Layering Transitions and Tribology of Molecularly Thin Films of Poly

Analytical Research Center, Kao Corporation, 2606 Akabane, Ichikaimachi,. Haga ... melt (Mw ≈ 80 000) as a function of the applied load (pressure) a...
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Langmuir 2003, 19, 7399-7405

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Layering Transitions and Tribology of Molecularly Thin Films of Poly(dimethylsiloxane) Shinji Yamada† Analytical Research Center, Kao Corporation, 2606 Akabane, Ichikaimachi, Haga, Tochigi 321-3497, Japan Received March 25, 2003. In Final Form: June 17, 2003 Friction measurements were carried out for molecularly thin films of a poly(dimethylsiloxane) (PDMS) melt (Mw ≈ 80 000) as a function of the applied load (pressure) and sliding velocity using the surface forces apparatus. The PDMS films exhibit apparent layering transitions when the thicknesses of the films are decreased to the order of molecular dimensions. For four-layer and three-layer films, “solidlike” sliding is observed and the shear stresses are on the order of 105 Pa. Further compression and simultaneous lateral motion squeeze out the PDMS molecules to a final residual film two molecular layers in thickness, whose shear properties include “viscous” characters, and the shear stress increases abruptly by a factor of 6-8. This shear property change may arise from the different sliding mechanisms of “adsorbed” and “mobile” molecular layers. When thicknesses of the films are three layers and above, the first layers adjacent to mica substrates are strongly adsorbed onto substrate surfaces and immobile during sliding; shear is accomplished by the slipping of “mobile” middle layers (results in low friction). For the two-layer film (adsorbed layers in direct contact), sliding involves the deformation of adsorbed PDMS segments and wall slip, resulting in high friction and surface damage (wear). For PDMS films, a “fluidlike” response appears when molecules are squeezed out to a final residual thickness (two layers), which is very different from the typical behavior of most of the confined fluid systems (solidlike shift is commonly observed due to confinement). Effects of the substrate-molecule interaction strength on the layering structures and shear properties are also discussed.

Introduction When fluid molecules are confined in a narrow gap between two smooth surfaces, their dynamic properties are completely different from that of the bulk.1-6 The molecular motions are highly restricted, and the system shows “solidlike” responses when sheared slowly. This “solidification” behavior of confined fluids has been studied by a number of authors experimentally and theoretically, and two major effects have been proposed that lead to the phase transitions: (i) the layering of molecules at surfaces1,2,7 and (ii) a molecular volume decrease due to confinement.6,8-11 These two effects appear simultaneously, but the extent of their contribution could be different for various confined “solidified” systems. Generally, irregularly shaped liquids and most of the polymer melts have a low ability to pack into layer structures; such systems solidify in confined geometries presumably † Telephone: +81-285-68-7414. Fax: +81-285-68-7418. E-mail: [email protected].

(1) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1991. (2) (a) Thompson, P. A.; Grest, G. S.; Robbins, M. O. Phys. Rev. Lett. 1992, 68, 3448. (b) Rabin, Y.; Hersht, I. Physica A 1993, 200, 708. (3) Granick, S. Science 1991, 253, 1374. (4) Israelachvili, J.; Berman, A. D. In CRC Handbook of Micro/ Nanotribology, 2nd ed.; Bhushan, B., Ed.; CRC Press: Boca Raton, FL, 1999; Chapter 9. (5) Heuberger, M.; Zach, M.; Spencer, N. D. Science 2001, 292, 905. (6) Robbins, M. O.; Muser, M. H. In Modern Tribology Handbook; Bhushan, B., Ed.; CRC Press: Boca Raton, FL, 2001; Vol. 1, Chapter 20. (7) (a) Klein, J.; Kumacheva, E. Physica A 1998, 249, 206. (b) Klein, J.; Kumacheva, E. J. Chem. Phys. 1998, 108, 6996. (c) Kumacheva, E.; Klein, J. J. Chem. Phys. 1998, 108, 7010. (8) Luengo, G.; Schmitt, F. J.; Hill, R.; Israelachvili, J. Macromolecules 1997, 30, 2482. (9) Yamada, S.; Nakamura, G.; Amiya, T. Langmuir 2001, 17, 1693. (10) Yamada, S. Tribol. Lett. 2002, 13, 167. (11) Yamada, S.; Nakamura, G.; Hanada, Y.; Amiya, T. Tribol. Lett. 2003, 15 (2), 83-89.

