Superlubricity by polyimide-induced alignment

We have investigated the lubrication alignment behavior of point-plane contact and plane-plane contact between the GCr15 steel and polyimide (PI) friction pair using nematic liquid crystals (LCs) as the lubricant. In this system, rubbing orients the macromolecular PI molecules, and the oriented PI molecules induce alignment of the LC molecules in contact with or close to the oriented PI molecules. The LC molecules are aligned in the wear scar grooves of the PI film, and alignment extends to the GCr15-steel counterpart. Alignment of the LC molecules is correlated with the strong interaction force between the PI and LC molecules, the stable coordination structure of the LCs and GCr15 steel, and the weak interaction between the LC molecules. We performed simulations of the pretilt angle of PI and LCs and discussed the relationship between the pretilt angle and the friction properties. Owing to the small pretilt angle between PI and the LCs, the LC molecules orient almost parallel to the PI material, which is beneficial for superlubricity of this type of friction system.


Introduction
Production and human society are inseparable from friction and lubrication, and energy and resource issues related to human development are closely related to friction and lubrication. In high-performance lubrication systems, as one of the most effective ways to improve production efficiency and reduce energy consumption, superlubricity has attracted increasing attention. Superlubricity refers to friction behavior with a friction coefficient in the order of 0.001 or less, and it is expected to greatly reduce frictional energy consumption, material wear, and frictional noise, and achieve precise mechanical control [1][2][3][4][5][6].
In previous work, we discovered a superlubricity system composed of a nematic liquid crystal (LC) lubricant and the GCr15 steel and polyimide (PI) rubbing pair [30]. We preliminarily studied the alignment superlubricity phenomenon of point-plane contact between widely used GCr15 steel and PI. It is considered that alignment of the LCs on PI is the key www.Springer.com/journal/40544 | Friction to the superlubricity state of the friction system. Owing to the limited practical application scenarios of this contact method, in this study, we further investigated the lubrication alignment behavior of point-plane contact and plane-plane contact between the GCr15 steel and PI friction pair using a nematic LC lubricant. The study provided some experimental data for the use of superlubricity behaivor on surface contact movement. We also proposed the mechanism of the lubrication alignment behavior, the PI alignment led to the superlubricity phenomenon of the system in which the LCs acted as lubricants.
An important material of the lubricating system is PI. It is introduced into tribological system design as a friction pair material, and it is still used as an alignment agent for LCs, effectively controlling the orientation of lubricant molecules, and its friction pair is still most commonly GCr15 steel. PI is a type of mature high-performance engineering plastic. It is a polymer containing an imide group, and it is obtained by polycondensation of dianhydride and diamine. PI has excellent high-and low-temperature resistance, chemical stability, mechanical properties, and dielectric properties. There are a large number of commercial PI materials with characteristic structures to meet various requirements, such as alignment materials in the field of optoelectronics and composite-bearing materials in the field of machinery [31][32][33]. Because of the good characteristics of PI, its molecular structure can be modified according to the requirements of its use, and thus it has great application prospects as a structural or functional material. In addition, as a molecular orientation material, different structures will lead to different orientations.
In this study, nematic LCs were used as a lubricant. Nematic LCs are a one-dimensional ordered phase. The long axis of the molecules is basically arranged in parallel in one direction, the viscosity is small, it has fluidity similar to that of ordinary liquids, and the molecules are not arranged in layers. The directions of the molecules are parallel or nearly parallel to each other, the short-range interaction between the molecules is weak (van der Waals force), and common nematic LCs are mostly rod-like structures, which are easy to align. When LCs are mentioned, people will think of optoelectronic materials. At present, LCs are still mainly optimized as optoelectronic materials, and there is almost no structural design specifically for tribological materials, although tribologists have paid attention to LCs as potential new lubricants from the perspective of conventional lubrication for many years [34][35][36][37][38].
When LCs function as optoelectronic materials, a LC aligning agent must be used. PI is currently the most widely used LC aligning agent in industry, and it can control the pretilt angle of a LC to align it in a certain direction [39,40]. In current industrial production, rubbing alignment is a simple and relatively stable method to control the alignment of LCs. By rubbing, scratches are left on the PI film to form grooves. A certain anchoring force is formed between the LCs and PI, the LCs are aligned along the grooves in the rubbing direction in the natural state, and a fixed pretilt angle is formed between the LCs and PI. The structural characteristics of the PI and LC molecules affect the pretilt angle. Therefore, in this study, we calculated the pretilt angle, analyzed the factors that influence the pretilt angle, and investigated the correlation between the pretilt angle and the superlubricity properties.

