Probing the Lubrication of Shear-Induced Self-assembled Layer on Amorphous Carbon Films in Methane Atmosphere

Demand for reduction in friction and improvement in wear resistance of moving parts propel exploration in frictional origin of amorphous carbon (a-C) film lubricating properties based on the interfacial states. Methane, as an ideal energy carrier and industrial raw material, is one of active gases. Consequently, the relations between the tribological behaviors of a-C film under methane atmosphere and load or interfacial states were discussed based on experimental and theoretical methods. It illustrated that, as the load increased, tribological system exhibited various interfacial shear strength at a load of zero and pressure dependence of the shear strength. The origin was that the distributions of adsorbates across the sliding interface which were similar to self-assembly layer changed with the load, leading to the source of energy dissipation. Therefore, the load dependence of the tribological properties of a-C films conformed to the Hertz elastic contact model by stages.


Introduction
Friction exists in our daily life, resulting in nearly 20% of the total energy consumption [1]. Thus, the adverse effects of friction are reduced by covering the moving parts with solid lubrication films [2][3][4]. Amorphous carbon (a-C) film, with excellent tribological performances, is widely applied in various industrial fields [5][6][7]. Nevertheless, the tribological performances of a-C film are complicated functions of test conditions and interfacial structures, leading to the empirical nature of interfacial regulation [8]. Thus, it is essential to understand the basic issue or the origin of friction based on the interfacial states.
The achievements toward interfacial states of a-C film have provided basic knowledge on regulating tribological performances of a-C film in certain conditions. Specifically, based on the factor that an atomic-scale structural mismatch between two surfaces leads to vanishing friction, an atomicscale structural superlubricity in nitrogen atmosphere is achieved by the combination of carbonaceous materials (a-C film and fewlayer graphene) with nanometer-sized diamond particles [9]. The mechanism is the formation of nano-scrolls acting as miniature ball bearings on the sliding interface. The similar antifriction effect is found in the combination of a-C film with two-dimensional and zero-dimensional nanomaterials under certain conditions [10][11][12]. And then, a-C film is designed with micro-nano structures, such as fullerene-like [13] and onion-like [14] structures, allowing regulation in a-C film with low-shear interface. Research on nature of surface and interface chemistry of doping a-C film during sliding in moisture condition gives the experimental information of the buried sliding interface at the nanoscale [15]. Afterward, an appropriate silicon and oxygen are incorporated in a-C film to form a silica-like tribolayer which shields moisture effect, thus achieving robust superlubricity of a-C film in moisture condition. Present characterization technologies can't give the information about the states of adsorbates or groups on the surfaces during sliding. It is undoubtedly a great obstacle to understand the key concern about tribological performances of a-C film. Large-scale density functional tight-binding (DFTB) molecular dynamics (MD) simulations of diamond surfaces in various amount of confined water unveil atomic-scale friction mechanisms of water lubrication, showing distinct water-induced reconstruction of diamond surfaces with increasing water molecules [16]. Besides, DFT is used to analyze surface stability of diamond (111) configuration with Pandey reconstruction under various amounts of water and reveals the various distributions of dissociated groups on surface [17]. These theoretical calculations give the deeper insight into the interfacial structures and states for surface and interface of materials in atomic scale, allowing the further understanding about the interfacial evolution behaviors of materials during activities. Consequently, the combination of theoretical calculations and experimental technologies provides an effective way for understanding and regulating the frictional properties of a-C film. Natural gas that consists of methane is widely used in power generations and fueling of transportation systems. In those industrial practices, it is efficient, durable, and costeffective to improve the wear resistance properties of moving parts including fuel injectors, seal packs, and pistons [18,19]. On the other hand, methane, as a kind of active gas, gives information about the basic issue of friction for a-C film under atmosphere. Therefore, the interfacial states for a-C film in methane are explored to understand the basic issue of friction.
Here, load influences in the tribological behaviors of a-C film under methane atmosphere were explored to reveal the interfacial evolution process for film based on experimental and theoretical methods. The frictional behaviors of a-C film in methane atmosphere were attributed to adsorbates bonding with carbon dangling bonds across the sliding surface. Additionally, the distributions of adsorbates varied with the strain along perpendicular to interface, leading to the various and 0 for tribological systems at distinct load stages. This work provides theoretical basis to optimize a-C film applied in natural gas. Meanwhile, it gives the deeper insight into the origin of friction for a-C film under atmosphere.

