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Friction of Gels. 3. Friction on Solid Surfaces Jianping Gong, Yoshiyuki Iwasaki, and Yoshihito Osada* Graduate School of Science, Hokkaido UniVersity, Sapporo 060-0810, Japan
Kazue Kurihara and Yasuhiro Hamai Institute for Chemical Reaction Science, Tohoku UniVersity, 2-1-1 Kitahira, Aoba-ku, Sendai, Miyagi 980-77, Japan ReceiVed: January 22, 1999; In Final Form: April 10, 1999
Frictions of several kinds of hydrogels, poly(vinyl alcohol) gel, gellan gel, poly(2-acrylamido-2-methylpropanesulfonic acid) gel, and its sodium salt gel, sliding on glass plates as well as on Teflon plates have been investigated both in air and in water. The frictional force and its dependencies on the load are quite different depending on the chemical structures of the gels, surface properties of the opposing substrates, and the measurement condition. The gel friction is explained in terms of interface interaction, either attractive or repulsive, between the polymer chain and the solid surface. Surface adhesion between glass particles and gels measured by atomic force microscopy showed a good correlation with the friction, which supports the polymer repulsion-adsorption model proposed by authors.
I. Introduction One of the most rapidly growing areas of tribology is in the field of biosystems, in particular, in the human and animal joints.1-5 Animal joints have friction coefficients in the range 0.001-0.03, which are remarkably low even for hydrodynamically lubricated journal bearings.1 However, there are several subjects to be addressed. One of them is to explain why the cartilage friction of the joints is so low even under such conditions as those in which the pressure between the bone surfaces reaches values as high as 3-18 MPa and in which the sliding velocity is never greater than a few centimeters per second.1 Under such conditions, the lubricating liquid layer cannot be sustained between two solid surfaces and the hydrodynamic lubrication does not work. The cartilage that consists of a three-dimensional collagen network filled with a synovial fluid1-5 provides the low friction of joints. Cartilage cells synthesize a complex extracelluar matrix (ECM); the weight bearing and lubrication properties of cartilage are associated primarily with this matrix and its high water content. The main macromolecular constituents of extracelluar matrix are the proteoglycan, aggrecan, and the cross-linked network of collagen fibrils.6 We consider that the role of solvated polymer network existing in extracellular matrix as a gel state is critically important in the specific frictional behavior of cartilage. To investigate the general features in tribology of a solvated polymer matrix, the friction of various kinds of hydrogels should be investigated. A polymer gel consists of an elastic cross-linked macromolecular network with a liquid filling the interstitial space of the network. The network holds the liquid in place through its interaction forces and so gives the gel solidity and coherence, but the gel is also wet and soft and capable of undergoing large deformation. A gel is neither a solid nor a liquid but has some features of both. Because of their specific structure, gels exhibit a variety of unique behaviors such as phase transition,7 chemomechanical behavior,8 presence of unfrozen water,9 shape
memory effect,10 etc. Hydrogel has a great potential as a soft and wet stimuli-responsive material.11 In a previous short letter,12 we have reported the unique features of frictional behavior of polymer gels when slid against themselves and against solid surfaces in air. The frictional force of gels showed specific dependencies on the load W and the sliding velocity V, which are totally different from those of solids. Most importantly, the coefficient of friction of gels, µ, changes in a wide range and exhibits very low values (µ ≈ 0.001), which cannot be obtained from the friction between two solid materials. A model describing the frictional force produced when a polymer gel is sliding on a solid surface has been proposed from the viewpoint of solvated polymer repulsion and adsorption mechanism at a solid surface.13 In this paper, we report in detail the frictional behavior of various gels on solid substrates both in air and in water. The main gel samples used in this work are the following: nonionic synthetic gel, poly(vinyl alcohol) (PVA); partially charged polysaccharide gel, gellan; fully charged polyelectrolyte gel, poly(2-acrylamido-2-methylpropanesulfonic acid) (PHAMPS) and its sodium salt (PNaAMPS). We attempt to explain the gel frictions on solid surfaces in terms of the adhesion-repulsion model together with the experimental results by atomic force microscopy (AFM). II. Experiments Materials. PVA (molecular weight: Mw ) 90 000) was purchased from Wako Chemical Industries, Ltd. and used without further purification. Gellan was provided by San-engen FFI Co., Ltd. and was purified to deacetylate it before use. The metal content in this sample was analyzed and are as follows: K, 20 800 µg/g; Na, 1900 µg/g; Ca, 5120 µg/g; Mg, 1460 µg/g. 2-Acrylamido-2-methylpropanesulfonic acid (HAMPS) (Tokyo Kasei Co., Ltd.) was used as received. Its sodium salt (NaAMPS) was obtained by neutralization of HAMPS with sodium hydroxide (Junsei Chemical Co., Ltd.). N,N′-Methyl-
10.1021/jp9902553 CCC: $18.00 © 1999 American Chemical Society Published on Web 05/18/1999
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CHART 1
Figure 1. Tribometer used for gel friction measurement.