Point-plane contact
To study the friction characteristics of the PI/GCr15 friction pair, tribological tests were performed with a microtribometer (UMT-3, CETR) using mixed LCs as a lubricant for point-plane friction. During the test, a GCr15 steel ball (4.76 mm in diameter) of 51103-type thrust ball bearing produced by NSK was used as the static test piece (upper sample). The 6FDA-ODAtype PI film was attached to the smooth surface of the metal disc, which was then mounted on the fixed disc of the testing machine as the rotating disc specimen (lower sample). LCs (0.1 mL) were added between the GCr15 steel ball and 6FDA-ODA PI film. The radius of the annular friction path was 8.5 mm, and the test load was applied vertically through the center line of the ball specimen. The test was performed at ambient temperature (25 °C) using a normal load of 5 N with clockwise rotation. Eleven cycles of 3,600 s with a rotation speed of 50 rpm (44.48 mm/s) were continuously performed for the same friction pair.

Preparation of a plane on a GCr15 steel ball
Before performing the friction test, a plane was prepared on a GCr15 bearing steel ball. Using a microtribometer (UMT-3, CETR), a GCr15 steel ball (4.76 mm in diameter) of 51103-type thrust ball bearing produced by NSK was used as the static test piece (upper sample). Abrasive paper was attached to the smooth surface of the metal disc, which was then mounted on the fixed disc of the testing machine as the rotating disc specimen (lower sample). First, without lubrication, sandpaper (180 mesh) was attached to the smooth surface of the metal disc, and the disc was rotated at 60 rpm. The radius of the annular friction path was 8.5 mm and the load was 5 N. There was point-plane contact, and the operation time was 5 min. Next, the GCr15 steel ball was rotated 90° clockwise, and the disc was rotated for 5 min under the same conditions. The GCr15 steel ball was then rotated counterclockwise by 90°, returning it to the original position. The sandpaper was then replaced with 1,000 mesh sandpaper, and the disc was rotated for 3 min under the same test conditions. Finally, the GCr15 steel ball was rotated clockwise by 90°, the sandpaper was with 2,000 mesh sandpaper, and the disc was rotated for 5 min with the other test conditions unchanged to obtain a plane on the GCr15 steel ball. The plane was observed with a scanning electron microscope (SEM, JSM-6300).

Friction test
At ambient temperature (25 °C), a plane-plane contact friction test was performed with a microtribometer (UMT-3, CETR). The upper sample was the GCr15 steel ball with a plane, the lower sample was the 6FDA-ODA-type PI film, and mixed LCs were used as a lubricant. In the test, the rotation mode was clockwise, the radius of the annular friction path was 8.5 mm, and the GCr15 steel plane was in plane-plane contact with the 6FDA-ODA-type PI film. The mixed LC lubricant (0.1 mL) was added between the GCr15 steel plane and ODA-6FDA PI film. The test time, load, and velocity were adjusted according to the test requirements.

Friction test at different velocities
First, friction tests were continuously performed for 3,600 s at 50, 100, 150, 200, 250, 300, 350, and 400 rpm using the same friction pair, that is, eight cycles of testing, with a load of 5 N. Using the GCr15 steel plane after testing at 5 N, the PI film was replaced with a new PI film, new LCs were added, and a www.Springer.com/journal/40544 | Friction friction test was continuously performed under the same conditions as the 5 N test but with a load of 7 N. The reason for choosing the maximum speed of 400 rpm is that the rotating part of the microtribometer (UMT-3) is at the lower end of the machine, and if the speed is too high, the LCs will be thrown out.
Another set of tests were performed with the same experimental conditions as described in the previous paragraph, except that the speed was started at 400 rpm, dropped to 50 rpm, and the decrement gradient was 50 rpm.

Friction test at different loads
Using the same steel plane as that used in the friction tests at different velocities (Section 2.2.2.2.1), the PI film was replaced with a new film and new LCs were added. Friction tests of the same friction pair were then continuously performed for 3,600 s from 5 to 95 N with an incremental gradient of 10 N at a velocity of 250 rpm.

Comparative test with n-hexadecane as the lubricant
Two friction tests were performed at a speed of 250 rpm, a load of 20 N, and an experimental time of 5 h with clockwise rotation using n-hexadecane (n-C 16 H 34 ) and mixed LCs as the lubricant.

Infrared analysis of LCs and compounds on the steel ball
The infrared (IR) spectra of the compounds were detected by IR spectrometer (Nicolet 6700), LCs were analyzed using IR absorption method. The compounds on the worn surfaces of the steel balls used in Section 2.2.2.2.3 were investigated by IR reflection method, and the influence of the reference (steel ball surface) was deducted.

Surface topography analysis of the friction pairs
The surfaces of the friction pairs used in Section 2.2.2.2.3 were analyzed by a white-light interferometer (AE-100M), a white-light confocal three-dimensional surface profiler (Micromeasure 2), and a SEM (JSM-6300).

