 a crosssectional image of the contact area can be continuously monitored during sliding. Fringes of equal chromatic order (FECO) are obtained by passing a beam of white light through the substrate surfaces, which allows the measurement of the film thickness D (accuracy of 0.2 nm) and the size of the contact area A in real time. From the shape of the FECO, any wear or damage to the surface can be easily detected as soon as it occurs, allowing one to distinguish between undamaged sliding and friction with wear. All of the results reported in this article were obtained with atomically smooth undamaged mica surfaces (wearless friction). The experimental room was kept at a fixed temperature of 23 ( 0.2 °C.
Results When a droplet of DBHE was confined between two mica surfaces by normal compression, the thickness reached a hardwall distance of D ) 1.7 ( 0.1 nm. The dynamic thickness (thickness during sliding) equaled the static hard-wall thickness; no dilatency effect was detected during sliding. Friction Traces. Figure 3 shows the typical examples of friction traces (friction force versus time plots) obtained from the confined DBHE films. The friction traces exhibited different sliding behaviors depending on the sliding velocity. At low sliding velocity (Figure 3a), smooth sliding was observed (F ) Fk1, smooth I regime). When the moving direction of the bimorph slider (lower surface) was reversed, sliding stopped momentarily as the two stuck surfaces moved together in the opposite direction until the critical friction was again attained and sliding was resumed. We observed static friction (stiction spike) in this smooth I regime. At high sliding velocity (Figure 3c), smooth sliding was again observed (F ) Fk2, smooth II regime). In this regime, no static force was observed after the change in the driving direction. Between the two smooth regimes, unstable sliding
Dynamic Transitions in Thin Liquid Films
Figure 3. Typical friction traces of the confined DBHE film at three different sliding velocities. The applied normal load is 10 mN (P ) 4.9 MPa). Three different sliding regimes are observed. (a) Smooth I regime (V ) 0.0014 µm/s). Smooth sliding is observed. After a change in the driving direction, static friction is observed. (b) Transition regime (V ) 0.14 µm/s). The friction force exhibits cyclic bumps and valleys. The friction force at the bottom of the valleys (Fk1) almost equals the kinetic friction force in the smooth I regime. The friction force at the top of the bumps (Fk2) almost equals the kinetic friction force in the smooth II regime. (c) Smooth II regime (V ) 1.4 µm/s). Smooth sliding is again observed. Note that no static force is observed after the change in the driving direction in this regime.
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Figure 5. Kinetic friction force F as a function of applied load L at two different sliding velocities. The two velocities are in the smooth sliding regimes (V ) 0.007 µm/s in the smooth I regime and V ) 1.4 µm/s in the smooth II regime).
Figure 6. Kinetic shear stress S () kinetic friction forces/contact area ) F/A) as a function of applied pressure P at two different sliding velocities (data corresponds to the results of Figure 5). For the sliding at V ) 0.007 µm/s, the shear stress is almost independent of the applied pressure, and S ≈ 0.13 MPa. At V ) 1.4 µm/s, the shear stress decreases with the applied pressure.
Figure 4. Kinetic friction forces as a function of sliding velocity at different applied pressures. Solid symbols are for the smooth sliding regimes. Open symbols are for the maxima (top of the bumps) and minima (bottom of the valleys) in the transition regime. Critical velocities Vc1 and Vc2 that separate the different friction regimes are also shown.
was observed (transition regime): the friction force exhibited cyclic “bumps and valleys”. The friction force at the bottom of the valleys equaled the kinetic friction force in the smooth I regime (F ) Fk1), and the friction at the top of the bumps almost equaled the kinetic friction force in the smooth II regime (F ) Fk2). This transition was reversible; increasing sliding velocity induced the transition from the smooth I to smooth II regime, and decreasing sliding velocity at the same contact position caused a transition back to the smooth I regime. Kinetic Friction Behavior. Figure 4 shows the relationship between kinetic friction force and sliding velocity at different applied pressures. As was already mentioned, friction behavior was divided into three different regimes: the smooth I regime at a sliding velocity below the critical velocity of V ) Vc1, the smooth II regime above Vc2, and the transition regime between the two critical velocities. The friction forces in the transition regime are represented by open symbols, and friction force maxima (top of the bumps) and minima (bottom of the valleys) are plotted. Friction forces increased with the increase in applied loads (pressures). At low loads or pressures (L < 20 mN, P < 6.5 MPa), the friction forces in the smooth I regime (Fk1) almost equaled the friction force minima in the transition regime, and the force in the smooth II regime (Fk2) almost equaled the force
Figure 7. Effect of stopping and restarting on the friction force. Sliding is stopped for a certain time t and then restarted; meanwhile, the friction force is continually measured as a function of time. If the stopping time t is shorter than a well-defined time τn, then there is no change in the friction when it is restarted. However, when t exceeds τn, a stiction spike appears whose height increases with t. The stiction spike height is defined as ∆F ) (Fs - Fk1). Sliding conditions: L ) 20 mN (P ) 5.8 MPa) and V ) 0.07 µm/s (transition regime). In this case, τn ≈ 10 s.
