Anomalous Friction between Agar Gels under Accelerated Motion

Oct 1, 2018 - Understanding the friction phenomena on a gel surface under accelerated conditions is important for the design of functional materials...
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Anomalous Friction between Agar Gels under Accelerated Motion Koki Shinomiya,† Hiroyuki Mayama,‡ and Yoshimune Nonomura*,† †

Department of Biochemical Engineering, Graduate School of Science and Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa 992-8510, Japan ‡ Department of Chemistry, Asahikawa Medical University, 2-1-1-1 Midorigaoka-Higashi, Asahikawa 078-8510, Japan

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S Supporting Information *

ABSTRACT: Understanding the friction phenomena on a gel surface under accelerated conditions is important for the designing of functional materials. However, there are few reports on friction under such conditions. In the present study, the effects of velocity, normal force, and gel hardness on the friction force were evaluated between two agar gels under sinusoidal motion. We found a friction phenomenon with an extremely low friction coefficient on the gel surfaces: the friction coefficient became less than 0.02 when sliding velocity increased. In addition, the profile of the friction coefficient was different between outward and homeward processes in the reciprocating sliding motion. In the outward direction, the low friction coefficient was maintained even if the sliding velocity decreased. On the other hand, the friction coefficient increased with sliding velocity in the homeward direction. This characteristic friction profile is caused by a long relaxation time on the gel surfaces. When the gel substrate is rubbed for a shorter time than the relaxation time, the morphology of the gel surface becomes unstable. Under such conditions, the formation and extinction of a thick liquid film can induce a super lubrication state and the asymmetric friction phenomena. These findings are useful not only for developing functional materials but also for understanding nonequilibrium phenomena in soft biological systems.

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apparent contact area A [F ∝ WαAβ(α + β ≑ 1)].14 In addition, the friction coefficient on a gel surface is about 10−1 to 10−3, which is lower than those on common solid surfaces.13,14 The low friction phenomena are attributable not only to the surface lubricity but also to the fluid load support in the liquid phase of hydrogels.15−21 A model from the viewpoint of polymer−solid surface repulsion and adsorption has been accepted to explain the friction behavior of gel against the substrate surface.15,16 For example, in the case of hydrogels consisting of a common polyelectrolyte (carrying the charges of same sign), the friction in water is strongly dependent on the charge of the counter surfaces. When the counter surface has a similar charge with the gel, the friction becomes dominated by the hydrated lubrication: a thick water layer is formed at the interface due to osmotic repulsion of the overlapping electrical double layers of the charged surfaces. In addition, a biphasic theory has been accepted to explain tribology of articular cartilage and hydrogels in boundary lubrication:18−21 because the applied load is supported by the liquid phase, the friction resistance generated between the solid−solid phases is low. Murakami et al. estimated the effects of interstitial fluid pressure and fluid flow on the friction behavior using finite element analysis based on this theory.20,21

INTRODUCTION Gels and their composite materials are used in various fields because of their flexibility, ability to retain shape, and extremely high lubricity. For example, a cross-linked poly(vinyl alcohol) gel is a candidate material for use as an artificial cartilage and the hybrid gel prepared by combination of freeze−thawing and cast−drying methods has superior friction properties.1,2 Hydrogels containing silk protein and sodium dodecyl sulfate exhibit compressive and tensile moduli of 3.0 and 3.3 MPa, respectively.3 These mechanical strengths are almost the same as those of living tissues such as cartilage, tendon, and ligament. A stimuli-responsive gel that converts a chemical reaction into a mechanical response, that is, expands or contracts because of an external stimulus such as temperature or pH change, has been reported.4,5 Although a typical hydrogel has a low mechanical strength, a doublenetwork gel that uses two different polymers, namely, poly(2acrylamido-2-methylpropanesulfonic acid) and poly (acrylamide), has a high compressive fracture stress of 10−60 MPa.6 In addition, a rough hierarchical structure carved onto the agar gel surface was used to model the mucosa on the tongue and small intestine, and it has been used to study the interfacial phenomena of hydrophilic biosurfaces.7−12 Friction on a gel surface is a complex physical phenomenon, and attempting to explain it based on the classical theory is difficult.13−21 The friction force F on a gel surface is proportional to not only the normal force W but also the © XXXX American Chemical Society