because of the molecular volume decrease (confinementinduced glasslike transitions).6,10-14 On the other hand, for regularly shaped (spherical or linear chain) liquids, apparent layer structure formations are often observed that could have a large effect on the solidification behavior.15 In the latter case, density of molecules in the film is not uniform but oscillates with a repeat spacing corresponding to the molecular dimensions, higher near solid walls and lower at the middle part of the film.1,13,16-19 This oscillatory density profile implies the inhomogeneous molecular mobility (viscosity) in the film. Particularly, the first layers adjacent to substrate walls behave very differently from the additional layers.16,17,20 Manias et al. employed non-equilibrium molecular dynamics computer simulations on the dynamics of confined oligomer melts whose thickness was in the range up to 10 molecular layers.16,17,21 They found that the first layers adjacent to two opposed substrate walls were more “viscous” than the middle part of the film. They also (12) (a) Demirel, A. L.; Granick, S. Phys. Rev. Lett. 1996, 77, 2261. (b) Demirel, A. L.; Granick, S. J. Chem. Phys. 2001, 115, 1498. (13) Granick, S. Phys. Today 1999, 52, 26. (14) Robbins, M. O.; Baljon, A. R. C. In Microstructure and Microtribology of Polymer Surfaces; American Chemical Society: Washington, DC, 2000; Chapter 6. (15) It is sometimes claimed that the molecular mechanism of solidification in a layered fluid is considered as “epitaxial crystallization” (ref 2). However, recent studies have revealed that even layered liquids show a gradual mobility decrease as a result of confinement, which is reminiscent of glasslike transitions (refs 12 and 13). (16) Manias, E.; Hadziioannou, G.; Bitsanis, I.; Brinke, G. T. Europhys. Lett. 1993, 24, 99. (17) Manias, E.; Bitsanis, I.; Hadziioannou, G.; Brinke, G. T. Europhys. Lett. 1996, 33, 371. (18) Dijkstra, M. Europhys. Lett. 1997, 37, 281. (19) Jabbarzadeh, A.; Atkinson, J. D.; Tanner, R. I. J. Chem. Phys. 1999, 110, 2612. (20) Mugele, F.; Persson, B.; Zilberman, S.; Nitzan, A.; Salmeron, M. Tribol. Lett. 2002, 12, 123. (21) Manias, E.; Hadziioannou, G.; Brinke, G. T. J. Chem. Phys. 1994, 101, 1721.

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reported that the viscosity of the middle part was only slightly higher than the bulk viscosity. Salmeron and coworkers studied the shear properties of the molecularly thin films of chain alcohols experimentally using the surface forces apparatus (SFA).20,22,23 They found that the first layers adjacent to the mica substrates acted as “selfassembled monolayers” and exhibited solidlike sliding features; additional liquid (bilayers) between the fixed monolayers behaved like a liquid whose viscosity was close to its bulk value. These studies imply the possibility that in a number of nanotribological studies solidlike properties for molecularly thin liquid layers were observed because they might probe mainly the properties of the first adsorbed layers. In this study, the shear properties of the molecularly thin films of a poly(dimethylsiloxane) (PDMS) melt were investigated using the SFA. It is known that PDMS tends to order into layers parallel to substrate surfaces even though it is not a simple liquid having a low molecular weight; an oscillatory force-distance profile with a periodicity corresponding to the width of the PDMS chain was reported.24 Friction of the PDMS film between mica substrates (strongly adsorbing surfaces) was measured as a function of the applied load (pressure) and sliding velocity. Results are analyzed from the viewpoint of the relation between friction properties and the number of molecular layers, and the molecular mechanisms of the dynamics, especially the sliding of the first layers and additional layers, are discussed. The layering of molecules is strongly affected by the surface properties of the substrate materials.3,16,19,21 Therefore, measurements were also made for a weak adsorbing substrate (hydrocarbon surfactant monolayer-coated mica), and the effects of the substrate-molecule interaction strength on the friction properties are also analyzed in this paper. Experimental Methods The PDMS melt investigated in this study is a commercial silicone oil obtained from Toray Dow Corning Silicone Co., Japan, and was used without further purification. The weight-average molecular weight Mw is about 80 000 (bulk viscosity ηbulk ≈ 160 Pa s), and the estimated polydispersity of the sample is 1.4. The width of the PDMS chain is about 0.7 nm.24 The SFA used in this study was a SFA3 (SurForce Corp., U.S.A.)25 modified for sliding experiments, which has been described in previous publications.8,26 Briefly, two cylindrical mica surfaces were positioned in a crossed cylinder configuration and were used to confine the polymer melt samples. When the mica substrates were installed into 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 polymer melt sample (volume ∼ 0.1 mL) was rubbed over the substrate surface using a thin syringe needle. When brought together under an external load L (pressure P), the surfaces become flat because of the elastic deformation of the glue layer under each mica substrate, as is shown in Figure 1. The PDMS molecules are squeezed out from the contact interface under compression and finally form a layer structure (see also Figure 2). Lateral motions (reversible cycling) at constant velocity V (0.001-1 µm/s) were applied, and the resulting friction force F was measured (with an accuracy of 0.02 mN) at given normal load L (pressure P in the range of ∼5 MPa). With the use of multiple beam interferometry, a cross-sectional image of the contact area can be continuously monitored during sliding.27 (22) Mugele, F.; Salmeron, M. Phys. Rev. Lett. 2000, 84, 5796. (23) Mugele, F.; Salmeron, M. J. Chem. Phys. 2001, 114, 1831. (24) Horn, R. G.; Israelachvili, J. N. Macromolecules 1988, 21, 2836. (25) Israelachvili, J.; McGuiggan, P. M. J. Mater. Res. 1990, 5, 2223. (26) Yamada, S.; Israelachvili, J. J. Phys. Chem. B 1998, 102, 234.