Materials
Unbalanced magnetron sputtering ion deposition system was carried out to grow a-C film on a highly polished flat 304 C stainless steel (SS) substrate (3 cm × 3 cm × 0.3 cm in dimensions). And the detailed deposition procedure of film has been reported elsewhere [20]. Following the Cr/a-C:Cr transition layer is a-C layer. Deposition parameters are given in Table 1. The prepared film was approximately 2.9 μm and possessed a roughness (Sa), which was measured by optical profilometry, of about 25 nm. Nano-indenter (TTX-NHT 2 , Anton Paar, Austria) was used to obtain the hardness and Young's modulus of a-C films. And the indenter load was 10 mN. The average hardness and Young's modulus, which were obtained with four tests, were about 16.3 ± 0.3 and 216.7 ± 1.5 GPa, respectively. Besides, commercially available 440 C SS ball with a hardness of ~ HRC = 55, a Young's modulus of ~ 200 GPa, and a surface roughness of 30 nm was used as a counterpart ball in test.

Friction Tests
The 440 C SS ball with a diameter of 6 mm was loaded on the as-deposited a-C film at normal forces ranging from 0.2 N to 3 N. And the various normal forces increased in sequence of 0.2, 0.25, 0.28, 0.5, 1, 1.75, 2, and 3 N, corresponding to the mean Hertzian contact pressure of 254, 274, 284, 345, 434, 526, 550, and 630 MPa, respectively. These tests were carried out via the reciprocating model on a high vacuum tribometer (HVTRB, Anton-Paar) under a vacuum degree of 3.0 × 10 -3 Pa and a methane pressure of 250 Pa. The tribometer has been reported in previous work [21]. In these tests, average speed of 2 cm/s was obtained with a frequency of 2 Hz and half amplitude of 2.5 mm here. The test was conducted at room temperature (293 ± 1 K) with a sliding duration of 3000 laps. Each condition was operated three times on a fresh track with a new counterpart ball.

The Friction Coefficients of a-C Film Under
Various Loads Figure 1a displays the frictional curves of a-C film at different loads under a vacuum degree of 3.0 × 10 -3 Pa. There are two identifiable types of friction behaviors: (1) 0.2 to 1 N and (2) 1.75 to 3 N. The curves obtained with applied loads in range of 0.2 to 1 N reach its steady state after a run-in period (1500 cycles), during which a carbonaceous transfer film is developed on the counterpart ball. Therefore, the steady-state friction coefficient below was recorded after 1500 cycles. However, when the normal load is above 1.75 N, the friction coefficient fluctuates around 0.8, and then, the film is worn out quickly. Figure 1b gives the frictional curves of the a-C film tested at various loads under a methane pressure of 250 Pa. Each frication curve is steady after a run-in period (800 cycles), during which the friction coefficient increases to a peak quickly and then decreases drastically to a value much lower than the initial value.
To further reveal the load influences in the frictional behaviors of a-C film, the relations between loads and the average steady-state friction or friction coefficient are analyzed, as shown in Fig. 2a and b, separately. It is widely known that if a tribological system conforms to Amonton's law of friction, the friction coefficient is independent of load and the friction can be expressed as follows: where F represents friction force, μ represents a constant, and L represents the load. From Fig. 2a, the average steadystate friction obtained in vacuum against normal load could be linearly fitted with a slope of 0.792 ( R 2 = 0.99 ), illustrating the compliance of the tribological system with the Amonton's law of friction. The linear extrapolation of the friction forces under a methane pressure of 250 Pa results in finite intercept at zero contact load without passing through the origin in the plot. Meanwhile, one can draw that only a slight increase in friction is produced in methane by the increased normal contact pressure from the raising of normal load, compared with the big increase at vacuum condition. This behavior can be explained by considering the Hertzian elastic contact model. It can be described with a Hertzian evolution relation, and the relationship between friction coefficient and Hertzian pressure is given in Eq. (2) [22].
where F is a product of the real contact area and shear strength of the lubricant material, A r ⋅ τ . And is the pressure dependence of the shear strength, P H is the Hertzian pressure, 0 is the interfacial shear strength at a load of zero. From Fig. 2b, it is obvious to observe the result that while friction coefficient for the film under a vacuum degree of 3.0 × 10 -3 Pa is independent of inverse Hertzian pressure, the friction coefficient of film tested at various loads in a methane pressure of 250 Pa increased obviously with inverse Hertzian pressure, which is in accordance with the Hertzian evolution relation. It should be stated that increased normal load on the film can lead to a raising stress, resulting in plastic deformation, cracking, and spalling of film. Here, film begins to wear off under a load of 3 N (Fig. S1). Meanwhile, it is amazing to find two stages in frictional

