Probing the intriguing frictional behavior of hydrogels during alternative sliding velocity cycles

Understanding the friction behavior of hydrogels is critical for the long-term stability of hydrogel-related bioengineering applications. Instead of maintaining a constant sliding velocity, the actual motion of bio-components (e.g., articular cartilage and cornea) often changes abruptly. Therefore, it is important to study the frictional properties of hydrogels serving under various sliding velocities. In this work, an unexpected low friction regime (friction coefficient μ < 10−4 at 1.05×10−3 rad/s) was observed when the polyacrylamide hydrogel was rotated against a glass substrate under alternative sliding velocity cycles. Interestingly, compared with the friction coefficients under constant sliding velocities, the measured μ decreased significantly when the sliding velocity changed abruptly from high speeds (e.g., 105 rad/s) to low speeds (e.g., 1.05×10−3 rad/s). In addition, μ exhibited a downswing trend at low speeds after experiencing more alternative sliding velocity cycles: the measured μ at 1.05 rad/s decreased from 2×10−2 to 3×10−3 after 10 friction cycles. It is found that the combined effect of hydration film and polymer network deformation determines the lubrication and drag reduction of hydrogels when the sliding velocity changes abruptly. The observed extremely low friction during alternative sliding velocity cycles can be applied to reduce friction at contacted interfaces. This work provides new insights into the fundamental understanding of the lubrication behaviors and mechanisms of hydrogels, with useful implications for the hydration lubrication related engineering applications such as artificial cartilage.

There are a number of published studies explaining the mechanism of hydrogel friction and lubrication [21][22][23][24][25][26]. Hydrogels exhibit low friction behavior in water due to hydration lubrication [23,27,28]. Specifically, the hydrogel surface may consist of dangling polymer chains, which are similar to polymer brushes [29]. And those hydrated polymers can significantly reduce friction at the interface [30][31][32][33][34]. Besides, Kurokawa et al. [25] proposed an adsorptionrepulsion model to describe the friction characteristics of hydrogels. In the adsorption state, the attractive force between the polymer chains and the substrate hindered the relative motion of the hydrogel and the substrate, thus exhibiting a large frictional force. In the repulsive state, a hydration film appeared on the hydrogel-substrate interface and significantly reduced the friction. In addition, Cuccia et al. [26] presented that the hydrodynamic flow through the hydrogel network dominated the friction behavior of hydrogels at low sliding velocities, and μ showed a slow transient relaxation on long time scales.
However, most of the previous work only concerns the friction properties of hydrogels when the sliding velocity changes continuously and uniformly. In fact, the friction velocity of biopolymers in living organisms often varies and even undergoes a sudden change. As shown in Fig. 1(a), the articular cartilages experience friction during jumping as the knee joint bends at different angles. Importantly, the speed of sliding between the knee cartilages decreases abruptly when people land on the ground ( Fig. 1(b)). Moreover, the abrupt speed change of knee joint happens in other sports such as football, basketball, and rugby. There have been some investigations on the transient frictional behavior when the sliding velocity changes. Kim and Dunn [35] found that the friction behavior of hydrogel under constant sliding was strongly influenced by friction history. Therefore, they built a complex fluid model to predict transient frictional behavior based on sliding velocity [36]. However, this model could only explain the transient response and lubrication hysteresis when the sliding velocity changes slightly. To date, there is a lack of research on the friction behavior of hydrogels when the sliding velocity changes abruptly over a wide range. In this work, a rheometer was used to study the tribological properties of polyacrylamide (PAM) hydrogel under the sudden change of sliding velocities (also known as velocity jump). The sliding velocity was controlled to change abruptly between low speed (1.05×10 -3 rad/s) dominated by elastic friction, high speed (105 rad/s) dominated by hydrodynamic lubrication, and intermediate speed (1.05 rad/s) where both friction mechanisms co-existed. Compared with the friction coefficient of shearing hydrogels under a constant speed, the measured μ decreased sharply after alternating the sliding speed between high speed and intermediate/low speeds. Systematic friction tests were conducted to understand the mechanism of the ultra-low friction after experiencing alternative sliding velocity cycles. The formation of hydration film and the adsorption of the polymer chains on the friction pair are found to play important roles. In general, this work offers a reasonable explanation for the tribological behavior of biopolymers when the sliding velocity changes abruptly, and provides guidance for the application of hydrogels in robot joint and cartilage replacement.