Calculation of the pretilt angle between the LCs and PI
The alignment between the LCs and PI can be described by the pretilt angle, that is, with no electric field, the LC director forms a certain angle with the PI surface, which is the pretilt angle. To further understand the interaction between PI and the LCs, we performed molecular dynamics simulations. All of the simulations were performed by the Forcite module in the Materials Studio 5.5 software package (Accelrys Software Inc., San Diego, CA, USA) with the Dreiding force field. The van der Waals interactions were calculated by a truncated method (cubic spline) and the cut-off distance was 12.5 Å, the electrostatic interaction was calculated by the particle-mesh Ewald method, the temperature and pressure were controlled by the Nosé-Hoover and Berendsen methods, respectively, and the simulation time step was 2 fs. The simulation process was divided into two stages: (1) Structure preparation (a) Construction of the PI bulk simulation system. Twenty-seven PI (6FDA-ODA) chains were placed in the simulation system. Each chain contained eight repeating units, and the initial conformation was the extended conformation. These chains were placed in parallel in a box with dimensions of 200 Å × 200 Å × 200 Å. First, a constant number of particles, pressure and temperature (NPT) simulation under normal temperature and high pressure (298 K, 0.1 GPa) was performed. The pressure was then gradually relaxed to normal pressure (0.1 GPa → 0.01 GPa → 0.1 MPa, the simulation times were 60, 40, and 40 ps, respectively). Next, an NPT simulation was performed at normal temperature and pressure, followed by a constant number of particles, volume and temperature (NVT) simulation at normal temperature for 600 ps.
(b) Construction of the PI-film simulation system. The Z axis of the above equilibrium PI system was extended to 150 Å, and then an NVT simulation was performed at room temperature and pressure for 600 ps.
(c) Construction of the LC bulk simulation system. Two hundred 3PEP5 and 200 3UTPP4 molecules were placed in a cubic box at a density of 0.01 g/cm 3 , respectively, and then a 50 ps NPT simulation was performed under normal temperature and pressure of 50 MPa.
(2) Pretile angle calculation The pretile angle in the following two cases were calculated: (a) LCs interact with PI film individually. The 3PEP5 and 3UTPP4 molecules that make up the mixed LCs were constructed, and a 2 ns NVT simulation was performed under normal temperature for each molecule. Ten conformations were randomly selected from the simulation trajectory of the final 1 ns and randomly placed in the PI-film simulation system so that the molecules did not touch each other. A 300 ps NVT simulation was then performed. The above simulation process was repeated 10 times for each molecule.
(b) Bulk LCs interact with PI film. Two LC bulk simulation systems were placed in the PI film system respectively. System was compressed by a 25 ps NPT simulation with normal temperature and pressure of 50 MPa. Then the relaxation was performed by NPT simulation from 300 to 500 K for 5 cycles of annealing schemes. Finally, a 300 ps NPT simulation was performed under normal temperature and pressure of 50 MPa, and the data were analyzed.

Molecular orientation analysis of 6FDA-ODA PI film
The surfaces of the 6FDA-ODA PI films were observed by a polarization microscope (CX40P). The samples included un-rubbing 6FDA-ODA PI film sample, after-dry-rubbing 6FDA-ODA PI film sample (rubbing were performed according to Section 2.2.1, at a speed of 200 rpm, a load of 2 N, and an time of 1 h, wherein the load was initially selected as 5 N , but the PI film was broken during the friction, so the load was selected as 2 N), and after-rubbing 6FDA-ODA PI film sample during LCs lubrication (rubbing was carried out according to Section 2.2.1, at a speed of 200 rpm, a load of 5 N, and an time of 1 h). Using silver particles as overcoating layer onto the PI films, the surface-enhanced Raman scattering (SERS) spectra of the un-rubbing 6FDA-ODA PI film sample and after-dry-rubbing 6FDA-ODA PI film sample (mentioned above) were detected by a laser confocal micro-Raman spectrometer (DXR). Two milliliters of 5% AgNO 3 solution was added to a clean test tube, and 25% NH 3 ·H 2 O solution was added gradually, a brown precipitate was formed. Next, NH 3 ·H 2 O solution was continued to add until the formed precipitate just dissolves, then silver ammonia solution was generated. In a clean 20 mL test tube was a piece of 10 mm × 10 mm PI film, and 5 mL silver ammonia solution and 2 mL formaldehyde solution were mixed in the test tube, which was heated in a water bath for a while, the solution turned to gray and black. Meanwhile the silver particles generated by reduction were deposited on the PI film. The PI film covered with silver overcoating was washed with distilled water and dried. The specimen was ready for Raman studies.

Friction tests of the PMDA-ODA PI film
The plane-plane friction test was carried out by replacing the PI(6FDA-ODA) film with commercial PMDA-ODA PI (DuPont). A plane was obtained on a GCr15 steel ball, as described in Section 2.2.2.1. The method for the plane-plane friction test is described in Section 2.2.2.2.
Friction tests of the same friction pair were continuously performed for 3,600 s at 5-185 N with an incremental gradient of 10 N at a velocity of 250 rpm.

