J. Phys. Chem. B 1997, 101, 5487-5489
5487
Friction of Gels Jianping Gong, Megumi Higa, Yoshiyuki Iwasaki, Yoshinori Katsuyama, and Yoshihito Osada* DiVision of Biological Sciences, Graduate School of Science, Hokkaido UniVersity, Sapporo 060, Japan ReceiVed: April 16, 1997; In Final Form: May 22, 1997X
The sliding friction of various kinds of hydrogels has been investigated, and it has been found that the frictional behaviors of these hydrogels do not conform to Amonton’s law F ) µW, which well describes the friction of a solid. Instead, the friction force F of the gel shows slight dependence on the load W in the investigated load range, while it strongly depends on the sliding velocity. Additionally, the frictional coefficient µ of the gel reaches a value as low as ∼10-3, which is smaller than those observed in solid materials.
1. Introduction 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. The gel state is neither solid nor liquid but has some features of both. Because of its specific structure, a gel exhibits a variety of unique behaviors such as phase transition,1 specific adsorption equilibrium,2 presence of unfrozen water,3 chemomechanical behavior,4 etc. Animal cartilage consists of a three-dimensional collagen network filled with a synovial fluid and has a very low friction coefficient.5 Thus, some attempts have been made to use poly(vinyl alcohol) (PVA) gel membrane as artificial articular cartilage in artificial joints made of polyethylene.6,7 These facts have inspired us to systematically investigate the frictional behaviors of a gel: how does a gel conform to the law of friction? Amonton’s law says that the frictional force F between two solids is proportional to the load W forcing them together, F ) µW.8 According to this law, the proportional coefficient µ, known as the frictional coefficient, depends on neither the sliding velocity nor the apparent contact area of two surfaces but depends only on the moving materials. µ usually lies in a range of 0.5-1.0.9 The obtained frictional forces of the gels, however, show slight dependence on the load W in the investigated range but strongly depend on the sliding velocity ν. Most importantly, these gels have frictional coefficients µ of ∼10-3, which is much lower than that observed in friction between solids. 2. Experimental Section Gellan and κ-carrageenan gels were prepared by conventional method, i.e., by cooling down their 3 wt % aqueous solutions from 90 to 4 °C and were left standing for 2 days at room temperature. Konjak gel (about 2 wt %) was purchased and used as received. PVA gel was prepared by the repeated freezing (-20 °C) and thawing (25 °C) method from 13 wt % aqueous solution of commercial PVA (molecular weight 9 × 104). Poly(2-acrylamido-2-methylpropanesulfonic acid) (PAMPS) (5 wt %) and its sodium salt (PNaAMPS) (4 wt %) gels were synthesized by the same procedure described in the previous paper.2 Samples were prepared in a laboratory-made glass mold * Corresponding author. E-mail:
[email protected]. X Abstract published in AdVance ACS Abstracts, July 1, 1997.
S1089-5647(97)01311-4 CCC: $14.00
Figure 1. Time profiles of the frictional force for gels sliding at a constant velocity of 30 mm/min (open symbols) or under a constant loading of 10 N (closed circles). (O) PVA gel, (3) PAMPS gel, and (0) gellan gel under various loads indicated in the figure. (b): PVA gel under various velocities (unit: mm/min) indicated in the figure. Contact area: PVA and gellan gels, 30 mm × 30 mm; PAMPS gel, 20 mm × 20 mm.
to give sheet-shaped gels with a thickness of 5 mm and then cut into a certain size for usage. The as-prepared surface of the gel was used for the friction measurement. The friction of a gel was measured at the room temperature using a tribometer (Heidon 14S/14DR, Shindom Sci., Co.). The sample was embedded in a square frame of adjustable size attached on the upper board and pressed against a piece of glass or other opposing plate (steel or gel), which was fixed on the lower board and was driven to move horizontally at a prescribed velocity and time. We have neglected the increase in the surface contact area under the load that is usually within several percent and have calculated the pressure normal to the surface using the values of surface area of gels free from load. A polymer gel is able to keep its shape but is deformable and fragile. The water contained in the gel does not flow like a liquid but gradually evaporates with time. Taking into account these characteristics, we have carefully prepared various kinds of gels with Young’s modulus around 103-104 Pa to make reproducible measurements. 3. Results and Discussion Figure 1 shows the time profiles of the frictional force F of the gels. After several unstable runs at the begin of measure© 1997 American Chemical Society
5488 J. Phys. Chem. B, Vol. 101, No. 28, 1997
Letters
Figure 3. Coefficient of friction µ as a function of sliding velocity V for various gels sliding against a glass. For one set of an experiments, the sliding velocity measurement was carried out using one sample, starting from lower velocity and increasing the velocity continuously without separating the two sliding surfaces during the interval of measurement. The sliding distances used in the measurement were adjusted from 14 to 30 mm depending on the velocity. (b) gellan gel, P ) 1.1 × 103 Pa; (0) κ-carrageenan gel, P ) 1.3 × 103 Pa; (O) PVA gel, P ) 2.2 × 103 Pa; (]) konjak gel, P ) 2.2 × 103 Pa; (3) PAMPS gel, P ) 1.3 × 103 Pa; (2) PNaAMPS gel, P ) 1.3 × 103 Pa.