maxima in the transition regime (see also Figure 3). Fk2 was larger than Fk1. At high loads or pressures (L > 30 mN, P > 8.1 MPa), the friction curves exhibited a maximum and a shallow minimum in the transition regime. The height of the bumps in the transition regime, ∆Fk ) (Fk2 - Fk1), decreased with the increase in applied loads or pressures (see also Figure 8). The critical velocities for the transition from smooth I to the transition
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Figure 8. Effect of applied pressure on stiction spike height ∆F (normalized by the contact area A) measured after different stopping times t. Sliding velocity V is 0.07 µm/s. The constant region at small t ( τn. For the results at P ) 4.2 MPa, ∆F/A reached a plateau when t > 100 s. Increasing applied pressure decreased ∆F/A, and no plateau region was observed for P > 4.7 MPa in the experimental stopping time range. We should note that τn is not very dependent on the applied pressure and is always ∼10 s.
Discussion Unstable Sliding Motions. The kinetic friction of the confined DBHE film exhibits unstable sliding motions in the sliding velocity range from about 10-2 to 1 µm/s (Figures 3 and 4). Unlike the regular sawtooth pattern commonly observed for confined lubricant liquids, the friction traces shows cyclic bumps and valleys during sliding. The shape of the friction traces implies that the sliding surfaces are not stuck during unstable motions. (Regular stick-slip includes the event that the two opposed surfaces are stuck to each other and move together at a given driving velocity.) In addition, smooth sliding regimes appear
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both below and above the unstable regime. These results imply that this unstable regime represents the transition not between the static and kinetic states as for common stick-slip friction but between two different kinetic states. The effective sliding velocity at the sliding interface does not equal the applied driving velocity used as the abscissa in Figure 4 (which is also the case for common stick-slip friction). The effective velocity should be varied within the range below Vc1 or above Vc2; we can deduce this because the friction force at the bottom of the valleys equals the force in the smooth I regime and the force at the top of the bumps equals the force in the smooth II regime (at low applied pressure). Dynamic Transitions between Two Kinetic States: Previously Proposed Models. There are two reported examples of dynamic transitions for molecularly confined lubricants between two kinetic states depending on the sliding velocity. One is the superkinetic friction of boundary monolayers in dry air.18,26 The system exhibits regular stick-slip friction at low sliding velocity, and above some critical sliding velocity, smooth sliding is observed. An extremely low friction state appears above the smooth regime as negative or inverted spikes. The molecular mechanism of the extremely low friction is interpreted by the shear alignment of hydrocarbon chains of the monolayers into a well-ordered (combed) conformation. The other example is inverted stick-slip friction for the boundary surfactant monolayers in water that was briefly mentioned in the Introduction. The stick-slip spikes point down rather than up (like those for superkinetic friction) and the stickslip regime is located between two smooth sliding regimes.20,21 The two different kinetic states associated with the dynamic transition are the elastic-adhesive model of friction for the low sliding velocity regime and viscous friction for high sliding velocity regime. Note that the both dynamic transitions (superkinetic sliding and inverted stick-slip) are observed for the friction between two adhesive surfaces. Adhesion Contribution to the Friction of the DBHE Film. The friction of the confined DBHE film studied here is also adhesion-controlled, which is deduced from the load (pressure) dependence of the kinetic friction force (shear stress). According to the simple theories of friction, the kinetic friction force Fk and kinetic shear stress Sk are given by1,27
F k ) C 1A + C 2 L Sk )
Fk ) C 1 + C2 P A
(1) (1′)
where C1 and C2 are constants, A is the contact area, and P is the applied pressure. The first term is the adhesion (surface forces) contribution to friction, and the second term is the load contribution (C2 equals the friction coefficient µ). For high loads, the relationship between A and L can be roughly expressed as A ∝ L2/3,28 and then we have
Fk ) C′1L2/3 + C2L
(2)
As shown in Figure 5, the friction of the DBHE film is not proportional to L but roughly scales as L2/3. Also, the shear stress at low sliding velocity is independent of the applied pressure (C2 (26) Yoshizawa, H.; Chen, Y.-L.; Israelachvili, J. Wear 1993, 168, 161-166. (27) Israelachvili, J. N. In Fundamentals of Friction; Singer, I. L., Pollock, H. M., Eds.; Kluwer Academic: Dordrecht, The Netherlands 1992; p 351. (28) Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc. London, Ser. A 1971, 324, 301-313.