Friction tests of the GCr15/ Cr12 friction pair
The upper sample was the GCr15 steel ball with a plane, the lower sample was the Cr12 steel plane (HRC 55) instead of the PI plane. The friction test was carried out at a speed of 250 rpm, a load of 20 N, and an experimental time of 5 h with clockwise rotation using mixed LCs as the lubricant.

Point-plane contact
Under the condition of point-plane contact, the system with the mixed LC lubricant and GCr15/PI (6FDA-ODA) friction pair maintained stable superlubricity at room temperature, a load of 5 N, and a linear speed of 44.48 mm/s (Fig. 2). The purpose of performing several sets of tests for the same friction pair was to simulate the working state of PI as a device when it was repeatedly used. The results showed that repeated use of the friction system under specific working conditions did not affect realization of stable superlubricity.

Plane-plane contact
One side of the steel ball was ground to an almost circular plane, which was observed by SEM. The diameter of the circular surface was about 1.9-2.0 mm, as shown in Fig. 3.

Friction tests at different velocities
The diameter of the circular plane of the GCr15 steel used in this test was 1.91 mm. In the mixed LC lubrication system, the ground GCr15 steel ball plane was matched with PI(6FDA-ODA), the load was maintained at 5 N, the test speed was increased from 50 to 400 rpm, and the incremental gradient was 50 rpm with plane-plane contact. The friction coefficient of the system gradually decreased with increasing speed (except for at 300 rpm). When the speed was increased from 200 to 300 rpm, the friction coefficient increased from 0.00217 to 0.00225. The difference between the two values was not large, and it was normal fluctuation in the experimental range, as shown in Fig. 4(a). Similarly, as shown in Fig. 4(b), when the load was increased to 7 N, the test speed increased from 50 to 400 rpm owing to replacement of the LCs and PI film, and the friction coefficient of the system still gradually decreased with increasing speed. A similar trend to the 5 N test was observed.
The diameter of the circular plane of the GCr15 steel used in this test was 1.91 mm. We performed another set of experiments under the same conditions as shown in Fig. 4, except that the test speed was reduced from 400 to 50 rpm, and the decrement gradient was 50 rpm with plane-plane contact, the results were shown in Fig. 5. Comparing Figs. 4 and 5, we found an interesting phenomenon, except that the state of the initial friction pair is not completely consistent, no matter whether the speed is gradually increased or decreased, when the speed is 50 rpm, the superlubricity phenomenon does not occur in the system, and a similar speed response phenomenon occurs. In the case of high rotation speed, whether it is from 100 to 400 rpm, or from 400 to 100 rpm, the system has achieved good friction-reducing effect, and it could even enter a stable superlubricity state. The results show that for this friction system, the speed is one of the important factors for obtaining the superlubricity state, and too slow speed is not conducive to obtaining the superlubricity phenomenon.

Friction tests at different loads
Using the flat steel sample used in the friction tests with different velocities (Section 3.1.2.1), the PI film was replaced and new LCs were added as a lubricant. A plane-plane friction test was then performed at a speed of 250 rpm with a starting load of 5 N increasing in steps of 10 N. When the load for testing was 95 N, the PI film was damaged. Under the same test conditions and using the same steel ball plane, the PI film was replaced and new LCs were added. Under the test conditions, the maximum load of the test was 94 N. The results are shown in Fig. 6. When the speed was 250 rpm, the system entered a stable superlubricity state almost at the beginning of the test. Although the friction coefficient changed with the increase of the load, it was generally in the superlubricity state. Combined with the results in   4, we consider that a higher friction speed and a certain load may have a significant effect on reducing the friction coefficient of the system with LCs as the lubricant and PI-GCr15 steel as the friction pair. Taking the area of the plane on the steel ball in the test as the bearing area, and calculating with the current maximum load of 94 N, the maximum pressure of the friction system was 32.82 MPa.

Comparative test with n-hexadecane as the lubricant
We compared the lubricating effect of the mixed LC lubricant with a different lubricant under the same test conditions. n-Hexadecane (n-C 16 H 34 ), a non-polar molecule, was selected as a lubricant. The diameter of the circular plane of the GCr15 steel ball used in the test with the n-hexadecane lubricant was 1.93 mm, and the diameter of the circular plane used with the LC lubricant was 1.90 mm. At a load of 20 N and a speed of 250 rpm, the friction coefficient was 0.05396 when n-hexadecane was used as the lubricant, and it was 0.002689 when the mixed LCs were used as the lubricant. That is, the friction system with the mixed LC lubricant was in a stable superlubricity state, as shown in Fig. 7.

