Superlubricity of silicone oil achieved between two surfaces by running-in with acid solution

Abstract

In this paper, we showed that the superlubricity of silicone oil can be achieved between friction surfaces (Si₃N₄/glass) by running-in with an acid solution. The friction coefficient of silicone oil can be reduced to about 0.004, which is only one-thirtieth of its original value (μ = 0.13). Experimental results indicate that the formation of a circular plane under the action of hydrogen ions on the worn region of the ball is closely linked to superlubricity, while the topography of the track on the glass substrate has no obvious effect on the superlubricity. In addition, the tribochemical reaction between Si₃N₄ and water can lead to the reduction of the friction coefficient in mixed lubrication, but it has no effect on the friction coefficient in hydrodynamic lubrication. According to these results, a superlubricity mechanism was proposed, in which the two friction surfaces form a micro-slope plain bearing, owing to the effect of hydrogen ions, and the silicone oil forms a hydrodynamic film at a certain speed.

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Introduction

The concept of superlubricity was invented in the early 1990s to describe the physical phenomenon in which the friction force between two sliding surfaces becomes zero.¹ But, in practice, when the sliding friction coefficient is less than 0.01, the phenomenon is referred to as superlubricity.² Obviously, achieving superlubricity is one of the most effective ways to save a huge amount of energy in mechanical systems. More importantly, in micro- and nanomachines with sliding components, one of the biggest obstacles to motion is friction, and these could therefore also benefit from superlubricity. Over the last two decades, a lot of effort has been dedicated to the matter by researchers in many fields, and thereby significant progress has been made in the experimental study of superlubricity.³ At present, it has been found that there are several kinds of solid lubricants that possess superlubricity properties, such as diamond-like carbon film (DLC),⁴ molybdenum disulfide (MoS₂),⁵ carbon nitride film (CNx),⁶ and highly oriented pyrolytic graphite at the nano-scale.^7,8 All of these can lead to a friction coefficient of less than 0.01 under some special conditions (e.g., vacuum or nitrogen protection). The superlubricity mechanism for these materials is mainly attributed to incommensurate contact or weak interfacial interactions.⁹

As well as solid lubricants, some liquid lubricants also have superlubricity properties if they are in coordination with friction surfaces. A typical example is ceramic material under water lubrication.^10–12 An ultra-low friction coefficient of 0.002–0.007 can be achieved due to the tribochemical reaction between the ceramic surface and water.¹³ In addition to this, Klein et al. found that the polymer brush immersed in water can lead to an ultra-low friction coefficient of about 0.001 below 7 MPa, due to the formation of a hydration layer.^14,15 Matta et al. found that a DLC film (ta-C) under pure glycerol lubrication can realize a friction coefficient of 0.007 due to the easy sliding on the tribo-formed OH-terminated surfaces.¹⁶ Arad et al. obtained a low friction coefficient of less than 0.003 by using polysaccharide solution extracted from red algae, because of the spiral chain structure of the polysaccharide.¹⁷ Recently, our group found that liquid superlubricity can be obtained with the lubrication of the mucilage of Brasenia schreberi,¹⁸ phosphoric acid,^19–21 and a mixture of polyhydroxy alcohol and acid.^22–24

From the examples above, it is easy to see that the liquid lubricants with superlubricity properties are all water-based. This is because applying pressure to water hardly increases its viscosity,²⁵ which can lead to an extremely low shear strength to reduce friction force under high contact pressure. However, as for oil-based lubricants, due to their viscosity increasing dramatically with pressure, the shear strength is usually much higher than that of water-based lubricants, which hinders the reduction of the sliding friction coefficient. There is a question of whether superlubricity can be achieved using oil-based lubricants. Obviously it is necessary to avoid the viscosity of the confined solution becoming high under pressure, and, simultaneously, to form a lubricating film in the contact region. In the present work, a new method to achieve the superlubricity of oil-based lubricants was proposed; that is, treating the friction surfaces (silicon nitride/glass) by running-in with an acid solution. Here, silicone oil was chosen as an example of an oil-based lubricant, and a detailed investigation on the mechanism by which superlubricity was achieved has been discussed.