enebisacrylamide (MBAA) (Tokyo Kasei Co., Ltd.), used as a cross-linking agent, was recrystallized from ethanol. Potassium persulfite (Tokyo Kasei Co., Ltd), which was used as a radical initiator, was recrystallized from water. Gel Preparation. Physically cross-linked PVA gel was prepared by a repeated freezing (-20 °C) and thawing (25 °C) method from a prescribed PVA aqueous solution (5-10 wt %). The gellan solutions were prepared by heating the mixture of powdered gellan and the distilled water above 90 °C and poured into the cell maintained at a given temperature, with a great care for no mixing of bubbles. Physically cross-linked gellan gel was prepared by cooling its 3 wt % aqueous solution from 90 to 4 °C and was left standing for 2 days at room temperature. Chemically cross-linked poly(2-acrylamido-2-methylpropanesulfonic acid) (PHAMPS) and its sodium salt (PNaAMPS) gels were prepared by radical polymerization of a 1.0 mol/L aqueous solution of HAMPS(or NaAMPS) monomer in the presence of a calculated amount of MBAA and 0.001 mol/L potassium persulfite. The polymerization was carried out at 60 °C for 12 h under a nitrogen atmosphere. The detailed procedure of the polymerization was described elsewhere.8,11 All samples were prepared between two parallel glass plates separated by a spacer 5 mm thick (PVA, gellan) or 2 mm thick (PHAMPS, PNaAMPS) to give sheet-shaped gels. After gelation, PVA gel and gellan gel were used as prepared. PHAMPS and PNaAMPS gels were immersed in a large amount of water for 1 week to equilibrate and wash away the residual chemicals. At the equilibrium swelling state, the thickness of the PHAMPS and PNaAMPS gels were 5 and 4 mm, respectively. The molecular structures of the main polymers used in this work are shown in Chart 1. In addition to the mentioned samples, polysaccharide gels of agarose and κ-carrageenan were also used in this work. The detailed sample preparation procedures were described in a separate paper.14 Measurements. The friction force of a gel was measured in air and in water at room temperature using a commercialized tribometer (Heidon 14S/14DR, Shindom Sci., Co.) that is shown in Figure 1. The as-prepared surface of the gel was used for the measurements. Samples of 5 mm thickness were cut into certain size for usage. Except for the study of the dependence of friction on gel size, the size of the PHAMPS and PNaAMPS gels measured in air were 2 cm × 2 cm, and other samples were 3 cm × 3 cm. The sample was embedded in a square frame of adjustable size attached on the upper board and pressed against a piece of solid surface that was fixed on the lower board and was driven to move horizontally and repeatedly at a prescribed velocity at a distance of 90 mm. As the opposing
Figure 2. AFM equipment used to measure the surface adhesive force between gels and the glass sphere.