Structural Characterization of Sliding Surfaces
Structural analyses of sliding interfaces provide information about mechanism for load influences in the frictional behaviors of a-C film in methane atmosphere. Therefore, the structures of sliding surfaces were examined via Raman spectrum and transmission electron microscopy (TEM). Figure 3a and b display the select regions of Raman spectrum characterization and Raman spectra of wear tracks and wear scars. One can draw that pristine and worn films present typical characteristics of a-C film that a broad peak in the frequency ranging from 900 -1800 cm −1 is observed. Then the peak could be fitted into two peaks (D peak and G peak) by Gaussian method. As we all know, D peak results from the breathing mode of sp 2 C atoms in rings, while the G peak results from the stretching vibration of all pairs of sp 2 C atoms in both rings and chains. Fig. S2 displays that ID/IG of a-C film increases after sliding, illustrating the graphitization of a-C film. From Raman spectra in Fig. 3, transfer films exhibit two separating peaks at 1358 cm −1 and 1600 cm −1 , which are the typical characteristics of graphitized carbonaceous material. The TEM samples of transfer film were prepared with focused ion beam (FIB) technology to further analyze the structures of sliding interface. And the results are given in Fig. 4. The microstructure of transfer film in Fig. 4a illustrates that the tribofilm under a load of 0.25 N consists of several layers containing a "tumor-like" amorphous layer near the sliding interface. And it is obvious that there are many nanoclusters induced by accumulation of "tumor-like" carbonaceous material in tribofilms. From Fig. 4b, the tribofilm under a load of 1 N is found to contain a rodlike amorphous layer near the sliding interface. No nanocrystals are observed in the transfer film under the two loads. Additionally, two tribofilms possess the similar amorphous outmost working layer. These results illustrate the differences