Materials and method

The silicone oil ((CH₃)₃SiO[(CH₃)₂SiO]_n-Si(CH₃)₃) with six different levels of viscosity (100, 200, 350, 500, 750 and 1000 mPa s, 25 °C) was purchased from Chinese medicine group. The four kinds of acid (sulfuric acid (H₂SO₄), hydrochloric acid (HCl), oxalic acid (H₂C₂O₄) and aminosulfonic acid (HNO₃S)), sodium chloride (NaCl) and sodium hydroxide (NaOH) were all commercial products (J&K) with a purity of more than 99%. Before the tests, these acids were diluted or dissolved with de-ionized water (resistivity > 18 MΩ cm) to a pH value of 1.0. Moreover, NaCl was dissolved by de-ionized water to a concentration of 5% (pH = 7) and NaOH was dissolved by de-ionized water to a pH value of 13.

The friction coefficient was measured on a Universal Micro-Tribotester (UMT-3, Bruker, America) with a rotation mode of ball on disk. The ball was made of silicon nitride (Si₃N₄) with a diameter of 4 mm (R_a = 10 nm), and a glass slide (R_a = 5 nm) was used as the disk. Before the tests, the ball and glass slide were cleaned using acetone, ethanol and deionized water successively for 10 min in an ultrasonic bath and then dried using compressed air. The solutions above were introduced between the ball and the disk at a volume of 20 μL. The load applied to the disk was 3 N (the maximum contact pressure was about 700 MPa) and the rotation speed of the disk was changed from 2 rpm to 240 rpm with a track radius of 4 mm, corresponding to a sliding speed ranging from 0.0008 m s⁻¹ to 0.1 m s⁻¹. The friction coefficient under each of the different conditions was measured five times. The accuracy of the friction coefficient measurements was ±0.001. To obtain an accurate value of the friction coefficient, the measurement errors were eliminated by adjusting the levelness of the disk to obtain the same friction coefficients in two reverse sliding directions.²⁶ All of the tests were performed at a temperature of 25 °C and relative humidity of 20–40%.

To wash out the remaining acid solution on the friction surfaces after testing, the ball and the glass slide were first immersed in de-ionized water for about 5 min, and then the de-ionized water was sucked up by syringe, and finally the ball and the glass slide were cleaned using absorbent paper. The topography of the friction surfaces was investigated using an optical microscope (Olympus) and scanning electron microscopy (SEM, QUANTA 200 FEG) under a low vacuum. The detail of the worn region was investigated using atomic force microscopy (AFM, Nanoman VS), operating in tapping mode under ambient conditions.

Results and discussion

The friction coefficient of the 100 mPa s silicone oil between the original surfaces of Si₃N₄ and glass (not treated with acid) is shown in Fig. 1. It can be seen that the friction coefficient was reduced from 0.3 to 0.13 after a running-in period of 500 s. After that, the friction coefficient remained stable. However, if the original surfaces of the Si₃N₄ and glass were lubricated with H₂SO₄ (pH = 1) for 250 s first (the friction coefficient was reduced to 0.04 after a running-in period of 80 s), and then the friction coefficient of the 100 mPa s silicone oil was measured again between the two friction surfaces (the remaining H₂SO₄ solution on the friction surfaces was washed out before the measurement), it was found that the friction coefficient of the silicone oil was suddenly reduced to about 0.004 without a running-in period, as shown in Fig. 1. Comparing the two results, it is obvious that, after running-in the friction surface with H₂SO₄, the friction coefficient of silicone oil can be reduced to the order of magnitude of 0.001, and therefore enters the superlubricity regime. In addition, it was found that the ultra-low friction coefficient of 0.004 could be maintained for at least for 5 h, which indicates that the superlubricity state of the silicone oil is very stable.

Fig. 1 Friction coefficient with the lubrication of the 100 mPa s silicone oil, H₂SO₄ (pH = 1) and the 100 mPa s silicone oil after running-in with H₂SO₄ (pH = 1).