Received: July 4, 2018 Revised: September 24, 2018 Published: October 1, 2018 A

DOI: 10.1021/acs.langmuir.8b02251 Langmuir XXXX, XXX, XXX−XXX

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Langmuir In many cases, the moving velocity changes continuously when humans move their limbs or tongue.22,23 The motion of a living thing is a movement accompanied with acceleration and is different from uniform motion. In the case of changes in sliding velocity, some interesting nonlinear phenomena can be observed. Stribeck found that the friction state between two solid surfaces is classified into three states depending on the sliding velocity, the viscosity of the lubricant, and the normal force.24 Kurokawa et al. observed that the friction force on a gel surface changes nonlinearly with velocity in the process of transition from elastic friction to hydrodynamic lubrication.25 Stick−slip behavior on a gel surface occurs by not only velocity but also vertical pressure.26,27 When a gel sheet was pulled on a glass substrate, the spatio-temporal pattern of the contact region changed with the pull velocity; as the velocity decreases, the time dependence of the friction force shifts from a periodic to chaotic behavior.28 In addition, Dunn et al. found that the friction behavior of a hydrogel is different in the acceleration and deceleration phases or outward and homeward motions depending on any difference in the substrates.29,30 An experimental design, which reproduces sliding motion accompanied with acceleration, is important to understand complicated friction phenomena in living bodies. Therefore, we developed a friction evaluation system in which the friction probe moves regularly under sinusoidal motion.31,32 In the system, the motion is achieved through the Scotch-yoke mechanism, in which the rotational movement of an eccentric disk is converted into the reciprocating movement of a contact probe. In the present study, we systematically evaluated the friction force between two agar gel substrates under sinusoidal motion. By employing an original friction evaluation system, we studied the effects of velocity, normal force, and hardness of the agar gels on the friction force between the two samples. We believe that physical insights into the friction of gels under sinusoidal motion are useful not only for the development of biofunctional materials but also for understanding the nonequilibrium phenomena in soft materials and biological systems.

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Figure 1. (a) Sinusoidal movement sliding system. (b) Contact probe of the acrylic resin covered with the agar gel. (c) Conversion from the rotational movement of an eccentric disc to the sinusoidal reciprocating movement of the contact probe. (d) Conceptual diagram. (CD22100VM122, OPTEX FA Co., Ltd., Tokyo, Japan) attached to the side of the driving motor; light source = red laser diode (wavelength: 655 nm), displacement accuracy = 20 μm, and measurement range = ±50 mm. This device measured the friction force and normal force by two load cells. The measurement range of the forces was as follows: Fx = 0.06−9.9 N and Fz = 0.06−9.8 N. The detection limits of Fx and Fz were both 0.02 N: they are the minimum amount which is detectable as a signal. The agar gel substrates were fixed to an acrylic resin holder at both the lower and upper sides using an adhesive (Aron Alpha, Toagosei Co., Ltd., Tokyo, Japan) and double-sided tape (Nichiban Co., Ltd., Tokyo, Japan). The velocity V under the sinusoidal movement was calculated from the stroke length D, the angular velocity ω, and time T based on eq 1