solid surface, glass and poly(tetrafluoroethylene) (Teflon) plates were used in this study. These plates were carefully washed with a cleaner and rinsed in distilled water. They were dried in air before usage. For one set of experiments, the measurement was carried out using one sample. For example, the load dependence measurement was carried out using one sample, starting from the lower load and increasing the load continuously without separating the two sliding surfaces during the interval of measurement. The sliding velocity measurement was also carried out in the same way. The weight of the gel sample itself was neglected in calculating the load dependence, since the former is negligibly small in comparison with the latter. The amount of water contained in gels is characterized by the parameter q, the degree of swelling, which is defined by q ) (swollen sample weight)/(dry sample weight). The weight percentage of water in a gel c can be obtained using the relation of c ) (q - 1)/q × 100%. The compressive modulus E of the gels was measured using a tensile-compressive tester (Tensilon, Orientec Co.). A square gel of 3 cm × 3 cm in size and 5 mm in thickness was set on the lower plate and compressed by the upper plate that was connected to a load cell at a velocity of 1 mm/min at room temperature. From the obtained stress-strain curve, we have calculated the compressive modulus of each gel at a strain of less than 1%. Forces between glass surfaces and gels were measured on an atomic force microscope SPA300:SPI3700 model (Seiko Instruments Inc.) following the procedures by Ducker et al.15,16 As shown in Figure 2, a soda lime glass sphere of 13 ( 3 µm radius (R) (Polyscience Inc.) was used as a colloidal probe. The sphere was attached to the top of a rectangular cantilever of 100 µm length (RC800PSA, Olympus) by epoxy resin (Epikote 1004, Shell), and piezoforce displacement profiles between the glass sphere and a gel in pure water were recorded. A sliced piece of gel was attached to the scanner table. Prior to the force measurement, the glass sphere glued to the cantilever was
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cleaned by immersion in 1 N HNO3. The aqueous phase was exchanged using the peristaltic pump. The spring constant (k) of the cantilevers used was 1.0 N/m. The detailed procedures of the measurement were described elsewhere.17 A difference from previous procedures was that precise determination of the separation distance was difficult in the present work because of low elastic compressibility of thick gel samples. We set a break point from the linearity in the logarithmic plot of the force (upon compression) against the cantilever displacement as a zero displacement (corresponding approximately to the contact position between the colloidal probe and the gel surface) for ionized gels (PHAMPS, PNaAMPS, gellan). For a nonionic gel of PVA, a displacement where the repulsion appeared upon compression was taken as zero. III. Results and Discussion III.1. Friction Force. a. In Air. As described in the previous paper,12 the frictional force F shows several unstable runs at the beginning of measurement due to relaxation of the normal strain given by the load. However, it comes to exhibit constant values under a constant loading and sliding velocity. We observed no distinct change in the friction of gel samples with thicknesses from 4 to 8 mm during a continuous run for 120 min. Accordingly, the studies of the dependencies of friction on load, surface contact size, and sliding velocity have been carried out using samples with a thickness of 5 mm. Figure 3a shows the relations between the normal load and the friction force for PVA, the gellan, PHAMPS, and PNaAMPS gels being slid on the glass plate at a sliding velocity of 7 mm/ min. The measurement was performed in air, and the load was applied up to the value over which the gels were collapsed. The friction coefficient µ, which is defined as the ratio of the frictional force to load applied, is calculated and shown in Figure 3b. It is seen that the frictional behavior of these gels strongly depends on the chemical structure of the gels. F is almost constant (gellan gel), slightly increases (PVA gel), and strongly dependent (PHAMPS) with the load over the observed range of load. The F of the PNaAMPS gel showed a linear increase with the load with a value 1 order of magnitude lower than that of other gels. The friction coefficient µ for these gels accordingly shows unique load dependencies, which is quite different from those of solids. The µ of the PNaAMPS gel is constant over the change of the load, similar to those of rubber, but the value of µ is as low as 0.002, which is 2 orders of magnitude lower than those of solids. The µ of PVA, gellan, and PHAMPS gels decreases with an increase of the load. These results demonstrate