Because the viscosity and speed are two main factors influencing the friction coefficient of a liquid lubricant, the friction coefficients of silicone oils with six different levels of viscosity were first measured between the original surfaces (Si₃N₄/glass) and then measured between the friction surfaces (Si₃N₄/glass) after running-in with H₂SO₄ (pH = 1), as shown in Fig. 2. It was found that the friction coefficients of these silicone oils are all about 0.12 when measured between the original surfaces, and are therefore independent of their viscosity. However, the friction coefficients of these silicone oils are all less than 0.01 (and therefore achieve superlubricity) when measured between the friction surfaces after running-in with H₂SO₄. This indicates that running-in the friction surface with H₂SO₄ can lead to a remarkable reduction in the friction coefficient of silicone oil, regardless of its viscosity. Moreover, it was also found that the friction coefficient increased slightly as the viscosity increased.

Fig. 2 Final friction coefficients of silicone oils between the original surfaces (Si₃N₄/glass) and the surfaces after running-in with H₂SO₄ (pH = 1). The error bars present the standard deviations of five measured values.

To investigate the relationship between superlubricity and speed, the friction coefficients of the 100, 350 and 1000 mPa s silicone oils between the surfaces (Si₃N₄/glass) after running-in with H₂SO₄ (pH = 1) were measured at different rotation speeds, as shown in Fig. 3. As for the 100 mPa s silicone oil, it was found that superlubricity (μ < 0.01) could be achieved when the rotation speed was greater than 15 rpm, and that the friction coefficient decreased slightly with an increase in the speed from 15 rpm to 240 rpm. But when the rotation speed was less than 15 rpm, the friction coefficient increased greatly with a reduction in the speed, and the final friction coefficient was greater than 0.01 when the rotation speed was reduced to 6 rpm. As for the 350 mPa s silicone oil, the speed region that yielded superlubricity (higher than 15 rpm) was the same as that for the 100 mPa s silicone oil, but the change in the friction coefficient with speed was different. It could be seen that the friction coefficient was greatly reduced as the speed was increased from 2 rpm to 30 rpm, and was increased slightly as the speed was increased from 30 rpm to 240 rpm. As for the 1000 mPa s silicone oil, it was found that superlubricity (μ < 0.01) could be achieved across the whole range of rotation speeds (2 rpm to 240 rpm). In addition, the change in the friction coefficient with speed was similar to that of the 350 mPa s silicone oil. The friction coefficient was slightly reduced as the speed was increased from 2 rpm to 15 rpm and was slightly increased as the speed was increased from 30 rpm to 240 rpm. Taking into account these friction results, it was found that the curves of the friction coefficient against speed were consistent with the typical Stribeck curve,²⁷ which indicates that the superlubricity state is in the range of mixed lubrication (ML) and elastohydrodynamic lubrication (EHL).

Fig. 3 Friction coefficients of silicone oils (100, 350 and 1000 mPa s) between the surfaces (Si₃N₄/glass) after running-in with H₂SO₄ (pH = 1) at different rotation speeds. The error bars present the standard deviations of five measured values.

According to the above results, it can be seen that the superlubricity of silicone oils with different viscosities can be achieved at different speeds between Si₃N₄/glass surfaces after running-in with H₂SO₄. However, the reason that H₂SO₄ can lead to the remarkable reduction of the friction coefficient of silicone oil to achieve superlubricity is still not clear, and will be investigated in detail as follows. First, to determine which kind of ion in the H₂SO₄ solution plays the key role in achieving superlubricity, three other kinds of acid solution (HCl, H₂C₂O₄ and HNO₃S, pH = 1), as well as Na₂SO₄ and NaOH solutions, were chosen as pre-lubricants and each tested for about 250 s. It was found that the friction coefficients of these acid solutions were reduced to 0.03–0.05, just like H₂SO₄ in Fig. 1, but the friction coefficients of the Na₂SO₄ and NaOH solutions were still above 0.3. Subsequently, the remaining solutions on the friction surfaces were washed out, and then the silicone oils with three different levels of viscosity (100, 350, and 1000 mPa s) were added in the contact region, respectively. The friction coefficients of these silicone oils are shown in Table 1. It was found that the friction coefficients of these silicone oils can all be reduced to less than 0.01 between the friction surfaces after running-in with the three kinds of acid solution. This indicates that all of the acid solutions have the same effect of reducing the friction coefficient of silicone oil to achieve superlubricity. However, if the surfaces are treated by running-in with Na₂SO₄ and NaOH solutions the friction coefficients of these silicone oils become greater than 0.04. Based on these results, it can be concluded that the hydrogen ions in the acid solutions play the key role in achieving the superlubricity of silicone oil.