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Figure 1. Schematic drawing of the contact region in the SFA friction experiments. The PDMS melt forms a layer structure with a periodicity of about 0.7 nm (corresponds to the width of the PDMS chain) when compressed to a molecularly thin film. Lateral sliding motion (sliding velocity V) is applied to the lower surface, and the friction force F is measured by the deflection of friction springs that support the upper surface. The thickness of the film D and real contact area A are measured using an optical technique using multiple beam interference fringes (FECO).

Figure 2. Dependence of the dynamic thicknesses (thicknesses during sliding) on the applied pressure obtained for the PDMS film between bare mica substrates. The discrete thickness suggests the layer structure formation in the film. Fringes of equal chromatic order (FECO) are obtained by passing a beam of white light normally 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 (with a relative error of 10%) in real time. The experimental room was kept at a fixed temperature of 23 ( 0.2 °C. Friction forces at different applied pressures were measured at the same contact position of the same sample. Measurements were begun with sliding at the smallest applied pressure. When the pressure was changed (increased) to the next pressure, the contact interface was left to equilibrate for 1 h before restarting the lateral motions. The reproducibility of the friction measurements at different contact positions and different experiments was within the range of (15%. The weak adsorbing substrate surfaces were prepared by the self-assembly deposition of hydrocarbon surfactant.28 The doublechained surfactant DDAB (didodecyldimethylammonium bromide, ACROS Organics, U.S.A.) was used as received. The monolayer of DDAB was adsorbed from solution. The aqueous solution of DDAB (7 × 10-5 M) was prepared 1 day before the experiment. For the deposition, mica surfaces were immersed into the surfactant solution for 30 min. The surfaces were then slowly retracted from the solution and rinsed lightly in Millipore filtered water to remove any excess of surfactant. The surface energy of the DDAB-coated surface was 25 mJ/m2 (surface energy of bare mica is about 200-400 mJ/m2),3 and the molecular area was about 0.50 nm2 per molecule (corresponding to close packing of the chains for this double-chained surfactant).28 (27) (a) Israelachvili, J. J. Colloid Interface Sci. 1973, 44, 259. (b) Heuberger, M.; Luengo, G.; Israelachvili, J. Langmuir 1997, 13, 3839. (28) Gee, M. L.; Israelachvili, J. N. J. Chem. Soc., Fararday Trans. 1990, 86, 4049.

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Figure 3. Shear stresses as a function of the sliding velocity at different numbers of PDMS layers (different applied pressures). Solid symbols: bare mica systems. Open symbol: DDABcoated mica system. An abrupt shear stress increase is observed for the bare mica system during sliding at P ) 4.9 MPa and V ) 0.007 µm/s, corresponding to the layering transition from three to two layers.