Interfacial Analyses Based on First Principles Calculations
To gain the deeper understanding about the frictional mechanism for a-C film in methane atmosphere, first-principles calculations were carried out to obtain friction between sliding surfaces. In the first-principles calculations, the influence of a certain factor, such as surface passivation, on a-C film can be obtained by replacing a-C film with diamond (111) [24]. Based on the above experimental results, models, as shown in Figs. 5, 7 and 8, were constructed to gain a deeper insight into the processes of interfacial evolution process at atomic scale [24][25][26]. Figure 5b-d present the computational process about the effects of stress induced by compressive strain on structure. According to the formula about compressive strain: = c 1 − c 0 ∕c 0 , one can obtain the structures and stress under various compressive strain by optimizing the configurations with reduced and fixed length of c 0 . The calculated progress is based on density functional theory (DFT) approach, which is implemented by the CASTEP package within the Materials Studio framework [27]. During calculation process, the exchange-correlation energy is characterized via the generalized gradient approximation (GGA) in the form of the Perdewe-Burkee-Ernzerhof (PBE) function [28]. Additionally, a plane-wave cutoff energy of 650 eV  and Monkhorst-Pack k-point mesh density of (5 × 5 × 1) are adopted in this work. From Fig. 5c, methane molecule dissociates into methyl and hydrogen which bond with carbon dangling bonds across the interface of diamond (111). Figure 6a gives stress-strain relation of diamond (111)/ diamond (111) configuration under methane. The stress decreases with the increasing strain. As shown in Fig. 6b, the strain energy rises and its first derivative reduces with the increasing strain. It should be noted that strain energy is obtained by subtracting the energy of configuration under strain from the energy of configuration under equilibrium state. It is well known that there are two types of deformations for materials during compression process. The form of deformation belongs to elastic deformation at low applied strain, and with increasing applied strain, plastic deformation occurs. The plastic deformation occurs after the second yielding point where the strain energy reaches its maximum value. Of causes, there is the first yielding point, where the first derivative of strain energy reaches its minimum value. In this case, high strain is observed with small compression. No yielding point of configurations are observed at Consequently, the relaxed configurations under = 0, −0.04, −0.08, −0.12 were enlarged to eliminate the influence of the boundary and further explore the interfacial evolution processes for a-C film in methane via molecular dynamics (MD) simulations within first-principles calculation. The constant volume and energy (NVE) were carried out to conduct MD simulations with an initial temperature of 300 K. A plane-wave cutoff energy of 380 eV and Grimme method were adopted during MD simulations. In addition, the MD time step was 1.0 fs and the total MD simulation time was 1.0 ps. We want to state that, compared with other configurations (Fig. S3), the configuration given in Fig. 7 possesses the lowest energy. Therefore, the configuration given in Fig. 8 was chosen. Figure 7 displays the initial and reconstructed configurations for MD simulations. One can draw that dissociation groups bonded to carbon dangling bonds across the top and bottom layers are opposite at low applied strain, and they are staggered with increasing applied strain. After that, the methyl groups dissociate and carbon dangling bonds emerge under further compression. After the MD simulations of configurations, the top layer slides horizontally relative to the bottom one, allowing the analyses for sliding pathway of tribological systems under various strain. Figure 8 presents the schematic diagram of sliding pathway. Every sliding pathway is divided into forty-one steps by hand. Then the energy of each configuration is calculated. Interaction between layers is measured with separation work W sep and obtained with Eq. (3).
where E tot 12 is the total energy of the configuration while the distance between the top and bottom layers is 10 Å, E tot s is the total energy of the configuration after sliding and A is the interfacial area. It should be stated that the interaction between the upper and lower layers can be ignored when the distance is far enough [29]. Therefore, the distance between the upper and lower layers was increased to obtain the distance where the force can be ignored. Finally, 10 Å was determined. Then, deviation between the highest energy ( E max ) and lowest energy ( E min ) of the configuration in the sliding pathway is calculated to measure the sliding pathway under a certain load. Here, the load is obtained by fixing the length of c 0 to remain interlayer distance. Relative sliding between layers must overcome the potential energy corrugation of the sliding pathway, and thus, the friction behavior of system is closely related to the maximum potential energy barrier. Consequently, the average friction of system is evaluated by the first-order approximation of the critical force for overcoming the energy barrier, which is calculated with Eq. (4). where Δs is the sliding distance. It should be stated that only one sliding pathway under = −0.12 is analyzed due to the emergence of carbon dangling bonds. The W sep and F are presented in Fig. 9. It is obvious that the potential energy corrugation on the sliding pathway increases with strain. Meanwhile, relative sliding of each system along the � √ 310 � direction possesses the minimum friction among those sliding pathways. A great increase in friction of tribological system is observed under = −0.12 , resulting from the adhesion between sliding interface. Combined with Fig. 8, it can be seen that the adsorbates across the sliding surfaces arrange from headon mode to side-by-side mode with the increased strain during sliding. As interfacial adsorbates slide head to head at a low load, the adsorbates on top and upper and lower layers encounter each other, leading to the vibrational excitation of adsorbates. Then this energy is imparted from adsorbates to the rest of the lattice subsequently. This energy dissipation results in the friction of tribological systems [30]. When adsorbates on the top layer travel between adjacent adsorbate rows of bottom layer, in addition to the interaction with the bottom layer adsorbates, the adsorbates on the top layer interact with the carbon dangling bonds of second layer. Consequently, adsorbates with different arrangements on sliding interfaces, which are induced by various strain, interact in different modes, and thus the tribological system is in accordance with the Hertzian evolution relation corresponding to distinct stages with various and 0 .