Table 1 Friction coefficients of silicone oils (100, 350, and 1000 mPa s) between Si₃N₄/glass surfaces after running-in with three kinds of acid solutions (HCl, HNO₃S and H₂C₂O₄), as well as NaCl and NaOH solutions

	HCl	HNO3S	H2C2O4	NaCl	NaOH
Silicone oil (100 mPa s)	0.004	0.004	0.003	0.14	0.05
Silicone oil (350 mPa s)	0.006	0.006	0.007	0.08	0.05
Silicone oil (1000 mPa s)	0.007	0.008	0.008	0.09	0.05

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To determine how the hydrogen ions influence the friction coefficient of silicone oil, the topography of the friction surfaces after lubrication with H₂SO₄ was first investigated using an optical microscope, as shown in Fig. 4(a). It could be seen that a circular plane with a diameter of 260 μm appeared on the top region of the ball, and there were many micro-pits and micro-furrows in the track on the glass substrate. Moreover, the topography of the friction surfaces after the lubrication with other acid solutions was the same as that when H₂SO₄ is used. For comparison, the friction surfaces after lubrication with the NaCl solution, NaOH solution and silicone oil (without acid) were also investigated, as shown in Fig. 4(b)–(d). It could be seen that the topography of the worn region of the ball lubricated with NaCl solution was almost the same as that lubricated with NaOH solution; both of them became an elliptic plane with a deep ditch in the middle of the contact region, which was different from the regions lubricated with acid solutions. It was also found that the wear features of the glass substrate were different from those on the substrate lubricated by acid solutions. There were no micro-pits and micro-furrows in the track. After lubrication with silicone oil, it could be seen that the top region of the ball became an elliptic plane with a maximum diameter of 250 μm, and there was much wear debris accumulation in the track on the glass substrate. This indicates that the topography of friction surfaces induced by the action of hydrogen ions is totally different from that lubricated by the NaCl solution, NaOH solution and silicone oil, which may be the reason for the differences in their friction coefficients.

Fig. 4 Optical images of friction surfaces after the running-in period: (a) lubrication with H₂SO₄ (pH = 1), (b) lubrication with NaCl solution (pH = 7), (c) lubrication with NaOH solution (pH = 13), and (d) lubrication with the 100 mPa s silicone oil. The white arrows represent the sliding direction.

To further investigate the relationship between hydrogen ions and superlubricity, the lubricating behavior of the 100 mPa s silicone oil was investigated between the Si₃N₄/glass surfaces after running-in with H₂SO₄ solutions with different pH values, as shown in Fig. 5. When the pH value was equal to 0, the friction coefficient of the H₂SO₄ solution could be reduced to 0.08 after 80 s (inset of Fig. 5) and the friction coefficient of silicone oil could be reduced to 0.011, which indicates that superlubricity was not achieved in this case. When the pH value was in the range of 0.5–2, the friction coefficient of the H₂SO₄ solution could be reduced to 0.04 after a running-in period (100–200 s), and the superlubricity of silicone oil could be achieved (the friction coefficient was in the range of 0.003–0.006). However, when the pH value was increased to 2.5, there was no reduction in the friction coefficient of the H₂SO₄ solution, and the superlubricity of silicone oil disappeared (the friction coefficient was greater than 0.015). This indicates that the concentration of hydrogen ions in the acid solution is closely linked to superlubricity, and that a concentration of hydrogen ions that is either too high or too low does not benefit superlubricity.

Fig. 5 Friction coefficient of the 100 mPa s silicone oil between the surfaces (Si₃N₄/glass) after running-in with H₂SO₄ solutions with different pH values. The error bars are the standard deviations of five measured values. The insets show the friction coefficient curves of H₂SO₄ solutions with pH values of 0, 1.5 and 2.5.