Hydrogel preparation
PAM hydrogels are often used for studying the tribological properties of hydrogels due to its excellent mechanical properties and electrical neutrality [35,[37][38][39][40]. Therefore, pure PAM hydrogel was selected as the testing hydrogel in this work. According to previously reported studies [41,42], AM (3.0 g), BAM (1.5 wt% of AM), and Irgacure 2959 (1.5 wt% of AM) were dissolved in deionized water (10 g) to obtain a precursor solution of pure PAM hydrogel. Then, the prepared precursor solution was stirred for 30 min, followed by ultrasonic degassing. Afterwards, the hydrogel samples were obtained by UV curing the PAM precursor solution for 30 min using curing equipment (OmniCure S1500, Excelitas Technologies Corp.).

Friction tests
The friction tests were conducted on a rheometer (MCR 302, Anton Paar). As shown in Fig. 1(c), a glass substrate with a diameter of 25 mm was adhered to a parallel plate that acted as the upper surface. The hydrogel sample was immobilized at the bottom. The parallel plate and glass substrate were controlled to descend slowly until the normal force reached 1 N. In this case, it is reasonable to consider that the hydrogel surface was in contact with the glass substrate. The magnitude of the normal force was measured by a sensor (the accuracy is 0.01 N) in the rheometer. In addition, the relative distance between the hydrogel surface and the glass substrate was measured by the position sensor (the accuracy is 0.001 mm) in the rheometer. The interface between the substrate and the hydrogel was immersed in an aqueous solution in the friction tests, and the friction force (F f ) is calculated by Eq. (1) [43]: where T is the measured torque during friction tests and R is the radius of the contact circular area. μ is calculated by Eq. (2): where F n is the normal load force. The normal load exerted in all friction tests is set as 1 N (the pressure is 2,037 Pa). According to existing studies in the field [25,35,36], the friction mechanism of PAM hydrogel is dependent on friction speeds. As shown in Fig. 1(d), the frictional properties of hydrogels at low friction velocities are determined by the adsorption and dissociation between the polymer chains and the substrate at the interface, and the lubricating properties at high velocities are determined by hydrodynamic lubrication. At intermediate velocities, the adsorption-dissociation effect and hydrodynamic lubrication jointly determine the tribological properties of the hydrogel. In order to comprehensively understand the tribological properties of hydrogels under velocity jumps, the sliding velocity was made to change abruptly between three typical values (viz, 1.05×10 -3 , 1.05, and 105 rad/s) at different lubrication regions.
As shown in Table 1, systematical frictional tests were performed by changing the running time with different sliding velocities (v l = 1.05×10 -3 rad/s, v m = 1.05 rad/s, and v h = 105 rad/s). The section "Before training" and "After training" lasted for 600 s respectively, which could show the influence of friction training on the tribological properties of hydrogels. The "Training" section lasted for 200 s, during which the sliding speed of the system changed abruptly for several times between different values. Test 1, Test 2, and Test 3 all contain 400 s friction process in v m and 400 s friction process in v h , however, the number of sliding velocity jumps are different.

Results and discussion
Three different experiments were conducted to explore the frictional properties of hydrogels with velocity jumps between v m and v h (also named as Train 1, Train 2, and Train 3 hereinafter). As shown in Fig. 2(a), the blue area represents the sliding velocity of v h = 105 rad/s and the green area represents the sliding velocity of v m = 1.05 rad/s. In the first 600 s of the friction curve, the sliding velocity is v m and the μ of hydrogel decreases first and then increases slowly with time. When the sliding velocity changes from v m to v h , μ increases from 3.9×10 -2 to 4.7×10 -2 and then undergoes continuous decay. The reason for this decay is that the polymer chains extend in the direction of the sliding velocity. The action of water flow tends to entrain the polymer chains and re-orient them in the sliding direction, resulting in less shear resistance [35]. Therefore, the extended state of the polymer chains can further reduce the shear resistance and μ. After the velocity changes from v h to v m , the μ of hydrogel drops abruptly from 3.8×10 -2 to 8.2×10 -3 and then slowly increases. This dramatic decline in the coefficient of friction could be related to the extension of polymer chains on the hydrogel surface. This extended state of polymer chains arises when the sliding velocity changes from v m to v h and can be maintained under v h . Therefore, we hypothesized that repeating the v m → v h process could enhance the extent of polymer extension, align more polymer chains in the shear direction, and reduce the coefficient of friction at v m .