Figure 4. Shear stresses as a function of the applied pressure for the bare mica system at two different sliding velocities. When fitted to eq 2b, we obtain S0 ) 0.05 MPa and µ ≈ 0.020.04. Table 1. Powers of Eq 1 for the PDMS Films at Different Numbers of Layers and Substrates

Results

layers

R

The dynamic thickness (thickness during sliding) of the PDMS film between bare mica substrates was plotted against the applied pressure, and the result is shown in Figure 2. The dynamic thickness decreased with increasing applied pressure, and the film had discrete thicknesses of about 2.8, 2.0, and 1.3 nm, which corresponded to four, three, and two molecular layers, respectively.24 A layering transition from four layers to three layers occurred only by compression (P ) 3.7 MPa). However, the transition from three to two layers could not be attained by compression alone (P ) 4.9 MPa); the combination of compression and sliding motion was required to squeeze out the molecules to two molecular layers (see Figure 3). Further compression and simultaneous sliding did not lead to another layering transition to a monomolecular layer, but surface damage occurred instead (production of small mica flakes).29 For DDAB-coated mica surfaces, a two-layer film was obtained at the applied pressure P ) 3.0 MPa. We could not increase the applied load (pressure) for the DDAB-coated system because the surface damaged easily during sliding. This damage was presumably not due to the production of mica flakes but due to the DDAB monolayers coming off from the mica upon shearing, which formed small wear particles. Figure 3 shows the relationship between the shear stress (which equals the friction force divided by the contact area) and the sliding velocity at different numbers of molecular layers (different applied pressures), plotted on log-log scales. The results obtained from different substrate systems (bare mica and DDAB-coated mica) are plotted together. For the bare mica system, the shear stress increased with the decrease of the number of layers (increase of applied pressure). The effects of the number of layers (applied pressure) on the shear stress will be described later. The sliding velocity V dependence of the shear stress S can be fit by the following equation:

four three two two between DDAB monolayers

0.17 ( 0.00 0.13 ( 0.01 0.23 ( 0.01 0.18 ( 0.02

S∝VR

(1)

where R is a constant, which indicates whether the observed friction dynamics is purely “tribological” or involving “rheological” characters. The R values for each system obtained using eq 1 are listed in Table 1. The R parameter decreased at the layering transition from four (29) Israelachvili, J. N. In Fundamentals of Friction: Macroscopic and Microscopic Processes; Singer, I. L., Pollock, H. M., Eds.; Kluwer Academic Publishers: Norwell, MA, 1992; 351-385.

to three layers and then increased at the transition from three to two layers. The R parameter for the two layers between DDAB-coated mica surfaces was smaller than those for the two layers between bare mica surfaces, but rather close to those obtained for four layers between bare mica surfaces. The effects of the surface properties of substrate on the shear dynamics will be analyzed in the Discussion section. The shear stress increased with decreasing the number of molecular layers, but the rate of the increase along with the layering transitions was not constant, which is clearly shown in Figure 4 (for the bare mica system). The relationship between the shear stress and the applied pressure was plotted at two different sliding velocities. In this plot, the friction coefficient µ is obtained from the slope of the linear fit (Amontons’ law modified for molecularly smooth surfaces)4,26 according to

F ) F0 + µL

(2a)

S ) F/A ) F0/A + µL/A ) S0 + µP

(2b)

where F0 and S0 are constants, defined as the zero-load friction (adhesion contribution) and critical shear stress, respectively. For four-layer and three-layer films, the equation above was applicable and friction coefficients around 0.02-0.04 were obtained. However, the layering transition from three to two layers completely changed the shear properties: the shear stress increased by a factor of 6-8 and obviously deviated from the linear fits. This discontinuous change of the film properties was observed during sliding at V ) 0.007 µm/s and P ) 4.9 MPa (see Figure 3), which implies that a totally different sliding mechanism may appear when the molecules are squeezed out to two layers. Figure 5 shows the typical friction traces (friction force versus time plots) obtained in this study for the bare mica system; the effect of stopping and starting on the trace patterns is also included.9,26,30 For four-layer film (panel a), a constant kinetic friction force Fk was obtained during (30) Gee, M. L.; McGuiggan, P. M.; Israelachvili, J. N. J. Chem. Phys. 1990, 93, 1895.

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Figure 5. Typical friction traces (friction versus time plots) obtained for the bare mica system, showing the effect of stopping and starting on the trace patterns (sliding velocity V ) 0.07 µm/s). We observed two different types of friction traces. (a) When the thicknesses of the film are three layers and above, a “solidlike” friction trace is observed, characterized by the quick relaxation at stopping and appearance of the static friction force F ) Fs () Fk) when sliding is resumed. (b) When molecules are squeezed out to two molecular layers, the friction trace includes “viscous” characters: slow relaxation at rest and the lack of a static friction force at the restart of sliding. Note that the scales of the friction force for panels a and b are not the same. The two-layer film between DDAB-coated mica surfaces exhibited the “solidlike” friction traces similar to that shown in panel a.