IR analysis of LCs and compounds on the steel ball
We compared the IR spectra of LCs and the compounds on the tested steel ball lubricating with the mixed LCs mentioned in Section 3.1.2.3, as shown in Fig. 8. Since the steel ball was opaque, but could reflect light, the IR spectrum of the compound on the friction surface of the steel ball after the friction test was obtained from the IR reflectance test after deducting the influence of the reference (steel ball surface).
www.Springer.com/journal/40544 | Friction    Fig. 8(b) was a partial magnified IR spectrum. IR spectroscopy indicated that there were LCs on the friction surface of the steel ball lubricating with the mixed LCs after the test, because the main absorption peak of the compound on the surface of the steel ball was basically the same as that of LCs. However, as shown in Fig. 8(b), comparing the absorption peaks of the compounds on the friction surface of the steel balls with those of LCs, it was found that the shapes of the absorption peaks of the compounds on the steel balls became broad, such as 1,563, 1,438, 1,114, 962, 818, and 696 cm -1 , indicating that the symmetry of the organic molecules deteriorated. In addition, some new absorption peaks were also found, such as 1,692, 1,677, 1,482, and 938 cm -1 , which means that new chemical bonds appeared on the friction surface when lubricating with the mixed LCs.
We speculate that the LCs may act as a ligand to coordinate with Fe 2+ or Fe 3+ on the surface of the steel ball lubricating with the mixed LCs. The coordination changed the symmetry of the whole ligand molecule and the electron cloud distribution of some atoms, and also changed the configuration of the ligand. These factors caused the characteristic frequency of LCs as ligands to change compared to the state of the independent LC molecules, so we found that the characteristic peaks of the compounds on the steel balls changed compared to the LCs. It can indirectly prove the formation of the complexes. The frequency of coordination bond vibration is very low, generally appearing at 20-500 cm -1 . However, we used the infrared reflection method to test, the minimum wave number setting of the instrument is 600 cm -1 , we can only indirectly speculate that the complex is formed through some absorption peak changes. The structure of the complex will be further analyzed in detail by other methods in the follow-up study.

Surface topographies of the friction pairs
The samples mentioned in Section 3.1.2.3 were subjected to surface morphology analysis, and the results are given in Tables 1 and 2. The roughness of the original surface of the plane ground by the initial steel ball was relatively large (R a = 0.545 μm, Table 1). After the friction test using mixed LCs or n-hexadecane as the lubricant, the roughness of the steel ball plane decreased. After the mixed LC lubrication test, the roughness of the steel ball plane was 0.420 μm, and the roughness of the steel ball plane after the n-hexadecane lubrication test was 0.441 μm. That is, after the test using LCs as the lubricant, the plane of the steel ball was smoother than after the test using n-hexadecane as the lubricant. By SEM, it was observed that the groove marks on the surface of the wear scar of the sample steel plane obtained with LC lubrication were finer and more uniform than those of the sample steel plane obtained with n-hexadecane lubrication under the same test conditions. A white-light interference microscope image showed an interesting phenomenon. Regular concentric arcs appeared on the surface of the wear scar of the sample steel ball lubricated by LCs, as if there were molecules neatly arranged along the wear scar, which was indirect evidence of the directional aggregation of LCs on the plane of the steel ball.
We observed the PI counterpart after the tests ( Table 2). The surface of the PI film was very smooth before the test (casting method). However, after the mixed LC lubrication test, the wear surface of PI had obvious regular arc wear marks. These marks corresponded to the surface of the steel ball plane of the counterpart, which also had regular arc wear  (Table 1). Extensive arc wear marks were also observed when n-hexadecane was used as the lubricant. Rubbing treatment can promote orientation of the molecular chains on the PI surface, that is, the instantaneously generated high temperature can orient the molecular chains of the PI material in the near-surface area to generate an oriented surface, forming a dense structure on the PI surface, as shown in the images of the wear scar on PI after the rubbing test. We found that under the same test conditions, the wear scar formed on PI after rubbing using LCs as the lubricant was more obvious than when n-hexadecane was used as the lubricant. In contrast, the wear scar on PI using n-hexadecane as the lubricant was denser than that when LCs were used as the lubricant. However, the difference between the two images was not significant, which means that the instantaneous high-temperature alignment of the PI surface was little related to the structure of the molecules in contact with the surface. PI is a polar macromolecule, and alignment of the PI macromolecule will lead to alignment of small polar molecules in contact with and close to the PI macromolecule [42][43][44]. Therefore, the wear scars on the steel ball planes of the counterpart samples obtained after the lubrication tests are important.
After the LC lubrication test, alignment of the LCs was very obvious under induction of PI orientation, and the small LC molecules were epitaxially extended from the surface of the orientation layer in a similar manner to crystal epitaxy until the surface of the GCr15 plane of the friction pair. The LC molecules used in this study were nematic LCs, which have the following structural characteristics: (1) The geometry of the molecules is rod-like, and the aspect ratio is relatively large, generally greater than 4; (2) double bonds or triple bonds are often present in the central part of the molecule to form a conjugated system and obtain a rigid linear structure, or the molecule maintains a trans-structure type to obtain a linear structure; (3) the terminal end of the molecule must contain a polar group, or have strong polarizability. Owing to the LC molecules having such structural characteristics, under induction of PI, the LCs in contact with or close to PI can orient and align along the grooves of the wear scar, and alignment of the LCs will extend to the corresponding positions. The structure of non-polar n-hexadecane is very different from the structure of nematic LC molecules. The interaction force between n-hexadecane and PI is much weaker, and n-hexadecane is still a flexible molecule, so it is impossible for n-hexadecane to align on PI like a nematic LC molecule with a rod-like structure. Moreover, LC molecules are electron-rich systems. Thus, it is easy for a LC molecule to form a stable coordination structure with Fe 2+ or Fe 3+ , in which electrons are lost from the GCr15 counterpart, and adsorb on the counterpart. This feature can be observed in the white-light interference microscope image of the surface of the steel ball plane wear scar obtained after LC lubrication, in which there were obvious and regularly arranged micro-convex arrangements. However, a similar phenomenon was not observed in the white-light interference microscope image of the surface of the steel ball plane wear scar obtained with n-hexadecane lubrication.
Considering the image of the regular alignment traces on the plane of the steel ball and PI film, we speculate that under induction of PI, the LC molecules in contact with PI align along the grooves of the wear scar, whereas the LC molecules close to PI extend the alignment to the plane of the steel ball, and it is possible to form a stable chemical bond with Fe 2+ or Fe 3+ on the steel surface.