EXPERIMENTAL SECTION

Materials. Agar powder was purchased from Wako Pure Chemical Industries, Ltd. (Osaka, Japan). Water was purified using a Demi-Ace Model DX-15 demineralizer (Kurita Water Industries Ltd., Tokyo, Japan). A mixture of agar powder and deionized water was heated at 90 °C for 80 min under agitation at 500 rpm. An aqueous solution of agar was poured into glass Petri dishes (11 cm in diameter) and was left at room temperature for 90 min and then at 7 °C for 90 min. The agar gel was cut into shapes of 80 × 30 × 10 and 20 × 20 × 5 mm3, which were immersed in deionized water for 2 days. The Young’s modulus values of the obtained gels containing 2, 4, and 6 wt % agar were 0.44 ± 0.05 × 106, 0.90 ± 0.06 × 106, and 1.49 ± 0.14 × 106 Pa, respectively. We evaluated the surface geometry of 4 wt % agar gel using a laser microscope in our previous study.10 The roughness was as follows: the roughness parameters Ra, Rz, and Ry are 26, 316, and 430 nm, respectively. Measurements. Using the sinusoidal motion friction evaluation system, we evaluated the friction force between two agar gel substrates in deionized water (Figure 1). The lower substrate was covered with a 2 mm-thick water film. Sinusoidal motion was achieved through the Scotch-yoke mechanism, in which the rotational movement of an eccentric disk was converted into the sinusoidal reciprocating movement of a contact probe.31,32 A direct-current servomotor was used with the following specifications: rotation rate = 0.01−2.1 rad s−1 and sliding distance = ±2.5−20 mm. The moving distance of the contact probe was measured using a displacement sensor

V = |D|ω cos ωT

(1)

Here, the friction conditions were as follows: D = ±14.5 mm; ω = 0.01, 0.1, 1.0, and 2.1 rad s−1; sampling interval = 1 ms (2.1 rad s−1), 2 ms (1.0 rad s−1), 20 ms (0.1 rad s−1), and 200 ms (0.01 rad s−1); and normal force W = 0.29, 0.39, and 0.98 N. In addition, the maximum velocities Vmax for the angular velocities were 0.15 mm s−1 (0.01 rad s−1), 1.5 mm s−1 (0.1 rad s−1), 15 mm s−1 (1.0 rad s−1), and 30 mm s−1 (2.1 rad s−1). Each evaluation was conducted more than three times to confirm the repeatability of the friction data. The above evaluations were performed at 25 ± 1 °C and 50 ± 5% relative humidity. In addition, we evaluated the friction force between two agar gel substrates in deionized water under uniform motion. Section S1 in the Supporting Information and Figure S1 show details of the evaluation method and specifications of the device. B

DOI: 10.1021/acs.langmuir.8b02251 Langmuir XXXX, XXX, XXX−XXX

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RESULTS AND DISCUSSION Friction Profile on Agar Gel Surfaces. Figure 2 shows the typical profiles of the normal force, moving velocity, and

Figure 2. Temporal profile of the friction force (solid line), velocity (yellow line), and normal force (green line) of 4 wt % agar gels at ω = 0.01 rad s−1 and W = 0.98 N.

Figure 3. Effect of velocity on the friction coefficient of 4 wt % agar gels. (a) Stable pattern: ω = 0.01 rad s−1 and W = 0.98 N, (b) unstable pattern I: ω = 0.1 rad s−1 and W = 0.98 N, and (c) unstable pattern II: ω = 2.1 rad s−1 and W = 0.98 N.