steady sliding. When sliding was stopped, the force dropped quickly as a result of some relaxation processes in the film, and slow relaxation was continued during stopping. When sliding was resumed, the force immediately rose to a static friction force F ) Fs () Fk in Figure 5) and smooth sliding was observed again. It has occasionally been reported that a stiction spike was observed when the stopping time was longer than the characteristic “latency time”.9,26,30,31 However, we did not detect a spike in the experimental waiting time range (0-3600 s). The three-layer film between bare mica surfaces and two-layer film between DDAB-coated mica surfaces exhibited essentially the same friction traces (data not shown). On the other hand, the friction traces obtained from two layers between bare mica surfaces showed a different behavior (panel b). During steady sliding, the friction force showed smooth sliding (F ) Fk). When the sliding was stopped, relaxation processes occurred very slowly; the residual force decreased slowly and continuously with the stopping time in the range ∼3600 s. No static response was observed when the sliding was resumed. Discussion Layering Transitions and Friction Properties. As was already mentioned, the layering of molecules at surfaces and in confined geometries is commonly observed for regularly shaped liquids having low molecular weights; rather, polymer melts tend to form a disordered structure.1 One of the reasons for this is that the thicknesses of polymer-melt films under compression are usually de(31) Drummond, C.; Israelachvili, J. Macromolecules 2000, 33, 4910.

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termined by the radius of gyration of the molecules (Rg),32 which results in relatively large thicknesses compared with the molecular diameter. It is difficult for large (long) polymer molecules to fill the whole (thick) films by regularly ordered layers parallel to surfaces. However, PDMS studied here shows apparent layering transitions, which suggests that the thickness and structure of the film are mainly determined by the diameter of the siloxane chains. This is presumably due to the low chain entanglement effect of PDMS compared with hydrocarbon polymers coming from the flexible nature of the siloxane backbone and low intermolecular forces.33,34 A relatively large molecular diameter compared with hydrocarbon chains may also contribute to the layer formations. It is sometimes possible that a strong affinity between fluid molecules and substrate surfaces results in the layer formation. However, it is not considered to have a large effect on our systems because layering is observed also for a weak adsorbing substrate (DDAB-coated mica). Now the molecular mechanisms of the sliding of layered PDMS film are discussed. For the bare mica system, the observed shear behavior is very different between the film having thickness of three or more layers and that having two layers. Because of the high affinity between PDMS molecules and the mica substrate as was mentioned, the first layers adjacent to mica surfaces are strongly adsorbed onto substrates and cannot be removed with the maximum accessible pressures (∼10 MPa). Therefore, the shear property difference between films having thickness of three or more layers and those having two layers could be discussed from the viewpoint of whether the films have additional (nonadsorbed) layer(s) between two adsorbed layers. The four-layer film has two “mobile” layers in the middle part of the film, and three-layer film has one mobile layer; these two films exhibit essentially the same shear properties. The relationship between the shear stress and the applied pressure for the four-layer and three-layer films can be fit by one linear function (Figure 4 and eq 2b), indicative of the common sliding mechanisms (having the same friction coefficient). Friction traces imply “solidlike” sliding features such as quick relaxation at stopping and the appearance of static friction at the restart of the lateral motion (Figure 5). These observations suggest that shear of the four-layer and three-layer films is accomplished by the slipping at intermolecular layers. The effect of the sliding velocity on the shear stress (Figure 3) also suggests solidlike sliding behavior for the four-layer and three-layer films. The power of the shear stress-sliding velocity eq 1 (the R parameter) indicates whether the shear properties are solidlike (lateral motion is accomplished by the slipping of molecules) or liquidlike (rheological flow of molecules dominates the lateral motions). For an ideal friction system, R ) 0 (friction force is independent of sliding velocity, Amontons’ law), whereas R ) 1 for Newtonian fluids (shear force is proportional to sliding velocity). From this viewpoint, the R parameters for four and three layers are relatively smaller than that of a two-layer film, indicative of the large contribution of the intermolecular friction to the film properties. In addition, the R parameter for three layers is smaller than that of four layers, which suggests that decreasing the (32) Xu, L.; Ogletree, D. F.; Salmeron, M.; Tang, H.; Ma, X.; Gui, J. J. Chem. Phys. 2001, 114, 10504. (33) Alsten, J. V.; Granick, S. Macromolecules 1991, 23, 4856. (34) Demby, D. H.; Stoklosa, S. J.; Gross, A. In Synthetic Lubricants and High-Performance Functional Fluids; Shubkin, R. L., Ed.; Dekker: New York, 1993; Chapter 8.