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≈ 0 in Figure 6). Therefore, the friction of the confined DBHE film is adhesion-controlled. Static Friction (Stiction Spikes). The dynamic transition observed in this study is similar to inverted stick-slip behavior because the unstable regime of both systems is located between two smooth sliding regimes. However, the molecular mechanisms of the two kinetic states (smooth I and II) for the DBHE film should be different from those proposed for the inverted stickslip friction of the boundary surfactant monolayers in water. In the inverted stick-slip friction of the boundary monolayer system,19-21 the kinetic state for smooth sliding below the stickslip regime is attributed to the elastic-adhesive model of friction (as was already mentioned). In this model, the adhesive area consists of N independent “junctions”, each of which can stretch elastically up to its yield point. Each of the junctions detaches either spontaneously by thermal excitation or by the external shear forces. We define l* as the critical deformation at the yield point at an adhesive junction, τ0 as the time scale to break an adhesive junction as a result of thermal fluctuations under zero lateral stress, and τ as the time scale to activate or reactivate a junction thermally. For the inverted stick-slip system in the literature,21 both l*/τ0 and l*/τ are within the velocity range accessible by the sliding experiments. At very low sliding velocity, the adhesive junctions are always depinned by thermal fluctuations, and no static friction force (stiction spike) is observed. Increasing sliding velocity changes the relative number of bonded and detached junctions at the sliding interface, and the friction curve has a plateau in the l*/τ > V > l*/τ0 velocity region. This model is applicable to the adhesion-controlled friction system whose molecular mobility is relatively high. However, for the confined DBHE film studied here, stiction spikes are observed in the friction traces (Figure 3), and stopstart experiments apparently show the static friction after aging (Figures 7 and 8). These results suggest that τ0 and τ for the DBHE system are extremely large because of the confinement effect, so l*/τ0 is outside the velocity range accessible by this experiment. As a result, adhesive junctions would never be depinned by thermal fluctuations but are always broken by the imposed lateral deformation.20,21 Also, large τ gives τV/l* g 1, and adhesive junctions will be formed over a significant time, leading to some aging effects resulting in a static friction, which is observed in our system. The longer the aging time, the larger the number of adhesive junctions N at the contact interface, resulting in an increase in the stiction spike height with stopping time (Figures 7 and 8). Increasing applied pressure decreases the stiction spike height (Figure 8), because increasing pressure prolongs τ and then decreases N at a given aging time. This is the common stick-slip scenario; we estimate that there should be a transition between the static and kinetic states (smooth I) at very low sliding velocity, which is outside the range covered by this kinetic friction measurement (possibly below 0.001 µm/ s). We can estimate the critical velocity Vc of stick-slip friction for the transition between the static and kinetic states (smooth I) on the basis of the freezing-melting transition by eq 31,6,17
VC )
(Fs - Fk) 5Kτn
(3)
where (Fs - Fk) is the stick-slip amplitude, K is the spring constant of the friction measuring spring, and τn is the characteristic nucleation time of the film. When we insert the typical values obtained from this study, (Fs - Fk) ) 0.1 mN (we do not have the direct results for this parameter and thus estimated
this from Figure 7), τn ) 10 s (Figure 8), and K ) 5800 N/m, we obtain Vc ≈ 0.0003 µm/s, which agrees with the above expectation (Vc < 0.001 µm/s). This discussion supports the expectation of regular stick-slip friction (static-kinetic transition) at very low sliding velocity. We should note that eq 3 gives a good approximation to the stick-slip critical velocity for the phase-transition model but is not suitable for application to stickslip friction on the basis of other models, such as the rough surfaces, distant-dependent, and velocity-dependent models.1,6 Molecular Mechanisms of Two Kinetic Sliding States. It is difficult to estimate the molecular mechanisms of the two different kinetic sliding states observed in this study. However, recent theoretical work on inverted stick-slip friction by Filippov et al.22 gave us the idea to discuss the mechanisms. They confined two layers of particles (model of lubricant molecules) between two moving plates and calculated the friction force between the plates and the average velocities of the two layers of particles. They have concluded that inverted stick-slip stems from the bifurcation from one kinetic sliding regime to another. The kinetic regime at low sliding velocity is the trapped state: one layer of particles is trapped or adsorbed onto the moving plate and is immobilized, and the second layer is trapped on another plate. The kinetic regime at high sliding velocity is the decoupled