friction force between two agar gel substrates under the sinusoidal motion. The friction conditions were as follows: agar concentration in the gel = 4 wt %, ω = 0.01 rad s−1, and W = 0.98 N. In the region where the sliding velocity is positive or negative, the contact probe moves in the outward and homeward directions, respectively. Although the normal force was almost constant in the friction process, the friction force dynamically changed with time. In the outward direction, the friction force was 0.31 N at a static friction, which decreased to 0.25 N during the kinetic friction process. A similar friction profile was observed in the homeward direction. We found a time lag in the response of the friction force to the movement of the contact probe. The normalized delay time δ, which is obtained by dividing the time lag by the time of a cycle, was 0.019. It was found that δ was hardly dependent on the composition of the agar in the gels: 0.017−0.036, 0.017− 0.036, and 0.015−0.024 for 2, 4, and 6 wt %, respectively (Table S1). In the present study, three types of friction profiles were observed depending on the angular velocity and normal force. Figure 3 shows the typical relationships between the friction coefficient and the velocity when two 4 wt % agar gels were rubbed together under various conditions. The friction coefficient was obtained by dividing the friction force by the normal force. The features of each friction profile are as follows. (a) Stable pattern: In the case of ω = 0.01 rad s−1 and W = 0.98 N, a stable pattern was observed, in which similar profiles were produced during the outward and homeward processes (Figure 3a). Static friction with a friction coefficient of 0.32 was observed at sliding velocity V = 0.03 mm s−1 in the outward process, and the friction coefficient decreased with increasing sliding velocity. At maximum velocity Vmax = 0.15 mm s−1, the friction coefficient was 0.24.

(b) Unstable pattern I: In the case of ω = 0.1 rad s−1 and W = 0.98 N, unstable pattern I was observed, in which the profile of the homeward direction was different from that of the outward direction (Figure 3b). The friction coefficient of the outward direction was larger in the acceleration phase than that in the deceleration phase, and that of the homeward direction was larger in the deceleration phase than that in the acceleration phase. In the outward direction, static friction with a friction coefficient of 0.30 was observed at V = 0.45 mm s−1, and the friction coefficient decreased with increasing sliding velocity. In the homeward direction, static friction with a friction coefficient of −0.13 was observed at V = −0.24 mm s−1, and the friction coefficient increased with sliding velocity. (c) Unstable pattern II: In the case of ω = 2.1 rad s−1 and W = 0.98 N, unstable pattern II was observed. In this profile, a friction phenomenon with an extremely low friction coefficient occurred from the deceleration phase on the outward direction to the acceleration phase on the homeward direction. In addition, the friction profiles of the outward and homeward directions were significantly different from each other (Figure 3c). In the outward direction, a static friction with a friction coefficient of 0.30 was observed at V = 10 mm s−1. After that, when the sliding velocity increased, the friction coefficient became less than 0.02 which is similar with the measurement accuracy of the load cell: a friction phenomenon with an extremely low friction coefficient occurred. Even if the sliding velocity decreased, the low friction coefficient was maintained. In the homeward C

DOI: 10.1021/acs.langmuir.8b02251 Langmuir XXXX, XXX, XXX−XXX

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Comparison of Friction under Sinusoidal Motion and Uniform Motion. To understand the effects of acceleration, we compared the results under sinusoidal motion with that under uniform motion (Section S4 in the Supporting Information and Figure S3). Even in the case of higher sliding velocity than V = 10 mm s−1, unstable pattern II was not observed under uniform motion (Figure S4). In addition, the friction coefficient under sinusoidal motion was one-half to one-third of that under uniform motion (Section S5 in the Supporting Information and Figure S5). Effects of acceleration during sinusoidal motion may cause the friction phenomenon with an extremely low friction coefficient. Stribeck Curve. To understand the lubrication mode under sinusoidal motion, we analyzed dependence of the friction coefficient on the Sommerfeld number S by the Stribeck curve (Section S6 in the Supporting Information and Figure S6). At any agar concentration in the gel, significant change of the lubrication mode was not observed. Estimation of the Thickness of the Water Film. To understand the mechanism of a friction phenomenon with an extremely low friction coefficient, the thickness of the water film h between the agar gel surfaces was estimated using eq 217