Pretilt angle between the LCs and PI
During the modeling process, we placed PI(6FDA-ODA) molecular chains in a parallel manner, which approximated the alignment state of PI molecules after rubbing. The density of the constructed PI system was 1.24 g/cm 3 , and its reported experimental value was 1.41-1.46 g/cm 3 [45]. The surface tension of PI was calculated by where  is the surface tension value of PI, film E and bulk E are the PI-bulk and PI-film energy values, respectively, and A is the area of the PI film. The calculated surface tension was 59 mJ/m 2 , and its reported experimental value was 46 mJ/m 2 [46]. Since the density and surface tension data obtained by the simulation are reasonable, it helps us to judge that the pretilt angle calculated by the simulation is reasonable. The orientations of all of the LC molecules in contact with the surface of the PI film in the simulation system were analyzed. The results are shown in Fig. 9. The orientations of the two types of LC molecules were concentrated around 0°, and the pretilt-angle distribution of 3UTPP4 was wider than that of 3PEP5. According to Ref. [47], the pretilt angle of the PI(6FDA-ODA) should be small, which is consistent with the calculated results. It should be noted that only 10 LC molecules were placed in the system during the analysis, and there was almost no interaction between the LC molecules. Therefore, when the number of LC molecules increases and the film is formed, the interaction between the LCs will tend to make the orientation consistent, and the pretilt angle distribution will become more concentrated.
We also simulate the systems with bulk LC molecules and PI film under pressure of 50 MPa and the results are shown in Fig. 10. The orientations of the two types of LC molecules were concentrated at small angles, and the pretilt-angle distribution of 3UTPP4 was wider than that of 3PEP5.
These calculated results are consistent with previous reports in Ref. [47], and can reasonably explain the results of the friction test. It can also help us understand that after rubbing, the alignment of the PI-induced LC molecules is related to the strong interaction force between PI and the LCs, and the weak interaction between the LCs.
The pretilt angle is determined by the interaction between the LCs and PI. When the pretilt angle is very small, the LC molecules will lie almost flat on the surface of PI. In addition, owing to the anisotropy of the alignment layer surface caused by rubbing, the LC molecules interact with the molecules of the anisotropic alignment layer. Owing to the different force in each direction, to achieve the minimum stable state, the LC molecules will arrange along the direction of the maximum force, that is, the LC molecules will be regularly arranged along the grooves of the wear scar of PI.