As shown in Figs. 2(b) and 2(c), the sudden change of v m → v h was performed 5 times (Train 2) and 10 times (Train 3), respectively. The strategy of conducting alternative sliding velocity cycles is named as "friction training" hereinafter and the training process can be divided into three sections: (i) before training, (ii) during training, and (iii) after training. In the before-training section, the friction behavior of the hydrogel is exactly the same as that before the velocity jump in Train 1. Then, when the sliding velocity changes abruptly from v m to v h , the friction coefficient Springer.com/journal/40544 | Friction suddenly increases and then slowly decreases. The effect of v m on the friction behavior of hydrogel at v h is shown in Fig. S1(a) in the Electronic Supplementary Material (ESM). In the first 600 s of the friction curve, the friction coefficient of hydrogel at v h gradually decreases and then remains stable at about 0.12. After 5 times of the process v m → v h , the hydrogel friction coefficient decreases and then remains stable at about 0.11. Obviously, it can be observed that the process v m → v h does not change the trend of the friction curve at v h but slightly reduces the hydrogel friction coefficient at v h . However, the μ of hydrogel under v m decreases gradually with more sliding velocity jumps. The main reason for this decrease is that repeating the process of v m → v h intensifies the extension of polymer chains and re-orients more polymer chains to the sliding direction. In the after-training section, the μ shows similar variation tendency to that of Train 1, but exhibits a lower starting point and a faster rising rate. As shown in Fig. 2(d), the μ after training in Train 3 is 1/6 of the minimum μ before training, while the μ in Train 2 and Train 1 is 1/4 and 1/2 of the minimum μ before training. Therefore, friction training can significantly reduce μ when the sliding velocity changes from v h to v m . Moreover, this phenomenon can be observed on different friction pairs. As shown in Fig. S2 in the ESM, when iron and polyethylene glycol terephthalate (PET) were used as the opposite shearing substrate, the hydrogel also exhibited low friction coefficient under alternative sliding velocity  cycles. In order to further explore the mechanism of the extremely low μ after sliding velocity jump, we fitted the friction curve after training in Train 3. The time-dependent responses can be fitted by a stretched exponential decay [26,35]. As shown in Fig. 2(e), the significant rise in μ within 600 s after training can be expressed in terms of exponential relaxation as Eq. (3): where t 1 is the time constant, μ 0 is the μ at the beginning of the after-training part, μ e is the μ at the end of the after-training part. The friction coefficient vs time curve can be well fitted by Eq. (3) with the adjusted R 2 of 0.99, but there is a large deviation in the first 20 s, which could be considered as the transition stage for the establishment of friction in another regime ( Fig. 1(d)). Therefore, the friction curve has been divided into two parts and the first 20 s of the curve is separately fitted using Eq. (3) (Fig. 2(f)). According to Table 2, the fitted curve for the first 20 s exhibits a faster rate of change compared to the overall fitted curve (the average slope of the first 20 s is 140 times higher than the overall average slope). According to the fitting results, the after-training friction behavior could be considered as two steps recovery, which can be hardly explained by the change of the polymer network alone. The lubrication of the hydrogel under v h is dominated by hydrodynamic lubrication, while the friction under v m is determined by the combination of hydrodynamic lubrication and the adsorption of polymer chains. Therefore, the hydration film formed in hydrodynamic lubrication may exist transiently in the transitional state after the velocity jump, and work together with the change of the polymer networks to result in the extremely low μ. This speculation will be further estimated in the following section.
The tests above mainly focused on investigating the friction properties with the sliding velocity changing between high speed (v h ) and middle speed (v m ), additional friction tests with alternative sliding velocity cycles were designed to explore the frictional characteristics with a sudden change between high speed (v h ) and low speed (v l ). As shown in Figs. 3(a)-3(c), the blue area represents the sliding velocity of v h = 105 rad/s, and the yellow area represents the sliding velocity of v l = 1.05×10 -3 rad/s. As shown in Fig. S1(b) in the ESM, the friction coefficient of hydrogel at v h decreases and then remains at about 0.105 in the first 600 s of the friction curve. In the last 600 s of the friction curve, the hydrogel friction coefficient decreases and then remains stable at about 0.092. It can be concluded that the process v l → v h does not change the trend of the friction curve at v h , but slightly reduces the friction coefficient of hydrogel at v h . When the sliding velocity changes from v h to v l in Train 4, as shown in Fig. 3(a), the μ of hydrogel drops abruptly from 4.56×10 -2 to 4.37×10 -4 , which is much lower than that without the velocity jump (9.66×10 -4 ). The observed decline in μ could be explained by the mechanism we proposed in the process v h → v m that the polymer chains are entrained to the sliding direction. As shown in Figs. 3(b) and 3(c), the μ of the hydrogel at low speed decreases significantly with more v h → v l changing cycles. This phenomenon can be explained by the continuous extension of polymer chains caused by multiple velocity jumps. As shown in Fig. 3(d), the μ of hydrogels after 10 jumps of v h → v l is 1/21 of the minimum value without friction training, and the μ after 5 or 1 jump is 1/11 or 1/3 of the minimum value without training. The friction curve of the after-training section in Train 6 is fitted by an exponential empirical equation.