Thin Films of Poly(dimethylsiloxane)

number of “mobile” layers shifts the dynamic phase of the system to a more “solidlike” state. Low friction of four-layer and three-layer films (µ ) 0.02-0.04) implies that slip occurs between molecular layers (“film slip”); no “wall slip” is expected. Because of the strong adsorption of PDMS molecules to the substrate, adsorbed layers are stuck to surfaces and immobile during sliding, which will be discussed further in the following. In addition, the low friction and easily expellable feature of mobile layer(s) may suggest that PDMS molecules in the layers tend to have a flat conformation and belong to a specific layer (low interdigitation), despite the relatively large molecular weight. Slipping may include rolling or shear-induced alignment of PDMS chains within the “mobile” layer planes.30 This might be one of the reasons that PDMS melts have unique performance as lubricants compared with hydrocarbon materials. When molecules are squeezed out to a final residual film two layers in thickness, the tribological features are completely changed from those of three layers and above. The applied pressure dependence of the shear stress deviates from the linear fits of four-layer and three-layer films (Figure 4), and the shear stress increases by a factor of 6-8. The friction trace (Figure 5) includes “viscous” characters (slow relaxation at rest and no static response at the commencement of sliding). In addition, the R parameter for the two-layer film is relatively larger than those of the four-layer and three-layer films (Table 1). These observations imply that a rather “viscous” molecular mechanism, such as the deformation of siloxane segments, might be involved during sliding in addition to the typical tribological mechanisms (rolling or aligning of chains). Such molecular mechanisms in the adsorbed layers are accompanied with the lateral motion (slippage) at the molecule/substrate interfaces. This slippage involves the breaking of adhesive junctions between molecular segments and mica substrates, resulting in a large friction force and wear (damage of mica surfaces). Wall slip generates a much larger friction force (shear stress) than intermolecular slip (film slip); this is the reason that we do not expect “wall slip” for four-layer and three-layer films. The effects of surface properties on the dynamics of layered films can be analyzed by the comparison of the results obtained from the bare mica substrate (strongly adsorbing surface) and from the DDAB-coated mica substrate (weak adsorbing surface). The amplitude of the shear stress for two layers between the DDAB-coated surfaces is apparently smaller than that for two-layer film between bare mica surfaces, but rather close to those for four-layer and three-layer films (Figure 3). The R parameter agrees with that for four layers (Table 1). In addition, a solidlike friction trace is observed, which indicates the slipping between layers (data not shown). Although the two layers are directly attached to each substrate surface, the DDAB coating on mica significantly reduces the adhesion between the PDMS molecules and the substrates. Therefore, the two layers are not adsorbed to substrates but behave as “mobile” layers upon shearing. This dynamic structure is similar to that of the four-layer film between bare mica substrates; the DDAB monolayers on each substrate correspond to the adsorbed first layers, and shear is accomplished by the slipping of the middle two “mobile” layers. The DDAB monolayers and the first PDMS layers adsorbed to mica surfaces for films having thicknesses of three layers and above may play the same role: weak adsorbing coating of the mica substrate. Because both produce CH3-terminated surfaces, shear mechanisms of

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Figure 6. Schematic illustrations of the dynamic layer structures of PDMS films. (a) When thicker than three molecular layers, the first layers adjacent to the mica substrates are strongly adsorbed on surfaces and immobile during sliding. Shear is accomplished by the slipping of “mobile” middle layer(s). The two layers between DDAB-coated surfaces (weak adsorbing surfaces, b) behave as the “mobile” layers. Therefore, the shear properties of systems a and b are very close to each other. For the two-layer film between bare mica surfaces (adsorbed layers in direct contact, c), shear involves the deformation of the adsorbed PDMS segments and wall slip, which result in the “viscous” dynamic features and surface damage.

“mobile” layers (middle part in the four-layer and threelayer films between bare mica surfaces and two layers between DDAB surfaces) are not very different. However, the amplitude of the friction (shear stress) is lower for the bare mica system. This is probably because (i) the density of the CH3 group at the substrate surface is higher for DDAB surfaces than that for adsorbed PDMS layers and (ii) adsorbed PDMS layers could have a “cushion” effect because of the large compressibility of siloxane chains.34 The molecular mechanisms of the sliding of layered PDMS films at different numbers of layers and different substrates are schematically shown in Figure 6. Heterogeneous Effective Viscosity. As was described in the Experimental Methods section, the SFA allows us to measure the true contact area A and dynamic film thickness (distance between substrate walls) D accurately during sliding. Because the geometry of two shearing surfaces in the SFA is the same as that of Couette flow (Figure 1), we can obtain the effective viscosity ηeff of intervening fluids by the following equation:

ηeff ) FD/AV ) S/γ˘

(3)

where F is the friction force, V is the sliding velocity, S is the shear stress, and γ˘ is the shear rate () V/D). This means that the friction of molecularly thin fluid films can be quantitatively described by their “viscosities”. This is one of the big advantages in using the SFA for tribological experiments. The effective viscosity calculation using eq 3 gives the average properties of whole films. However, as was already mentioned in the Introduction section, the dynamic properties of molecularly confined films are not uniform in the direction normal to the substrate because of the inhomogeneous density distributions (especially for layered fluids).35 Therefore, the “true” effective viscosity should be calculated by considering the heterogeneous lateral velocity distribution in the thickness direction and the “effective dynamic thickness”.16,17 For example, for the four-layer film studied here, the two first layers

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Figure 7. Effective viscosity (local viscosity, see Table 2 and text) obtained using eq 4 plotted against the “effective” shear rate. Solid symbols: bare mica systems. Open symbol: DDABcoated mica system. The data correspond to the results of Figure 3. Note that the effective viscosity of “mobile” layers is not very sensitive to the number of layers and surface properties of the substrate. Table 2. C and n Parameters for the PDMS Films at Different Numbers of Layers and Substrates, Obtained Using Eq 4a layers average viscosity four three two local viscosity four (two mobile layers) three (one mobile layer) two adsorbed two layers between DDAB monolayers

C

n

4.84 ( 0.00 5.03 ( 0.01 5.66 ( 0.02 4.80 ( 0.00 4.97 ( 0.01 5.66 ( 0.02 5.04 ( 0.02

0.83 ( 0.00 0.87 ( 0.01 0.77 ( 0.01 0.83 ( 0.00 0.87 ( 0.01 0.77 ( 0.01 0.82 ( 0.02

a Viscosity is calculated in two ways. Average viscosity is obtained using “total” film thicknesses. Local viscosity is obtained using “effective” thicknesses for each sliding system.

adjacent to substrates are immobile during sliding (as was already mentioned). Therefore, the “effective dynamic thickness” is not equal to the total film thickness (2.8 nm) but the thickness of the middle “mobile” layers (1.5 nm, obtained by subtracting the adsorbed layer thickness from the total film thickness); the velocity slope should be applied to the two middle layers. On the basis of this idea, the effective viscosity was calculated for the shear stresses shown in Figure 3, and the results were plotted on loglog scales, as is shown in Figure 7. We should note that the effective thickness and total thickness are the same for the two adsorbed layers between bare mica surfaces and the two layers between DDAB-coated mica surfaces. The effective viscosity decreases linearly with the increase in the shear rates (shear thinning) according to

log ηeff ) C - n log γ˘

(4)

where C and n are constants. According to the simple comparison between eq 1 and eq 4, we obtain n ) 1 - R. The C and n values for the each PDMS film are obtained using eq 4 and listed in Table 2 (expressed as the local viscosity). The average viscosity is also calculated using the total film thickness shown in Figure 2, and the results are included in Table 2. It is obvious that the n parameter represents whether the shear behavior is “tribological” or involving the “rheological” characters (as we already (35) Recent experiments by Granick and co-workers have revealed that the heterogeneous mobility of confined fluids was observed not only in the thickness direction but also within the planes because of the strong inhomogeneity of normal pressure for “Hertzian” contact (Mukhopadhyay, A.; Zhao, J.; Bae, S. C.; Granick, S. Phys. Rev. Lett. 2002, 89, 136103).