direction, the friction coefficient increased with sliding velocity. At maximum velocity Vmax = −30 mm s−1, the friction coefficient was −0.52. In the case of ω = 2.1 rad s−1, significant oscillation was observed regardless of the normal force and the hardness of agar gel (Section S3 in the Supporting Information). When the temporal profile was analyzed by Fourier transform, a remarkable peak was observed at 67 Hz (Figure S2). This oscillation can be caused by inertia or natural oscillation. However, even in the case of ω = 1.0 rad s−1, which did not have significant oscillation nor the remarkable peak at 67 Hz, unstable pattern II was obtained. Therefore, we believe that some factors such as inertia or natural oscillation do not significantly affect the categorization of the friction pattern. Friction Pattern Diagrams. To survey the observed friction behavior, a friction pattern diagram is useful, which can be seen in Figure 4. These diagrams allow us to understand the

h=

η×V f

(2)

where η is the viscosity of the lubricating film, V is the sliding velocity, and f is the friction force per unit area. The viscosity of water is 8.9 × 10−4 Pa s.33 The contact area of the friction surface is 4 × 10−4 m2. The average friction force was adopted as the friction force in eq 2. This is the average value of the absolute friction force values for one cycle. Table S1 shows the values of the average friction force obtained under each friction condition. We adopted the average sliding velocity Vav for each angular velocity as the sliding velocity: Vav = 0.1 mm s−1 (0.01 rad s−1), 1.0 mm s−1 (0.1 rad s−1), 10 mm s−1 (1.0 rad s−1), and 20 mm s−1 (2.1 rad s−1). Here, we considered the friction between the two agar gel substrates containing 4 wt % agar. Table S1 shows the values of h obtained under each friction condition. Under angular velocity ω = 0.01 rad s−1 at which the stable pattern was obtained, the values of h were in the order of 0.1 nm. At ω = 0.1 rad s−1, unstable pattern I was obtained, and the values of h were larger than those under the stable pattern: the expected film thickness was in the order of 1 nm. In addition, when ω = 2.1 rad s−1, the unstable pattern II was obtained, and the expected film thickness was in the order of 10 nm and was several hundred times thicker than that of the stable pattern. Even in the case of 2 and 6 wt % agar gels, the values of h were in the same order under each condition of ω and increased with sliding velocity. This suggests that the existence of a thick water film leads to a high-lubrication effect under the conditions of a high sliding velocity. The Relaxation Time from a Static Friction Process to a Kinetic Friction Process. A characteristic time scale is important to understand the temporal change from static friction to kinetic friction. Figure 5 shows a typical temporal friction profile of agar gel surfaces. Here, the friction profile was approximated using an exponential decay function. Decay of stress for the Maxwell model has been expressed using a similar function.34 The relaxation time τ at the time of transition from static friction force to kinetic friction force was derived using eq 3

Figure 4. Dependence of velocity and normal force on the friction pattern of agar gels. (a) 2 wt % agar gels; (b) 4 wt % agar gels; and (c) 6 wt % agar gels. (◯) Stable pattern; (□) unstable pattern I; (△) unstable pattern II; (×) no typical pattern.

dependence of velocity and normal force on the friction pattern when we studied 2, 4, and 6 wt % agar gels. As the gels became harder, the friction conditions of the unstable patterns I or II increased. When 2 wt % agar gels were rubbed together, both unstable patterns could be expressed under three conditions. When 4 or 6 wt % agar gels were rubbed, unstable pattern I or II was expressed under nine or ten conditions, respectively.

F = F0 + Fd e−(t − t0)/ τ D

(3) DOI: 10.1021/acs.langmuir.8b02251 Langmuir XXXX, XXX, XXX−XXX

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Figure 5. Relationship between the friction force and time of 4 wt % agar gels: ω = 0.1 rad s−1 and W = 0.98 N. The black line is the fitting result using eq 3.