Since v l and v m are in different lubrication regimes ( Fig. 1(d) where A, m, and n are the parameters obtained by fitting the empirical equation. As shown in Fig. 3(e), the friction coefficient vs time curve within 600 s after training can be accurately fitted by Eq. (4) with www.Springer.com/journal/40544 | Friction an adjusted R 2 of 0.99. However, the friction curve deviates from the fitting curve significantly in the initial 2 s. We believe that this deviation is caused by a combination of hydrodynamic lubrication and polymer changes at the moment of v h → v l jump.
Additional friction tests were conducted to further understand the friction properties when the sliding velocity changes abruptly between v m and v l at different lubrication regions. As shown in Figs. 4(a) and 4(b), after the sliding velocity changes from v m to v l , the μ   | https://mc03.manuscriptcentral.com/friction increases steadily from a higher starting point (1.73×10 -2 or 3.53×10 -2 for 1 or 5 times training) compared the one without training (2.35×10 -3 ). In contrast to the process of v h shown in Figs. 2 and 3, the v m process can neither cause large deformation of the polymer network nor the strong hydrodynamic lubrication. Therefore, the velocity jump process (v m → v l ) will not result in an extremely low coefficient of friction. This result supports our hypothesis that the change of the extension state of polymer chains, and the hydration film formed in hydrodynamic lubrication are the main reason for the ultra-low μ after velocity jumps.
In order to further study how velocity jumps affect friction performance, a pause section lasting for 10 or 30 s was introduced to Train 3 and Train 6 after friction training. It is anticipated that the extension of the polymer chains will recover and hydrodynamic lubrication will disappear during the time pause. As shown in Fig. 5(a), the hydrogels undergoing the v h → v m friction training does not exhibit extremely low μ after a 10 s pause. Besides, the shape of the friction curve after a 30 s pause is close to the curve without friction training (Fig. 5(b)). It can be seen that the friction behavior of the after-training part gradually resembles the behavior before training when the pause time extends from 10 to 30 s, resulting from the recovery of the polymer network. This phenomenon proves our assumption that the extension and the alignment of polymer chains on hydrogel surface is an important factor for understanding the effect of velocity jump on hydrogel lubrication. The instant high value of μ at the end of the time pause is caused by the peeling and breaking of the polymer chains adsorbed to the substrate. This conclusion is also confirmed by v h → v l alternated velocity test. As shown in Fig. 5(c), the initial μ of the hydrogel at v l after the time pause is higher than that without friction training (2.79×10 -3 vs. 1.82×10 -3 ), which proves that the polymer chains extended at v h is partially adsorbed to the substrate. As shown in Fig. 5(d), the initial μ after a pause of 30 s is much higher than that without friction training (4.09×10 -3 vs. 1.65×10 -3 ), which could be attributed to the adsorption of more polymer chains onto the glass substrate. Therefore, it can be concluded that one of the main reasons of the extremely low μ after velocity jump is that the adsorption of polymer chains onto substrate is hindered.