state: the particles are decoupled from the moving plates and move with different velocities in such a way that the average velocity equals half of the driving velocity. This theoretical analysis suggests that inverted stick-slip reflects a transition from film-slip to wall-slip conditions. We cannot apply this theory directly to our system because our results should not include the transition from film-slip to wall-slip conditions. Because of the large surface energy of mica surfaces (about 200-400 mJ/m2),9 molecules directly attached to mica surfaces are strongly adsorbed;6,29 the friction at the molecule/mica interface is much larger than the intermolecular friction.7,30 Therefore, if the transition from smooth I to smooth II reflects the transition from film-slip to wall-slip conditions, then the order of shear stress should increase discontinuously at the transition. However, the shear stresses for the two smooth regimes are rather close to each other (Figures 3 and 4). In addition, the shear stress for the two kinetic states is near 105 Pa, which is the typical value for the shear stress of molecularly thin films of a variety of hydrocarbon surfactants and liquids, where molecular slipping occurs between hydrocarbon segments.30,31 Therefore, the slipping in our system should occur within the film (film-slip) for both kinetic regimes. Another thing to be considered is liquid structure in the confined film. When the DBHE droplet is confined between two flat mica surfaces by normal compression, molecules are squeezed out of contact interface, and the liquid film thickness decreases. In this confinement process, molecules in the middle part of the film are expelled from the interface, and molecules adjacent to opposed mica surfaces constitute the final hard-wall film (D ) 1.7 nm). Of course, this is mainly due to the strong adsorption of molecules on mica surfaces, and the nonuniform density distribution of molecules (higher near the surfaces and almost the same as its bulk value in the middle part of the film32) could also make a contribution. Because the hard-wall thickness roughly corresponds to four molecular layers, the adsorbed thickness on each surface should be about two molecular layers. The DBHE molecule has an asymmetric molecular shape (Figure 1) and a small ability (29) Reiter, G.; Demirel, A. L.; Granick, S. Science 1994, 263, 1741-1744. (30) Yamada, S. Langmuir 2003, 19, 7399-7405. (31) Yamada, S. Tribol. Lett. 2002, 13, 167-171. (32) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1991; Chapter 13.
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Figure 9. Schematic of plausible models of the two different dynamic states of the DBHE film. (a) At low sliding velocity (smooth I), molecules in the film are adsorbed or trapped on two opposing mica surfaces, and slip occurs between the adsorbed layers. (b) At high sliding velocity (smooth II), molecules are stretched and/or ironed as a result of sliding;7 molecules in the middle part of the film could be decoupled from the adsorbed layers. Shear is accomplished by the slipping of the decoupled middle layer. See the text for details.
to pack into highly ordered layers,32 and the adsorbed molecules do not form discrete layers but interdigitate between layers (which is one of the reason that asymmetric liquid molecules generally form relatively thick hard-wall films32). On the basis of the above discussion, Figure 9 shows the schematic illustration of the plausible models for the two different kinetic sliding states. At low sliding velocity (smooth I regime, Figure 9a), the dynamic structure (structure during sliding) is not very different from the static structure in confinement.7 There are adsorbed layers (about two layers thick) on both surfaces that are immobile during sliding; slipping occurs between the two opposed adsorbed layers (trapped state of sliding). This sliding may involve the interdigitation and disentanglement of chains between the two absorbed layers as illustrated in Figure 9a. This model is consistent with the fact that the friction in this smooth I regime is ideally adhesion-controlled (C2 in eq 2 is zero, Figure 6). Increasing sliding velocity (and resulting large shear force) tends to stretch and/or “iron” the molecules, which reduces the effect of chain interdigitation between layers.7,33,34 Molecules in the middle part of the film are now “decoupled” from the adsorbing layers. Molecules directly attached to mica surfaces (preferably with a flat conformation7) are still adsorbed and immobilized; shear is accomplished by the slipping of the decoupled middle layers between opposed adsorbed layers (Figure 9b, decoupled state of sliding).30 In this sliding state, the film should have two slip planes (decoupled layer/adsorbed layer interfaces). In Figure 9, conformation changes of molecules are described only in the thickness direction, but of course the changes can occur in the
Figure 10. Schematic illustration of the friction force-sliding velocity curve for the confined DBHE film. There are at least three responsible friction states (static friction and smooth I and II) separated by two transition regimes (regular stick-slip and another unstable regime).