where F is the friction force, F0 is the friction force after relaxation, and Fd is the difference between the static friction force and the friction force after relaxation. In addition, t is the observed time and t0 is the time when the static friction force was obtained. In order to ensure a sufficient relaxation time of the friction force, analysis was carried out under seven conditions of the stable pattern at the lowest velocity (ω = 0.01 rad s−1). For example, when the 4 wt % agar gel was rubbed at ω = 0.01 rad s−1 and W = 0.98 N, the static friction force was 0.33 N at t = 20.2 s. Thereafter, at t = 37.6 s, the friction force became 0.25 N. If this relaxation process was approximated using eq 3, τ was 5.73 s. Table S1 gives the value of τ obtained under each condition, which was in the order of several seconds to several tens of seconds. This indicates that the mechanical relaxation of the agar gel is slower than those of general solids. Why do Anomalous Friction Phenomena Occur on Gel Surfaces? In the present study, we found a friction phenomenon, which has both an asymmetric friction behavior in the outward and homeward directions (unstable patterns I and II) and a friction phenomenon with an extremely low friction coefficient (unstable pattern II). In general, the friction phenomenon on a wet surface is analyzed using the Stribeck curve. The friction state is distinguished based on the relationship between friction coefficient and the Sommerfeld number S, which is described using eq 4

Figure 6. Interfacial conditions on agar gel surfaces. (a) Time of a half cycle is longer than τ, (b) time of a half cycle is slightly longer than τ, and (c) time of a half cycle is shorter than τ.

This residual strain causes both an asymmetric friction behavior and a friction phenomenon with an extremely low friction coefficient. In Figure 4b, we consider friction between two agar gel substrates containing 4 wt % agar. As shown in Table S1, τ of the 4 wt % agar gels was 6.16−7.20 s. Here, τ is the relaxation time of the transition from a static friction force to a kinetic friction force at angular velocity ω = 0.01 rad s−1, which is the lowest sliding velocity. On the other hand, the times of a half cycle for each angular velocity were 314 s (0.01 rad s−1), 31.4 s (0.1 rad s−1), 3.14 s (1.0 rad s−1), and 1.5 s (2.1 rad s−1). As shown in Figure 4b, when the time scale was shorter than τ [the time of a half cycle = 3.14 s (1.0 rad s−1) or 1.5 s (2.1 rad s−1)], unstable pattern II with an extremely low friction coefficient was obtained. Even in the cases of 2 and 6 wt % agar gels, unstable pattern II was obtained when the time of a half cycle was shorter than τ. In addition, unstable pattern I with an asymmetric friction profile could be the transient state between the stable pattern and unstable pattern II. When the time of a half cycle is slightly longer than τ, the super lubrication phenomenon does not occur because there is insufficient residual strain. Here, we considered the friction between two agar gel substrates containing 4 wt % of agar when time of a half cycle was 31.4 s at ω = 0.1 rad s−1 (Figure 4b). In that case, unstable pattern I with only an asymmetric friction profile was observed. This time of a half cycle of 31.4 s is somewhat longer than the relaxation time τ (6.16−7.20 s) for the transition from static friction to kinetic friction at ω = 0.01 rad s−1 on the 4 wt % agar gels. Even in the case of 2 and 6 wt % agar gels, where the time of a half cycle was about the same as τ, unstable pattern I was observed. Unfortunately, direct observation of the deformation of gel and formation of the thick water film is impossible. However, significant deformation was reported on the hydrogel surface

η×V (4) W When the viscosity of the lubricating film η and the normal force W is constant, S increases with velocity V. When we evaluate the friction with same samples under such conditions, the friction resistance should be constant if V is equal, regardless of not only the acceleration and deceleration phases but also the outward and homeward directions. Therefore, the asymmetric friction phenomena found in this study cannot be explained by this classic model. When the contact probe starts to move, the soft gel should be greatly distorted at the moment of static friction. When the time of a half cycle is long, this distortion is relaxed in a kinetic friction process. On the other hand, when the time of a half cycle is short, the distorted state is maintained during the reciprocating motion. If the gel is rubbed under a deformed condition, the friction profile should be asymmetric. Because water flows into the friction interface under such unstable conditions, the liquid film becomes drastically thick (Figure 6). S=