discussed by the R parameter). For Newtonian fluids, n ) 0, and for ideal friction systems, n ) 1. The mobile layer(s) of four-layer and three-layer films have relatively larger n values than two adsorbed layers, indicative of more solidlike sliding behavior. In addition, the C and n values are not very sensitive to the number of mobile layers or surface properties of the substrate, indicative of a common molecular mechanism during shear (slipping at intermolecular layers). As was already mentioned, some recent works17,20 warned that solidlike properties obtained for molecularly confined fluids mainly probed the first adsorbed layers, and the middle part of the film behaved as a bulklike liquid. However, this probably does not apply to our results. There are few differences in the C and n values for fourlayer and three-layer films between the average viscosity and the local viscosity, which suggests that the average dynamic properties obtained here mainly describe the behavior of the middle (mobile) part of the film. Further, the middle part of the film exhibits rather solidlike dynamic features. These findings suggest that the average viscosity calculated using the total film thickness should be an appropriate quantitative parameter to describe the shear properties of confined PDMS films. It is not always easy to know the “effective” dynamic thickness of confined fluids experimentally. Therefore, the average effective viscosity (calculated using the total film thickness) has been used by a number of authors to discuss the molecular mechanisms of the dynamics. The discussion given previously could support the validity of the finding on the confined fluid dynamics discussed in the literature using the average effective viscosity as a quantitative parameter. In general, increasing confinement shifts the dynamic properties of the systems to a more “solidlike” state. However, the PDMS film studied here exhibits the opposite behavior. Solidlike dynamic features such as static responses observed for four-layer and three-layer films disappear in the final residual film two layers in thickness. This liquidlike shift of the dynamic properties due to confinement has never been reported for hydrocarbon materials. This unique observation may come from the characteristic features of PDMS melts, such as the large flexibility of the siloxane backbone (free rotation of molecules along the Si-O and Si-C bond axes) and greater intermolecular distances,34 which lead to the capability of the deformation of molecular segments even when adsorbed on surfaces. Further Comparison with Previous Works. The literature data of the friction coefficient µ of the thin PDMS films obtained using SFA are higher than that obtained from Figure 4. Israelachvili reported the µ value for the PDMS melt (Mw ) 3700) as 0.42.29 McGuiggan and others reported 0.48 for PDMS (Mw ) 3700) at a sliding velocity V ) 1 µm/s.36 The latter value was obtained from the film having thicknesses from 2.0 to 1.5 nm (three to two molecular layers), and they did not observe any abrupt shear property changes along with the layering transitions. We cannot fully explain this discrepancy. However, if we disregard the effect of the layering transitions on the shear properties in Figure 4 and apply eq 2b directly to all the data points, we obtain µ ) 0.26 for V ) 0.014 µm/s and µ ) 0.45 for V ) 0.14 µm/s, which are very close to the literature data. Therefore, we believe that the friction coefficient near 0.4 in the literature could be (36) McGuiggan, P. M.; Zhang, J.; Hsu, S. M. Tribol. Lett. 2001, 10, 217.

Thin Films of Poly(dimethylsiloxane)

attained for PDMS films whose sliding features are dominated by the adsorbed layers.37 Conclusions The shear properties of the molecularly thin films of PDMS were investigated by use of the SFA, and the results were analyzed from the viewpoint of the relationship between the shear properties and the thicknesses (the number of layers). The following conclusions can be drawn from our results: (i) When thicknesses of the films are three molecular layers and above, the first layers adjacent to each mica substrate are strongly adsorbed on substrates and immobile during sliding. Shear is accomplished by the slipping of “mobile” middle layer(s), which results in the solidlike sliding and low friction. (ii) Increasing pressure and simultaneous lateral motions squeeze out the molecules to a final residual film two molecular layers in thickness (adsorbed layers in direct contact), whose shear properties include “viscous” characters. The amplitude of the friction (shear stress) is 6-8 (37) The molecular weight of the PDMS melt studied here is much larger than those investigated in the two papers. However, we believe that this does not produce a large difference in the friction coefficients. Generally, molecular weights strongly affect the radius of gyration (Rg) of polymers, which governs the thickness (and dynamic properties) of the compressed polymer film. However, as was described in the text, the thicknesses of PDMS films (and resulting film properties) are dependent on the molecular diameter and are not sensitive to Rg. Therefore, PDMS melts having different molecular weights could have comparable friction coefficients.

Langmuir, Vol. 19, No. 18, 2003 7405

times larger than that of the films having “mobile” middle layers because the shear of the two-layer film involves the deformation of adsorbed PDMS segments and wall slip. (iii) The surface modification of mica substrates by the self-assembly deposition of hydrocarbon monolayers reduces the PDMS molecule-substrate interaction strength; the first layers adjacent to substrate surfaces are now “mobile” during sliding. (iv) For the PDMS film, increasing confinement (decreasing the number of layers) shifts the dynamic properties from “solidlike” to rather “viscous” features (final twolayer film), which is a very different behavior compared with typical hydrocarbon fluids. This is probably due to the unique characteristics of PDMS melts, such as the large flexibility of the siloxane backbone and greater intermolecular distances. (v) The effective viscosity calculated using the Couette flow equation by inserting total film thickness as D (average viscosity) is not very different from that obtained by the “effective dynamic thickness” (local viscosity), which suggests that the average viscosity can be used as the appropriate quantitative parameter in SFA dynamic measurements to describe the shear properties. Acknowledgment. The author is grateful to G. Nakamura for valuable discussions and to Kao Corp. for permission to publish this paper. LA034511L