that the gel friction does not simply obey Amonton’s law18,19 of F ) µW, in which µ is a material constant, and show that the chemical structures of gels have a strong effect on the friction behavior. As shown in Figure 3b, PHAMPS and PNaAMPS gels are only different in their counterions, but they gives a striking difference in their friction on the glass surface. The linear dependence of friction on load established in solid friction is explained in terms of the yielding mechanism; i.e., the solid surface is not molecularly flat and the real contact area between two surfaces increases with an increase of load due to yielding. Thus, the friction has no dependence on the apparent contact area of the two solid surfaces, and Amonton’s law is held.19 To elucidate the feature of interface contact between the gel and the opposing plate, the frictional force of various kinds of gels was measured by varying the contact area of gel A under a constant load W. We found that the friction of the gel is
Figure 3. Dependencies of friction on load (a), the coefficient of friction on load (b), and the dependence of friction on the average strain (c) for various kinds of hydrogels slide on glass substrate. Sliding velocity: 7 mm/mim. Sample sizes for PVA, gellan, and rubber, 3 cm × 3 cm; PAMPS and PNaAMPS, 2 cm × 2 cm. Compressive modulus E: PVA, 0.014 MPa; gellan, 0.06 MPa; PHAMPS, 0.25 MPa; PNaAMPS, 0.35 MPa; rubber, 7.5 MPa. Degree of swelling q: PVA, 17; gellan, 33; PHAMPS, 21; PNaAMPS, 15. The measurement was carried out in air.
strongly dependent on the apparent contact area A. If we denote F ∝ WRAβ, we find a correlation between R and β, as shown in Figure 4. The figure shows that β ≈ 1 - R, which indicates that
F ∝ APR
(1)
where P ) W/A is the average normal pressure and R ) 0 - 1, depending on the chemical structure of the gel. This result demonstrates that the frictional force per unit area is related with the normal pressure P instead of the load W. However, from the above result, we cannot clarify whether the gel surface makes contact with the substrate on a molecular level and whether the apparent contact area equals the real contact area.
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Figure 4. Relation between R and β, where R and β stand for the exponents of the relation F ∝ WRAβ. R was measured at A ) 9 cm2; β was measured at W ) 0.98 N. Sliding velocity: 180 mm/min. Degree of swelling: PVA, 20; gellan, 33; κ-carageenan, 33; agarose, 50; PHAMPS, 17. The measurement was carried out in air.
Figure 5. Relations between gel friction and the degree of swelling. Load: 4.9 N (PVA, gellan); 9.8 N (PHAMPS, PNaAMPS). Gel size: 3 cm × 3 cm (PVA, gellan), 2 cm × 2 cm (PHAMPS, PNaAPMS). Velocity: 30 mm/min. The measurement was carried out in air.
For solid friction, eq 1 is also valid, with R ) 1. Therefore, we may consider that the R value might be related to the compressive modulus E. A polymer gel is easily deformable, owing to the presence of a large amount of water. Therefore, a small pressure would be sufficient to cause the gel deforming to a molecular level to make contact with the opposing surface. To elucidate the effect of the compressive elastic modulus E on the R value, the average strain of the gel under the pressure λ ) P/E is shown in Figure 3c. As shown in the figure, the strains of gels under the experimental load range are more than several percent higher than that of a rubber, needless to say, much higher than that of solid. Since the surface roughness of gels and the glass should be much lower than this large deformation, it is reasonable to believe that the whole gel surface makes contact with the substrate. All the gel samples were measured under a similar strain range; nevertheless, they showed quite different pressure dependencies. This indicates that the different pressure dependence of gel friction is not related to the large deformation of the gel. The friction of gel showed clear dependence on the sliding velocity, as shown in the previous paper.12 The velocity dependence suggests that the hydrodynamic lubrication might make an important contribution in the gel friction. The amount of water absorbed in the gel should play an important role for exhibiting the low friction. The influence of gel water content on the friction is shown in Figure 5. All the samples showed a decrease in the frictional force with an increase in the degree of swelling of the gel. This suggests that the higher the water content, the more the water is squeezed out of the gel under a
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Figure 6. Load dependence of gel friction on various substrates measured in water. Sliding velocity: 90 mm/min. Gel size: PVA, 3 × 3 × 0.8 cm3; PHAMPS, 3 × 3 × 0.6 cm3. Degree of swelling: PVA, q ) 10; PHAMPS, q ) 15. Elastic modulus: PHAMPS, 1.0 MPa; PVA, 0.024 MPa.