Observation of PI by a polarization microscope
The un-rubbing PI film was observed with a polarized microscope. The results are shown in Fig. 11(a), and no obvious structure was found. It indicated that PI was an amorphous polymer when un-rubbing, so the field of view of the polarized microscope was dark. In Fig. 11(b), the phenomenon of LCs dripping on PI was exhibited. The pattern was observed due to the anisotropy characteristic of LCs, which produced birefringence on the polarized light from the polarizer. Figure 11(c) illustrated that after dry rubbing, a clear pattern was found at the PI wear scar by using the polarized light microscopy, confirming the existence of anisotropic PI. It suggested that PI transformed from an amorphous structure to a crystalline state under friction, resulting in molecular orientation. The rearrangement of polymer required thermal motion, the frictional heat increased the temperature of the rubbing part of PI above the glass transition temperature, and the chain segments of PI moved in an orderly manner. When the temperature dropped, crystallization occurred at the rubbing site of PI. Crystallization made the microstructure of PI regular, compact, and ordered. Figures 11(d)-11(f) were the photographs of the different magnifications of LCs attached to the after-rubbing PI wear scar with LCs lubrication, which displayed that anisotropic LCs were attached to anisotropic PI. Figure 11 indicated that rubbing caused the crystallization in the wear scars of the PI film, and LCs could adhere to the wear scars of the PI. Figure 12 shows the SERS spectra of a PI film before and after rubbing, which illustrates for the rubbed film is almost identical to those of the unrubbed film, indicating that rubbing is not strong enough to affect the bulk PI structure. However, we performed SERS analysis on the PI film before and after rubbing, and it was obvious that the intensity of some peaks of the un-rubbing PI was significantly higher than that of the after-rubbing PI. The SERS selection rule for molecules adsorbed on metal surfaces is that molecular vibrations involving motions perpendicular to the surface should be enhanced in the spectra, while those involving motions parallel to the surface weakened [48,49]. It indicated that after rubbing, some functional groups of PI changed from being perpendicular to being parallel to the surface. Comparing the spectra of PI before and after rubbing，significant changes were found in the intensity of the aromatic in-plane  stretching at 1,604 cm -1 , the CF 3 stretching at 1,280 cm -1 , and the CF stretching at 1046 cm -1 . It suggested that the surface structures of the PI films before and after rubbing were different, indicating that the rubbing process significantly rearranges the surface orientation distribution of molecules. According to the SERS selection rule for molecules adsorbed on metal surfaces, it was shown that some groups in the main chain and branched chains of PI molecules were oriented parallel to the surface of PI after rubbing. It also confirmed the results of the polarized light microscope, the microstructure of after-rubbing PI became regular, dense, and ordered, which was consistent with PI crystallization after rubbing.

Friction tests with the PMDA-ODA PI film
When 6FDA-ODA PI was used, stable superlubricity was obtained for the friction system under certain conditions. Moreover, according to the calculated results, a small pretilt angle can be obtained between 6FDA-ODA PI and LC molecules, such as 3PEP5 or 3UTPP4, which is beneficial for realization of the superlubricity state. Therefore, we used another PI material with a similar alignment effect, DuPont's commercial PI(PMDA-ODA) film, for testing. According to the literature, the PMDA-ODA-type PI alignment film can produce a pretilt angle of 1.5° with a mixture of LCs with a cyano terminal, or 1.0° with a mixture of fluorinated LCs [50].
The diameter of the circular plane of the GCr15 steel ball in this test was 2.00 mm. The results are shown in Fig. 13. Starting at 5 N, a stable superlubricity effect was obtained with a gradient of 10-175 N. Because the thickness of PMDA-ODA-type PI was 127 μm, which was significantly thicker than the 6FDA-ODA PI film (30 μm) that we used, the test was stopped at 185 N (when the load was increased to 185 N, the PI film ruptured). This indicates that a small pretilt angle between the LC molecules and PI film is the key to obtain a stable superlubricity state. Taking the nominal contact area as the real contact area, the maximum pressure of the set of tests is 55.73 MPa.

Friction tests of the GCr15/Cr12 friction pair
We compared friction coefficients of the GCr15/Cr12 pair with GCr15/PI(6FDA-ODA) pair under the same test conditions (Fig. 14). The diameter of the circular plane of the GCr15 steel ball used in the test with the Cr12 steel was 1.83 mm, and the diameter of the circular plane used with PI(6FDA-ODA) was 1.90 mm. At a load of 20 N and a speed of 250 rpm, the friction  coefficient was 0.03242 when GCr15/Cr12 was used as the rubbing pairs, however it was 0.002689 when the GCr15/PI(6FDA-ODA) were used as rubbing pairs. That is, under the same test conditions, since the PI film was replaced by Cr12 steel as the friction pair, the system did not appear superlubricity phenomenon within 5 h of the test. It shows that PI material is the necessary material for the system to obtain superlubricity. Rubbing causes the PI material to align, and the PI alignment layer induces alignment of LCs, which is a necessary step for the system composed of the PI-GCr15 steel friction pair and LC lubricant to achieve superlubricity behavior.
Moreover, this result also indirectly indicated that the superlubricity behavior mechanism of the system with LCs as lubricant and PI material as friction pair was not the result of hydrodynamic effect of the LCs. Because one of the characteristics of hydrodynamic lubrication is that the friction and wear characteristics mainly depend on the viscosity of the liquid, and are independent of the material characteristics and morphology of the rubbing pair surfaces. Obviously, the test result was related to the friction pair material. As shown in Fig. 14, the friction coefficient decreased from 0.07 at the beginning to 0.02 with time, and it was basically stable after the test time of 14,400 s. The friction coefficient value was in the range of friction coefficient (0.05-0.10) of steel/steel friction pairs lubricated with mineral oil containing oiliness additives, which belonged to boundary lubrication with a good lubrication effect. It can be found that LCs is a good boundary lubricant for steel/steel friction pairs, but it is impossible to produce hydrodynamic lubrication effect under this test condition. Therefore, we speculate that the superlubricity of the friction system composed of the PI-GCr15 steel friction pair and room-temperature LC lubricant is related to the alignment of the PI and LC molecules, rather than the result of the hydrodynamic effect of the LCs.