E

DOI: 10.1021/acs.langmuir.8b02251 Langmuir XXXX, XXX, XXX−XXX

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Education, Culture, Sports, Science, and Technology, Japan (MEXT).

under critical conditions and analyzed by the biphasic model. Delavoipière et al. reported that the velocity dependence of friction force and contact shape is controlled by the Peclet number Pe, which is defined as the ratio of the time for draining the water out of the contact region to a contact time a/V, where V is the velocity and a is the contact radius.35 Although the contact shape remains unchanged during sliding under Pe < 1, the contact area decreased together with the development of a contact asymmetry when the velocity increased under Pe > 1. If the velocity is high and contact time is short, significant contact asymmetry occurs because Pe becomes large.

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(1) Murakami, T.; Sakai, N.; Yamaguchi, T.; Yarimitsu, S.; Nakashima, K.; Sawae, Y.; Suzuki, A. Evaluation of A Superior Lubrication Mechanism with Biphasic Hydrogels for Artificial Cartilage. Tribol. Int. 2015, 89, 19−26. (2) Murakami, T.; Yarimitsu, S.; Nakashima, K.; Sakai, N.; Yamaguchi, T.; Sawae, Y.; Suzuki, A. Biphasic and Boundary Lubrication Mechanisms in Artificial Hydrogel Cartilage: A Review. Proc. Inst. Mech. Eng., Part H 2015, 229, 864−878. (3) Li, Z.; Zheng, Z.; Yang, Y.; Fang, G.; Yao, J.; Shao, Z.; Chen, X. Robust Protein Hydrogels from Silkworm Silk. ACS Sustainable Chem. Eng. 2016, 4, 1500−1506. (4) Tanaka, T. Collapse of Gels and the Critical Endpoint. Phys. Rev. Lett. 1978, 40, 820−823. (5) Tanaka, T.; Fillmore, D.; Sun, S.-T.; Nishio, I.; Swislow, G.; Shah, A. Phase Transitions in Ionic Gels. Phys. Rev. Lett. 1980, 45, 1636−1639. (6) Gong, J. P.; Katsuyama, Y.; Kurokawa, T.; Osada, Y. DoubleNetwork Hydrogels with Extremely High Mechanical Strength. Adv. Mater. 2003, 15, 1155−1158. (7) Nonomura, Y.; Morita, Y.; Hikima, T.; Seino, E.; Chida, S.; Mayama, H. Spreading Behavior of Water Droplets on Fractal Agar Gel Surfaces. Langmuir 2010, 26, 16150−16154. (8) Nonomura, Y.; Chida, S.; Seino, E.; Mayama, H. Anomalous Spreading with Marangoni Flow on Agar Gel Surfaces. Langmuir 2012, 28, 3799−3806. (9) Oyama, T.; Mayama, H.; Nonomura, Y. Wetting Dynamics of Oil-in-Water Emulsions on Agar Gel Surfaces. Chem. Lett. 2013, 42, 871−872. (10) Seino, E.; Chida, S.; Mayama, H.; Hotta, J.-i.; Nonomura, Y. Wetting Dynamics of Colloidal Dispersions on Agar Gel Surfaces. Colloids Surf., B 2014, 122, 1−6. (11) Kudo, A.; Sato, M.; Sawaguchi, H.; Hotta, J.-i.; Mayama, H.; Nonomura, Y. Adhesion and Disintegration Phenomena on Fractal Agar Gel Surfaces. J. Oleo Sci. 2016, 65, 909−912. (12) Okamoto, M.; Shinomiya, K.; Mayama, H.; Nonomura, Y. Evaluation of the Frictional Properties of Oil-in-Water Emulsions on Fractal Agar Gel Surface. Chem. Lett. 2017, 46, 172−174. (13) Gong, J.; Higa, M.; Iwasaki, Y.; Katsuyama, Y.; Osada, Y. Friction of Gels. J. Phys. Chem. B 1997, 101, 5487−5489. (14) Gong, J.; Iwasaki, Y.; Osada, Y.; Kurihara, K.; Hamai, Y. Friction of Gels. 3. Friction on Solid Surfaces. J. Phys. Chem. B 1999, 103, 6001−6006. (15) Gong, J.; Osada, Y. Gel Friction: A Model Based on Surface Repulsion and Adsorption. J. Chem. Phys. 1998, 109, 8062−8068. (16) Gong, J. P.; Kagata, G.; Osada, Y. Friction of Gels. 4. Friction on Charged Gels. J. Phys. Chem. B 1999, 103, 6007−6014. (17) Gong, J. P.; Iwasaki, Y.; Osada, Y. Friction of Gels. 5. Negative Load Dependence of Polysaccharide Gels. J. Phys. Chem. B 2000, 104, 3423−3428. (18) Mow, V. C.; Kuei, S. C.; Lai, W. M.; Armstrong, C. G. Biphasic Creep and Stress Relaxation of Articular Cartilage in Compression: Theory and Experiments. J. Biomech. Eng. 1980, 102, 73−84. (19) Ateshian, G. A. The Role of Interstitial Fluid Pressurization in Articular Cartilage Lubrication. J. Biomech. 2009, 42, 1163−1176. (20) Sakai, N.; Hagihara, Y.; Furusawa, T.; Hosoda, N.; Sawae, Y.; Murakami, T. Analysis of Biphasic Lubrication of Articular Cartilage Loaded by Cylindrical Indenter. Tribol. Int. 2012, 46, 225−236. (21) Murakami, T.; Yarimitsu, S.; Nakashima, K.; Yamaguchi, T.; Sawae, Y.; Sakai, N.; Suzuki, A. Superior Lubricity in Articular Cartilage and Artificial Hydrogel Cartilage. Proc. Inst. Mech. Eng., Part J 2014, 228, 1099−1111. (22) Nonomura, Y.; Miura, T.; Miyashita, T.; Asao, Y.; Shirado, H.; Makino, Y.; Maeno, T. How to Identify Water from Thickener Aqueous Solutions by Touch. J. R. Soc., Interface 2012, 9, 1216−1223.