certain load. This water might form a thin film layer and serves as a lubricator, leading to a boundary lubrication or even to a hydrodynamic lubrication. Among these gels, PNaAMPS gel shows a most significant decrease in frictional force with an increase in the degree of swelling, while the PHAMPS gel, like the PVA and gellan gels, has a less significant dependence on the degree of swelling. Since PHAMPS gel has the same chemical structure of the polymer network as that of the PNaAMPS gel, this significant difference again suggests that the simple weeping mechanism is not enough to explain the gel friction. b. In Water. To investigate the effect of water, the gel friction was further investigated in water media. The friction coefficients of gels in water are much smaller than those in air. F obtained in water with a sliding velocity of 7 mm/min (the velocity in Figure 3) was too low to measure by the tribometer. To increase the absolute friction value, we had to perform the measurement with an increased sliding velocity of 90 mm/min, which is more than 1 order of magnitude larger than that in Figure 3. Figure 6 shows the load dependence of PVA and PHAMPS gels on the glass surface in water. The friction of the PVA gel shows almost the same load dependence as that in air. The frictional force of the PHAMPS gel is much lower than that of PVA with two load dependence profiles: it shows a strong load dependence at low load and a less strong load dependence at high load that is similar to behavior of PVA. Such a load dependence of friction was reversibly observed when increasing or decreasing the load. However, if PHAMPS is allowed to slide on a Teflon plate, the friction-load profile remarkably changes. As shown in Figure 6, the behavior of PHAMPS on Teflon is similar to that of PVA on glass, showing a monotonic increase with the load. These data demonstrate that besides the chemical structure of the gel, the surface property of the opposing substrate is crucial in friction, and the interaction of the gel network with the substrate should be taken into account. The above experimental results show that the frictional behaviors of the gel are strongly dependent on the chemical structure of the gel and on the opposing substrate. A mechanism in terms of hydrodynamic lubrication, weeping, or boundary lubrication can, to some extent, explain some of the experimental results but cannot consistently explain all of the phenomena. Apparently, the specific frictional behavior of the gel should be attributed to the structural feature of the gel, that is, the strongly water-solvated polymer network. A theoretical model for the friction of gel on the solid surface has been proposed
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Figure 7. Relations between the displacement of AFM cantilever and the interaction force between the glass particle attached to the AFM tip and the gels. Degree of swelling: PVA, 20; gellan, 33; PHAMPS, 21; PNaAMPS, 15. The measurement was carried out in water.
from the viewpoint of solvated polymer repulsion and adsorption mechanism on a solid surface.13 The model says that the polymer network on the surface of the gel will be repelled from the surface if it is repulsive or will be adsorbed onto the solid surface if it is attractive. In the former case, the viscous flow of solvent between the solid surface and the polymer network will make a dominant contribution to the frictional force. In the latter case, however, the adsorbing chain will be stretched when the solid surface makes a motion relative to the gel. The elastic force increases with the deformation and eventually detaches the adsorbing polymer network from the substrate, which in turn appears as the frictional force. The model predicted the following. (1) When the substrate is repulsive, the frictional force is lower than the attractive case, and it linearly increases with the pressure and velocity when the compressive strain (normal load) is not very high. (2) When the substrate is attractive, the frictional force increases with the attraction strength. For weak attraction, the pressure dependence of the frictional force is much weaker than in the repulsive case. It becomes stronger when the attraction strength increases. The frictional force exhibits a peak when the velocity is increased. According to this model, the