It is speculated that the hydration film formed during hydrodynamic lubrication may affect the adsorption rate of polymer chains after velocity jumps. Therefore, the effect of the hydration film was also verified by monitoring the film thickness change during friction tests. Previously reported results indicate that www.Springer.com/journal/40544 | Friction the lubrication between the hydrogel and the substrate is dominated by hydrodynamic lubrication at the friction speed of v h , and a hydration film is formed between the hydrogel and the surface [37,44,45]. The relative gap was obtained by measuring the distance between the hydrogel and the substrate by the rheometer. As shown in Figs. 6(a) and 6(b), the relative gap decreases to a stable state in 2 s after the speed jumps of v h → v l and v h → v m , indicating that the hydration film gradually disappears in 2 s. Water in the hydration film flows at high speed with the rotation of the substrate at v h , and it will keep flowing for a short time due to inertia when the velocity changes, thus, the hydration film will not disappear immediately. Importantly, the hydration film effectively prevents the contact of the hydrogel to the substrate after velocity jump, so that the polymer chains on the hydrogel surface cannot be dynamically adsorbed to the substrate. Therefore, it can be regarded that the hydrogel is in hydrodynamic lubrication with the sliding velocity of v l or v m in a short time after the velocity jump of v h → v l or v h → v m , which is the reason for the extremely low μ when the velocity jump occurs. In addition, the deviation between the fitted curve and the friction curve in the initial part (Figs. 2(e) and 3(e)) can also be explained by the slow disappearance of the hydrated film. As shown in Figs. 6(c)-6(f), within a short time after the speed jump of v h → v l or v h → v m , the adsorption-desorption process between the polymer network and the substrate does not reach a stable state with the presence of the hydration film. Specifically, the adsorption rate of the polymer chains to the surface is much higher than the desorption rate. Therefore, the friction curve of this process (the first 20 s in Fig. 2(e) and the first 2 s in Fig. 3(e)) is quite different from the overall friction curve. This distinction will disappear when the adsorption-desorption process reaches equilibrium. When the sliding velocity is v m , there is an inflow and outflow of water in the gap, which delays the disappearance of the hydrated film and makes it more difficult for the polymer chains to adsorb to the substrate after the velocity jump of v h → v m . However, the polymer chains can easily adsorb to the substrate after v h → v l because there is no hydration film at velocity v l . Therefore, the adsorption-desorption process can reach equilibrium more quickly after v h → v l compared with v h → v m (2 s vs. 20 s).
The outcome that the friction coefficient μ decreases significantly when the shear velocity is changed abruptly can be applied to improve the performance of artificial joints. As shown in Figs. 7(a)-7(c), three friction experiments that run for 400 s under v m and v h are designed, named Test 1, Test 2, and Test 3, respectively. In Test 1, a friction process for 400 s was performed at v m and v h successively. In Test 2 and Test 3, 5 and 10 speed jumps of v h → v m were added, respectively. The average μ of Test 1, Test 2, and Test 3 in the overall friction process (red lines in Figs. 7(a)-7(c) and summarized in Fig. 7(d)) are measured to be 0.0495 ± 0.0025, 0.0395 ± 0.0035, and  0.033 ± 0.001, respectively. Obviously, adding speed jumps of v h → v m in the friction process can significantly reduce the measured μ of the hydrogel, which is helpful in reducing friction and energy consumption on the artificial joint.

Conclusions
In summary, the hydrogel friction behavior under alternative sliding velocity cycles has been investigated. The results show that the friction coefficient μ between hydrogel and glass dramatically decreases when the sliding velocity drops from a high velocity (105 rad/s) to a relatively low velocity (1.05 rad/s or 1.05×10 -3 rad/s). Moreover, repeating the speed jump (friction training) can further reduce the μ of the hydrogel at a low speed. After 10 frictional velocity jumps, the μ of polyacrylamide (PAM) hydrogel at 1.05 rad/s and 1.05×10 -3 rad/s can reach 3×10 -3 and 9×10 -5 , respectively, which are 1/6 and 1/21 of the μ without alternative sliding velocity cycles. The extension and alignment of polymer chains in the direction of sliding have contributed to the extremely low μ after velocity jumps. In addition, the brief existence of hydration film after the velocity jump enables hydrogel to be hydrodynamically lubricated at low shearing velocities, which hinders the adsorption of polymer chains to substrates and significantly reduces the μ at the transition moment of velocity jump. Our study revealed the frictional behavior of hydrogels under velocity jump and explained its mechanisms, providing basic and experimental insights into understanding the frictional behavior in biosystems with variable and abrupt motions. In addition, with the elaborated application of velocity jump induced low μ via friction training, the energy loss and wear can be significantly reduced in engineering and medical devices. For future study, an ultralow μ with long-term stability and reliability would be achieved based on the fundamental mechanisms and advanced understanding of hydrogel friction demonstrated in this work.

Declaration of competing interest
The authors have no competing interests to declare that are relevant to the content of this article. The author Hongbo ZENG is the Associate Editor of this journal.
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