direction parallel to surfaces.35 Furthermore, we should mention that the height of the bumps ∆Fk, which could reflect the extent of shear-induced conformation changes in molecules between the two dynamic states, decreases with the increase in applied pressure (Figures 4 and 8). This is probably due to the lower ability of conformation changes to take place under high pressure. We do not have enough experimental evidence for these proposed models, and further investigation is required to understand the mechanisms underlying this phenomenon. Figure 10 and Table 1 schematically summarize the relationship between friction force and sliding velocity for the confined DBHE film.3 The friction curve should have at least three responsible friction states (regimes) separated by two transition (unstable) regimes. The regime at the lowest sliding velocity is the static friction. We observe this regime by stop-start measurement. The static friction regime and smooth I regime are separated by a regular stick-slip regime, which is not directly observed in this study. The sliding of the smooth I regime is the trapped state, which could be the slipping between adsorbed molecular layers on mica surfaces. The sliding in the largest velocity region should be the decoupled state; molecules in the middle part of the film could be decoupled from adsorbed layers and slipping occurs at the decoupled layer/adsorbed layer interfaces. The transition between smooth I and II regimes exhibits unstable sliding dynamics, which is observed in this study. In Figure 10, the friction below the static friction maximum (creep regime)3 and in the smooth I and II regimes is represented as the simple proportional dependence on the sliding velocity (F ∝ V), like a Newtonian liquid (F ) 0 at V ) 0). We have not directly obtained this relationship because of the limited sliding velocity range covered by this study, but this Newtonian-like dependence is expected from the theoretical investigations.3,14,20-22 The slope
Table 1. Characteristics of Different Sliding Regimes sliding regime
static friction regime
regular stick-slip regime
smooth I
dynamic transition regime
smooth II
velocity range (critical velocity, Vc)
extremely long time (aging) required
V < Vc (estimated Vc ≈ 0.0003 µm/s)
Vc < V < Vc1 (Vc1 ≈ 0.01-0.03 µm/s)
Vc1 < V < Vc2
Vc2 < V (Vc2 ≈ 0.3-1 µm/s)
friction features
stiction spike at the commencement of sliding (or after aging)
dF/dV < 0-minimum (dF/dV ) 0)
dF/dV > 0 (F ∝ V)
maximum (dF / dV ) 0) ≈ dF / dV < 0
dF/dV > 0 (F ∝ V)
possible sliding mechanisms
formation of adhesive junctions at interface
static-kinetic transition
slipping between adsorbed layers (trapped state)
transition between two kinetic states
slipping of decoupled middle layers between adsorbed layers (decoupled state)
Dynamic Transitions in Thin Liquid Films
of the F-V dependence (viscosity) is of course sensitive to the applied load (pressure); low load (pressure) decreases the slope and weakens the velocity dependence of the whole friction curve, which is observed experimentally in Figure 4.
Conclusions The friction properties of the molecularly thin films of an asymmetric ether, 1,3-dimethylbutyl hexadecyl ether (DBHE), confined between mica surfaces were investigated using the surface forces apparatus. Kinetic friction measurements exhibited a dynamic sliding transition depending on the sliding velocity: the friction force exhibited cyclic bumps and valleys in the sliding velocity range from about 10-2 to 1 µm/s (transition regime), and above and below the velocity range, smooth sliding was observed. Stop-start experiment showed a static friction state at very low sliding velocity. The results imply that there are at least three responsible friction statessstatic friction and smooth I and IIsdepending on the sliding velocity ranges, separated by (33) Yamada, S. Tribol. Online 2006, 1, 29-33. (34) Drummond, C.; Israelachvili, J. Macromolecules 2000, 33, 4910-4920. (35) Drummond, C.; Alcantar, N.; Israelachvili, J. Phys. ReV. E 2002, 66, 011705-1-011705-6.
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two transition regimes. The observed unstable sliding (bumps and valleys of the friction force) appears at the transition from one dynamic sliding state to another. Comparison with the theory of the inverted stick-slip friction22 suggests that the smooth regime at low sliding velocity (smooth I) is attributed to the trapped state of sliding, possibly the slipping between adsorbed DBHE layers. The smooth regime at high sliding velocity (smooth II) is attributed to the decoupled state of sliding, the molecular mechanism of which could be the slipping of decoupled molecules in the middle part of the film between adsorbed layers. A regular stick-slip regime is expected for sliding velocity below the experimental velocity range (transition between the static state and smooth I). The friction dynamics in the broad range of sliding velocity is summarized as a schematic friction force-sliding velocity curve, which represents the different sliding states and their transitions. Acknowledgment. I am grateful to Dr. Jacob Israelachvili, Dr. Carlos Drummond, and Dr. Yoshiaki Fujikura for enlightening discussions, to Mr. Yasuyuki Fujii for providing the ether sample, and to the Kao Corporation for permission to publish this article. LA701714G