Figure 2. Frictional force F as a function of load W (a) and the frictional coefficient as a function of pressure normal to the surface P (b). Sliding velocity: 7 mm/min. The duration of one run was 2 min, of 1 min forward and 1 min backward sliding. (b) gellan gel on glass; (1) gellan gel on steel; (4) gellan gel on gellan gel; (0) κ-carrageenan gel on glass; (O) PVA gel on glass; (.) water-soaked sponge on glass; (~) wet rubber on glass; ([) wet glass on glass; Young’s modulus: gellan gel, 6 × 104 Pa; κ-carrageenan gel, 5 × 104 Pa; PVA gel, 1.5 × 105 Pa. Contact area: 30 mm × 30 mm except κ-carrageenan gel (20 mm × 20 mm).
ment, F comes to exhibit approximately constant values under a constant loading and sliding velocity. However, when the load is increased, F does not exhibit an increase in proportionality with the increase of the load. For example, the F of the PVA gel increases only slightly when the load is doubled or tripled from 10 N. The friction of gels is slightly time dependent due to the loss of water by squeezing and partial evaporation, and the friction values of a gel have a transient nature. Taking into account this specific nature of the gel, we have studied the load dependence using one sample, continuously moving from lower to higher loadings. Figure 2a shows the dependence of loading for the gellan, the κ-carrageenan, and the PVA gels thus obtained. The gellan gel and the κ-carrageenan gel have been measured under a load up to 25 N and the PVA gel up to 100 N. These are the limit of loading over which the gels were collapsed. Unlike the behavior of solid materials, F is nearly constant (gellan gel and κ-carrageenan gel) or only increases slightly (PVA gel) over the range of W measured regardless of the opposing sliding
plates. Such behavior is observed only for the gels and not for other materials such as water-soaked sponge, wet glass, or wet rubber, which showed linear dependence on the load and confirmed to Amonton’s law as shown in Figure 2a (inset). Figure 2b shows the µ values calculated from the results of Figure 2a against P, the pressure normal to the surface. µ decreases with an increase in the load or the pressure and reaches a value on the order of 10-3 at P ) 104-105 Ν/m2, which is much smaller than values given in solid material, including poly (tetrafluoroethylene) for which µ ) 0.02-0.1.4 Water-soaked sponge, wet glass, and wet rubber showed almost constant µ values of 0.2-0.6 over a wide range of W. Further, we have found that the frictional force increases with an increase in the sliding velocity. The double-logarithmic plots of µ against V showed approximately linear relations in a range of 7-500 mm/min. For all gel samples measured, the slopes of the lines changes from 0.21 to 0.67, depending on the gel species (Figure 3). This kind of behavior of gels is also quite different from that of a solid material for which µ is independent of the sliding velocity, as prescribed by Amonton’s law. Obviously, the specific behavior of the gel friction should be associated with the water absorbed in the gel. Under the load, the gel deforms and a part of water might be squeezed out from the bulk gel and serves as a lubricator, leading to a boundary lubrication or even to a hydrodynamic lubrication. The strong dependence of the gel friction on the pressure P (Figure 2b) and velocity V (Figure 3) suggests a hydrodynamic lubrication mechanism. However, one should note that the hydrodynamic lubrication is usually sustained only when two solids rotate in a very high speed with lubricating oil. When two solid surfaces are allowed to slide under controlled conditions, the lubricant layer should be squeezed out quickly and the hydrodynamic lubrication cannot be sustained. This is why a water-soaked sponge conforms to Amonton’s law and does not exhibit hydrodynamic lubrication (Figure 2a, inset). The very strong hydration ability of the gel probably makes it possible to sustain the supposed hydrodynamic lubrication even at a very low sliding velocity and under a high pressure.
Letters The obtained results may further serve to construct a comfortable artificial joint using polymer gels. A detailed and quantitative study is now in progress and will be reported.
J. Phys. Chem. B, Vol. 101, No. 28, 1997 5489 (2) Okuzaki,H.; Osada, Y. Macromolecules 1994, 27, 502. (3) Woessner, D. E.; Snowden, B. S. J. Colloid Interface Sci. 1970, 34, 290. (4) Osada, Y.; Okuzaki, H.; Hori, H. Nature 1992, 355, 242.
Acknowledgment. This research was supported by the Proposal-Based Advanced Industrial Technology R&D Program from the New Energy and Industrial Technology Development Organization (NEDO) of Japan. It was also supported by Grantin-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan.
(5) McCutchen, C. W. Lubrication of Joints, The Joints and SynoVial Fluid; Academic Press, Inc.: New York, 1978; Vol. 10, p 437. (6) Bray, J. C.; Merrill, E. W. J. Biomed. Mater. Res. 1973, 7, 431. (7) Sasada, T.; Mabuchi, K. Proc. JSLE Int. Tribology Conf. 1985, 949. (8) Amontons, M. Mem. Acad. R. Sci. 1699, 206.
References and Notes
(9) Adamson, A. W. Physical Chemistry of Surfaces; John Wiley & Sons, Inc.: New York, 1990.
(1) Tanaka, T.; Nishio, I.; Sun, S. T.; Nishio, S. V. Science 1973, 218, 467.
(10) Moore, D. F. Principles and Applications of Tribology; Pergamon Press: Oxford, 1975.