The topography of the friction surfaces after lubrication by H₂SO₄ with different pH values was also investigated using an optical microscope, as shown in Fig. 6. When pH = 0 or 1.5, a circular plane appeared on the top region of the ball and there were many micro-pits and micro-furrows in the track on the glass substrate, which was the same as that shown in Fig. 4(a). But the worn area of the ball for pH = 0 was much less than that for pH = 1.5. When pH = 0, the diameter of the worn region was about 180 μm, corresponding to a contact pressure of 118 MPa. When the pH = 1.5, the diameter of the worn region was about 260 μm, corresponding to a contact pressure of 56 MPa. This indicates that the contact pressure for superlubricity (pH = 1.5) was much lower than that for non-superlubricity (pH = 0). Similarly, when pH = 0.5, 1 and 2, the contact pressure was also much lower than that for pH = 0 (the contact area increased with an increase in the pH). When pH = 2.5, the topography of the friction surfaces was totally different from that when pH = 0 or 1.5. There was a deep groove in the middle of the worn region, and the worn region of the ball was not a circular plane. Based on these results, it can be confirmed that the superlubricity is closely linked to the topography of the friction surfaces induced by hydrogen ions (the running-in mechanism of hydrogen ions was investigated in detail in our previous work²⁸). This result indicates that the topography that most benefits superlubricity is that in which the worn region of the ball becomes a large flattened plane under the action of hydrogen ions to reduce contact pressure.

Fig. 6 Optical images of friction surfaces after lubrication with H₂SO₄ solutions. (a) pH = 0, (b) pH = 1.5, and (c) pH = 2.5. The white arrows represent the sliding direction.

To further investigate how the topography of the friction surface influences the friction coefficient of silicone oil, an experiment was designed as follows. First, the friction coefficient of H₂SO₄ (pH = 1.0) was tested for 250 s (the friction coefficient was reduced to about 0.05) and then the H₂SO₄ solution left on the surfaces was washed out. Second, the glass substrate was changed to a new one without a wear track, and the ball was still the original one. Third, the friction coefficient of the 100 mPa s silicone oil was measured between the original ball and the new glass substrate under the same test conditions (load = 3 N, rotation speed = 180 rpm), as shown in Fig. 7. It was found that the superlubricity (μ = 0.005) of silicone oil could be achieved (without a running-in period) in this case. However, if the ball was changed to a new one, and the glass substrate was the original one, the friction coefficient of the 100 mPa s silicone oil was about 0.26, which was fifty times higher than that in the former case. Based on these two results, it can be concluded that the topography of the worn region of the ball plays the key role in the superlubricity, while the topography of the track on the glass substrate has no obvious effect on the superlubricity.

Fig. 7 Friction coefficients of the 100 mPa s silicone oil, after changing the ball and changing the glass substrate, between the surfaces after running-in with H₂SO₄ solution.

To better understand the beneficial effect of the worn region of the ball on the superlubricity, we used SEM (QUANTA 200 FEG) and AFM (Nanoman VS) to investigate the detail of the worn region of the ball after lubrication with the H₂SO₄ solution, as shown in Fig. 8(a) and (b). The SEM image shows that there are some large wear pits on the worn region of the ball and the AFM image shows that there are many wear particles deposited on the worn region of the ball. In addition, the original micro-pits on the Si₃N₄ surface cannot be observed by SEM and AFM, which indicates that these pits are filled by something. Because the tribochemical reaction between Si₃N₄ and water can occur during the running-in period (the hydrogen ions can accelerate the tribochemical reaction speed),²⁹ the following reactions were assumed to happen:

Si₃N₄ + 6H₂O = 3SiO₂ + 4NH₃ (1)

SiO₂ + 2H₂O = Si(OH)₄ (2)

Fig. 8 (a) SEM image of the worn region of the ball after lubrication with H₂SO₄ solution. (b) AFM image of the worn region of the ball after lubrication with H₂SO₄ solution. (c) SEM image of the worn region of the ball after treatment by HF solution. (d) AFM image of the worn region of the ball after treatment by HF solution.