Describe the Friction Coefficient with a Mathematical Model
Previous study about the shear properties of Langmuir-Blodgett layers during sliding stated the relation between the shear strength of L-B layer and the contact pressure. Meanwhile, it revealed the origin with mathematical model of activated processes developed by Eyring [31]. The mathematical model assumes that the motion of molecules has to overcome potential barriers (Q′) from their neighbors by shear stress and random thermal. And the product of the Boltzmann factor and the effective vibration frequency of molecules v is the average time (t′) for molecules passing through energy barrier, as shown in Eq. (5).
where Q � + ΩP − is the energy barrier, Ω and represent the pressure and stress activation volumes, separately. The average velocity V of molecules under the potential gradient is obtained by Eq. (6).
where b represents the distance by which the regular series of barriers are separated. And then, the sliding velocity V , which is proportional to V , can be obtained with Eq. (7) by introducing an unknown velocity V 0 .
It is equivalent to Eq. (9) Therefore, the relationship between friction coefficient and Hertz contact pressure, as given in Eq. (10).
During sliding, the gas adsorption across interface is dynamically stable, resulting in passivation groups across sliding interface. It is similar to the common self-assembly layer on substrate, such as L-B layer. We define it as the shear-induced self-assembled layer on the sliding interface. Therefore, Eq. (10) is suitable to sliding interface of a-C film under atmosphere. Combined with the calculated results, the increasing energy barrier Q � + ΩP − during sliding is found.
In summary, the interfacial evolution process of a-C film with various loads in methane atmosphere is revealed. During sliding, methane molecule dissociates into methyl and hydrogen, bonding to the carbon dangling bond across the sliding interface. The applied load affects the distribution models of adsorbates, leading to the different origin of energy dissipation for tribological systems. Specifically, the distribution of adsorbates on top and bottom surfaces transfers from head-on mode to side-by-side mode with the increasing load, as shown in Fig. 10. Consequently, the origin of energy dissipation changes from the interaction between adsorbates to interaction between adsorbates and carbon dangling bonds or adsorbates, resulting in the distinct and 0 for tribological systems under various stages of film's tribological performance.

Conclusions
The frictional behaviors of a-C film in methane atmosphere are explored with the load effects based on experimental and theoretical methods. It is found that the contact of a-C film and ball under various loads is in accord with the Hertzian evolution relation in stages. Specifically, as load increases, there are various pressure dependences of the shear strength ( ) and interfacial shear strength at a load of zero 0 . Experimental and model analyses on interfacial evolution processes reveal factors that determine the frictional behaviors of a-C film in methane atmosphere. It is the different arrangements of adsorbates on top and bottom sliding surfaces under various loads that lead to different kinds of groups, which interact with each other, and thus affect the load dependence of a-C film in methane atmosphere. Additionally, the role of the adsorption layer is consistent with self-assembled layer and thus is proposed as shear-induced self-assembled layer. This work presents a new phenomenon and supplements the tribological behaviors of a-C film in atmosphere.
Besides, it provides a theoretical basis for a-C film applied in methane.