low frictional force and the strong load dependence for the PNaAMPS gel on a glass surface suggests a repulsive interaction between the gel and the solid. This repulsive interaction might be attributed to the negativenegative charge interaction between the anionic gel and the glass surface, since, as is well-known, it is negatively charged in water.20 Also, the interaction between the PVA gel and glass might be attractive, since PVA gel showed a much higher friction with a less significant load dependence. The gellan gel might also have an attractive interaction but should be even weaker than that of PVA, since it has a lower friction than PVA and the load dependence is also weaker than PVA. III.2. Adhesive Force. To verify these suggestions, the adhesive forces of these gels with the glass surface have been
measured using the colloidal probe atomic force microscopy. Figure 7 shows the force-displacement curves of various samples with the glass sphere. Figure 7 clearly shows that the nonionic PVA gel has no appreciable force with the glass probe upon compression (or inward measurement), while it exhibits an adhesive force distinctively in outward measurements examining the adhesive force. Gellan gel has a weak repulsion, while PHAMPS and PNaAMPS gels show a strong electrostatic repulsion with the substrate, as expected. The weak repulsion between gellan and the glass could be attributed to the low charge density of -COO- in the gellan gel, while the strong repulsion for PHAMPS and NaAMPS gels should be associated with the high charge density of sulfonic acid groups on the gels. The results of AFM measurement coincides well with that of the frictional force, which increases in the order PNaAMPS < gellan < PVA in air or PHAMPS < PVA in water. That is, the stronger the repulsion, the lower the friction. An attractive interaction leads to a higher frictional force than that of repulsion. These results are quanlitatively in agreement with the theoretical prediction. From the above discussion, it is clear that the low friction of the PHAMPS gel on a glass plate in water (Figure 6) is due to the electrostatic repulsion between the PHAMPS gel and the glass plate. The high friction of the PHAMPS gel on a Teflon plate (Figure 6) should be attributed to the attractive interaction between the PHAMPS polymer network and the Teflon substrate, since in this case, no electrostatic repulsion exists and van der Waals interaction is prevailing. As shown in Figure 3, the friction of the PHAMPS gel measured in air was much higher than that of the PNaAMPS gel. However, the friction of PHAMPS measured in water is low in comparison with that of PNaAMPS, which is in agreement with the AFM result in that both gels showed a strong repulsion in water. The large difference of the PHAMPS gel friction between water and air suggests that the interaction
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between the PHAMPS gel and the glass surface is different in the different medium. This should be attributed to the pH dependence of the surface property of glass. The surface SiOgroup density of glass decreases with a decrease in pH and the glass surface becomes neutral at pH 3-4.21 Thus, the PHAMPS gel has an electrostatic repulsion with SiO- groups of the glass surface in the presence of large amounts of water. However, the proton of the PHAMPS gel, which is a strong polyacid, might interact with the glass surface in air, which annihilates the negative charges of glass surface. Thus, the electrostatic repulsion is suppressed and the friction force increases. On the other hand, a repulsive force always exists between the PNaAMPS gel and the glass surface either in air or in water. These results again demonstrate the predominant importance of the interface interaction in the gel friction. According to the repulsion-adsorption model, a water layer is formed at the interface when the gel-substrate interaction is repulsive and the friction dominated by the hydrodynamic lubrication. Supposing the water layer thickness is h, which is a function of pressure, the frictional force is expressed by19,20
F ) ηνA/h
(2)