Therefore, it can be inferred that there is a silica layer deposited on the worn region of the ball, which fills the original micro-pits on the Si₃N₄ surfaces. To confirm this inference, the ball was immersed in HF solution (30%) for 5 min, and then the worn region was investigated using SEM and AFM again. In this case, the silica layer and the wear particles from glass can be corroded by HF solution as follows:³⁰

SiO₂ + 4HF = SiF₄ + 2H₂O (3)

Si(OH)₄ + 4HF = SiF₄ + 4H₂O (4)

The worn region of the ball after the treatment by HF solution is shown in Fig. 8(c) and (d). It can be seen that the wear particles deposited on the worn region disappear and the original micro-pits on the Si₃N₄ surface appear, which confirms that the wear particles and the silica layer have been corroded by the HF solution. Comparing these images with that in Fig. 8(a), it can be concluded that the tribochemical reaction between Si₃N₄ and water can produce a silica layer that deposits on the worn region of the ball during the running-in period.

Do the wear particles and the silica layer produced by the tribochemical reaction influence the superlubricity? To answer this question, the friction coefficients of 100 mPa s silicone oil and 1000 mPa s silicone oil were measured at different speeds after the ball was treated with HF solution, as shown in Fig. 9(a) and (b). Compared with the friction coefficients of silicone oils that were not treated with HF, it can be seen that the friction coefficient of the 100 mPa s silicone oil on the surfaces treated with HF was almost the same as that on the surfaces that were not treated with HF when the rotation speed was higher than 60 rpm. However, when the rotation speed was lower than 30 rpm, the friction coefficient on the surfaces treated with HF was much higher than that on the surfaces that were not treated with HF. Similarly, the change in the friction coefficient of the 1000 mPa s silicone oil after being treated with HF is the same as that of the 100 mPa s silicone oil. It can be seen that treatment with HF can lead to a higher friction coefficient when the rotation speed is lower than 15 rpm, but it has almost no effect on the friction coefficient when the rotation speed is higher than 30 rpm. These results indicate that the wear particles and the silica layer only have an effect on the superlubricity when the friction pair is in mixed lubrication, and they have no obvious effect on the superlubricity when the friction pair is in full hydrodynamic lubrication. Because there are some asperities with direct contact when the friction pair is in mixed lubrication, it indicates that the silica layer produced by the tribochemical reaction can provide a low friction coefficient for boundary lubrication, which is in accordance with the friction result of ceramic material under water lubrication.¹³

Fig. 9 Friction coefficients of silicone oils (100 and 1000 mPa s) at different rotation speeds after the ball was treated with HF solution. The error bars present the standard deviations of five measured values.

According to these results and the analysis above, a lubrication model was proposed to account for the superlubricity, as shown in Fig. 10. Firstly, with the action of hydrogen ions, the worn region of the ball would become a circular plane due to wear. In this case, the flattened plane of the ball and the glass plate formed a micro-slope plain bearing (composed of an inclined upper surface and a horizontal lower one). Secondly, when the silicone oil was introduced between the two friction surfaces, a hydrodynamic film could be formed under the hydrodynamic effect. According to this lubrication model, if the rotation of the horizontal lower surface is changed to the opposite direction, the hydrodynamic effect would disappear because the gap between two friction surfaces increases along the direction of the rotation. It can be inferred that the friction coefficient would become high in this case. To confirm this inference, the friction coefficient of the 100 mPa s silicone oil was measured in two reverse sliding directions after running-in with H₂SO₄ (pH = 1), as shown in Fig. 11. It was found that the friction coefficient in the opposite sliding direction (relative to the sliding direction in which the running-in with H₂SO₄ was carried out) would increase to 0.14, which is about 35 times greater than the value in the other sliding direction. It was therefore confirmed that the superlubricity appears only when the hydrodynamic effect exists between two friction surfaces, which is consistent with the lubrication model above.

Fig. 10 Lubrication model of silicone oil between the Si₃N₄/glass surfaces after running-in with H₂SO₄ solution.