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CONCLUSION In the present study, the effects of sliding velocity, normal force, and hardness of gels on the friction force were evaluated under sinusoidal motion. We found some interesting friction phenomena on the gel surface: an asymmetric friction profile and a friction phenomenon with an extremely low friction coefficient. These characteristic friction phenomena could be caused by the softness of the gel and a water film on the surfaces. If the time of a half cycle was less than τ and the agar gel was rubbed with a reciprocating motion, the observed distortion remained. In this deformed state, water flows into the friction interface during the friction process. When a large amount of water flows onto the gel surfaces under highvelocity conditions, a high-lubrication state appears. Here, we considered the relationship between these findings and biological phenomena. It is important to maintain a lowload state for living things to live. In this study, we have found a friction phenomenon with an extremely low friction coefficient (unstable pattern II). Similar friction phenomena may occur at the biological surface and the tissue interface. The findings in this study will serve as a clue not only for developing biomaterials but also for understanding nonequilibrium phenomena in soft matter and biological systems.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.8b02251. Evaluation method of friction under uniform motion; friction parameters; analysis of friction oscillation; friction profile on agar gel surfaces under uniform motion; comparison of friction coefficient obtained under sinusoidal motion and uniform motion; Stribeck curve (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81-238-263164. Fax: +81-238-26-3414. ORCID

Yoshimune Nonomura: 0000-0003-0461-124X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by a Grant-in-Aid for Scientific Research (C) (grants no. 26390001) from the Ministry of F

DOI: 10.1021/acs.langmuir.8b02251 Langmuir XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.langmuir.8b02251 Langmuir XXXX, XXX, XXX−XXX