Here, η is the viscosity of liquid existing between the two surfaces, A is the surface area, and V is the relative velocity of the two sliding surfaces. From eq 2, the equivalent thickness h of the water layers can be estimated from the frictional force shown in Figures 3 and 6. By use of the value for bulk water viscosity (η ) 10-3 N s m-2), h was estimated to be 4-10 nm for the PNaAMPS gel and 1-3 nm for gellan gel in air from Figure 3. The latter seems to be too thin to behave as a perfect hydrodynamic water layer. This corresponds well to the AFM result, which showed a weak repulsion between the gellan and the glass. h for the PHAMPS gel sliding in water, which strongly depends on the load, is as large as 700-20 nm in the low-load range and 20-5 nm in the high-load range, as estimated from Figure 6. The formation of a much thicker water layer under a small load should be attributed to the strong electrostatic repulsive between the PHAMPS gel and the glass surface. When the load is increased, the two repelling surfaces approach each other and the water layer becomes thinner, leading to a higher friction. The much lower frictional forces in water than those in air should be attributed to the presence of abundant amounts of water that largely suppresses the attraction of the polymer to the solid surface and enhances the formation of the solvent layer. However, a water layer of 700 nm is considered to be too thick to be formed under the investigated pressure range. The transient process should be taken into consideration to estimate the water layer thickness. Detailed studies of the electrostatic repulsive case measured in water will be reported in a separate paper.22
IV. Conclusion Under the investigated experimental conditions, the magnitude of the gel friction on glass increases in the order of PNaAMPS < gellan < PVA. This result is compared with the surface adhesion forces obtained by using AFM. PNaAMPS showed a strong electrostatic repulsion with the glass surface, and gellan has a weak repulsive interaction, while PVA showed an attraction force. These results suggest that the sliding friction of gels is closely related to the polymer chain-substrate interaction and supports the theoretical prediction that the friction of a gel is dominated by the hydrodynamic lubrication mechanism when the gel-substrate interaction is repulsive and by the adhesion mechanism when the interaction is attractive. Acknowledgment. This research was supported by Grantin-Aid for the Specially Promoted Research Project “Construction of Biomimetic Moving System Using Polymer Gels” from the Ministry of Education, Science and Culture, Japan. We thank Mr. Masashi Mizukami for his assistance for the AFM measurement. We also thank Mr. Go Kagata for his preparation of AFM samples. References and Notes (1) McCutchen, C. W. Wear 1962, 5, 1. (2) McCutchen, C. W. Lubrication of Joints, The Joints and SynoVial Fluid; Academic Press: New York, 1978; Vol. 10, p 437. (3) Dowson, D.; Unsworth, A.; Wright, V. J. Mech. Eng. Sci. 1970, 12, 364. (4) Ateshian, G. A.; Wang, H. Q.; Lai, W. M. J. Tribol. 1998, 120, 241. (5) Hodge, W. A.; Fijian, R. S.; Carlson, K. L.; Burgess, R. G.; Harris, W. H.; Mann, R. W. Proc. Natl. Acad. Sci. U.S.A. 1986, 83, 2879. (6) Buschmann, M. D.; Grodzinsky, A. J. J. Biomech. Eng. 1995, 117, 179. (7) Tanaka, T.; Nishio, I.; Sun, S. T.; Nishio, S. V. Science 1973, 218, 467. (8) Osada, Y.; Okuzaki, H.; Hori, H. Nature 1992, 355, 242. (9) Woessner, D. E.; Snowden, B. S. J. Colloid Interface Sci. 1970, 34, 290. (10) Osada, Y.; Matsuda, A. Nature 1995, 376, 219. (11) Osada, Y.; Gong, J. P. AdV. Mater. 1998, 10, 827. (12) Gong, J. P.; Higa, M.; Iwasaki, Y.; Katsuyama, Y.; Osada, Y. J. Phys. Chem. B 1997, 101, 5487. (13) Gong, J. P.; Osada, Y. J. Chem. Phys. 1998, 109, 8062. (14) Iwasaki, Y.; Gong, J. P.; Osada, Y. J. Phys. Chem., submitted. (15) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature 1991, 353, 239. (16) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Langmuir 1992, 8, 1831. (17) Ishiguro, R.; Sasaki, D. Y.; Pacheco, C.; Kurihara, K. Colloid Surf. A 1999, 146, 329. (18) Amontons, M. Mem. Acad. R. Sci. 1699, 206. (19) Adamson, A. W. Physical Chemistry of Surfaces; John Wiley & Sons: New York, 1990. (20) Persson, B. N. J. Sliding Friction, Physical Principles and Applications; Springer: Berlin, 1998. (21) Shah, G.; Dubin, P. L.; Kaplan, J. I.; Newkome, G. R.; Moorefield, C. N.; Baker, G. R. J. Colloid Interface Sci. 1996, 183, 397. (22) Gong, J. P.; Kagata, G.; Osada, Y. J. Phys. Chem., 1999, 103, 6007.