Fig. 11 Friction coefficient of the 100 mPa s silicone oil between the Si₃N₄/glass surfaces after running-in with H₂SO₄ solution in two reverse sliding directions.

To confirm whether the lubrication model above is reasonable, the friction coefficient of silicone oil with this lubrication model (micro-slope plain bearing) was calculated according to the Reynolds equation, as shown in eqn (5)¹³

where h is the thickness of the lubrication film, η is the viscosity of the lubricant, U is the velocity, and p is the pressure. Solving eqn (5) giveswithwhere C_w and C_μ are constant, L is the width of the bearing, W is the applied load and m = h₁/h₀, where h₁ is the film thickness at the entry and h₀ is the film thickness at the exit. Here, we assume that the width (L) of the bearing is approximately equal to the diameter of the worn region of the ball (260 μm), and the inclination angle of the upper surface is 0.003°. Because the calculated result is based on full hydrodynamic lubrication, we chose the 350 mPa s silicone oil as an example and the range of the rotation speed was from 30 rpm to 300 rpm (in the region of hydrodynamic lubrication according to Fig. 3(b)). The calculated result is shown in Fig. 12. It was found that the calculated friction coefficient increased from 0.0017 to 0.0079 when the rotation speed was increased from 30 rpm to 300 rpm, which is in good agreement with the test results. However, the calculated friction coefficient is lower than the measured friction coefficient when the rotation speed is low, which is because the effect of surface roughness is not considered in the calculation model. When the rotation speed is too low to enter the mixed lubrication, the asperity contact has a great influence on the calculated friction coefficient.

Fig. 12 Calculated friction coefficient and measured friction coefficient of the 350 mPa s silicone oil between the Si₃N₄/glass surfaces after running-in with H₂SO₄ solution. The error bars present the standard deviations of five measured values.

The calculated friction coefficient indicates that superlubricity can be achieved with the micro-slope plain bearing under some specific conditions. Because the hydrodynamic lubrication formed in the slope plain bearing is mainly dependent on the pressure, speed, and viscosity, it is inferred that superlubricity can be achieved as long as the three parameters match up very well. To confirm this, we also tested the friction coefficient of other lubricants, such as polyether, oleic acid, ionic liquid, and liquid crystals (5CB) between the surfaces (Si₃N₄/glass) after running-in with H₂SO₄ (pH = 1), and found that their friction coefficients were all less than 0.01, which indicates that superlubricity can be obtained as long as the speed and the viscosity of these lubricants match up well. This work confirms that liquid superlubricity can be achieved not only by surface chemical action, such as a tribochemical reaction,¹¹ hydrogen bond network^16,19 and hydration layer,³¹ but it can also be obtained by hydrodynamic lubrication under some special conditions. However, the presence of acid and the limitation of friction pairs limit its application in actual mechanical systems. Therefore, we are trying to improve the above oil-based liquid superlubricity system according to the proposed superlubricity mechanism, and we believe that a new superlubricity system employing an oil-based lubricant could be designed to lubricate mechanical systems by further optimization in the near future.

Conclusions

In summary, the present work showed that the superlubricity of silicone oil can be achieved between friction surfaces (Si₃N₄/glass) after running-in with acid solutions. The role of acid solutions is to form a flattened plane on the worn region of the ball to reduce the contact pressure and simultaneously compose a micro-slope plain bearing with the glass substrate. The role of silicone oil is to form a hydrodynamic film between the two flattened surfaces. The role of the tribochemical reaction between Si₃N₄ and water is to provide a low friction coefficient in mixed lubrication, but it has no obvious effect on the friction coefficient in hydrodynamic lubrication. The liquid superlubricity is attributed to the formation of mixed lubrication and hydrodynamic lubrication in a micro-slope plain bearing. Superlubricity can be achieved as long as the speed and the viscosity match up very well. This finding may be very useful to assist us in designing mechanical bearings with superlubricity properties in the future.

Acknowledgements

The work is financially supported by the National Natural Science Foundation of China (51405256, 51222507, 51335005), National Key Basic Research Program of China (2013CB934202), and China Postdoctoral Science Foundation funded project (2014M550056).

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