PI-induced alignment
According to the friction tests, superlubricity of the GCr15 steel/PI rubbing pair and LC lubricant system can occur under certain conditions. The change of the surface caused by friction may be an important factor in the occurrence of superlubricity, that is, alignment of PI caused by friction may be the key step. As an alignment material, the rubbing treatment will promote the alignment of the PI surface molecular chains, that is, the instantaneous high temperature generated by the rubbing can align the PI molecular chains in the near-surface area, thereby generating an alignment surface, resulting in alignment of the liquid crystal molecules. After rubbing, the molecular chains on the PI surface form a good local and overall orderly arrangement. Rubbing not only forms a dense structure on the PI surface, but also induces the macroscopic orientation of the molecules in the rubbing direction [42][43][44].
In this study, the pretilt angle between the LCs and PI film was very small. That is, under the influence of intermolecular forces, the LC molecules "grew" on the PI surface in an almost parallel manner with alignment induction of the PI molecules, so that the LC molecules of the system formed a stable structure with a specific arrangement. The LC molecules were arranged in a directional manner by crystal epitaxy until the surface of the counterpart, and they formed stable chemical bonds. The relative positions between the LCs were irregular. Because the interaction between the LCs is much weaker than that between the LCs and PI, and LCs have liquid fluidity and low viscosity, the relative motion between the friction pair can almost be regarded as sliding between LC molecules arranged in parallel. Therefore, the friction system shows superlubricity in this case.
Nematic LCs usually maintain an alignment state parallel to the direction of the molecular axis, but | https://mc03.manuscriptcentral.com/friction they do not have a layered structure. The centers of gravity of these molecules are disordered, but their directors are roughly the same, and they will be aligned under induction of PI. This feature of LC molecules is similar to an interesting phenomenon in nature called the "fish swarm effect", as shown in Fig. 15(a). When fish swim in shoals in the sea, they do so in a manner that is both chaotic and orderly. Following ocean currents and in search of food sources, the shoal usually shows an orderly shape. Unlike humans, fish do not have a highly developed nervous system. Fish do not use conscious social organization to form a regularly shaped shoal, they rely on evolutionary instinct. Fish possess a special sensory system called the lateral line, which runs on either side of their body. They use the lateral lines of one or two adjacent fish as observation points to adjust their swimming direction and speed, thereby maintaining an appropriate distance from one another. This simple negative feedback mechanism allows the whole shoal to organize itself appropriately.
Each agglomeration reveals a new nature. Information feedback between the LC molecules is similar to the negative feedback mechanism in a shoal of fish. The grooves formed by scratches on the PI film by rubbing, the strong interaction between the LCs and PI, the stable coordination structure of the LCs and GCr15 steel, and the weak interaction between the LCs are adjusted in a similar fashion, resulting in self-organization of the entire friction system in a certain direction. Because the combination of LCs and PI with a small pretilt angle was selected in this study, the LC molecules were almost parallel to PI, just like the spontaneous chaotic and orderly arrangement of fish, as shown in Fig. 15(b). Therefore, the friction process is actually the free movement between the LC molecules, like a fish swarm. Owing to the very small viscosity of the LC molecules, and a collective group of LC molecules aligned in the same direction maintaining a particular state, the system shows superlubricity.
We propose the mechanism of superlubricity in the friction system with nematic LCs as the lubricant and GCr15 steel/PI as the friction pair. When PI is rubbed and aligned, and when the pretilt angle between PI and the LC molecules is small, the LC molecules in contact with PI are almost parallel to the surface of PI and align along the grooves on the PI, and the LC molecules close to PI extend and arrange to the counterpart, because of the strong interaction force between PI and the LCs. The electron-rich structure of the LC molecule will also form a coordination structure with the electron-deficient metal ions on the counterpart GCr15 steel, that is, the force between the two surfaces in contact with the LCs in this rubbing system is relatively strong, and the force between the LC molecules is very small, so the friction behavior of this system is the movement of aligned LC molecules. The LC molecules maintain an arrangement state parallel to the direction of the molecular axis and the viscosity of LCs is very small, which are beneficial for the system to reach a superlubricity state.

Conclusions
In the friction system composed of the polyimide (PI)-GCr15 steel friction pair and room-temperature liquid crystals (LC) lubricant, rubbing will cause the PI material to align, and the PI alignment layer will induce alignment of LC molecules in contact with and close to the PI alignment layer. According to the calculated results of the pretilt angle between PI and the LCs, alignment of the PI-induced LC molecules after rubbing is related to the strong interaction force between the PI and LC molecules, the stable coordination structure of the LCs and GCr15 steel, and the weak interaction between LC molecules.
If the pretilt angle between the PI material and LC molecules is small, the LC molecules will orient almost parallel to the PI material, which is beneficial for superlubricity of this type of friction system.