Molecular Dynamics Simulations of the Interaction Between Graphene and Lubricating Oil Molecules

The microscopic interaction between graphene and liquid lubricating oil molecules significantly affects the rheological and tribological properties of the solid–liquid lubricating system. In this study, the interaction between graphene and six kinds of alkane oil droplets with different chain lengths was investigated by molecular dynamics simulations. Interaction energy, atomic concentration distribution, mean square distribution, curvature, centroid, and inclination angle were used to quantitatively describe the effect of interaction differences on lubricating performance. The results demonstrated that with the increase of the carbon chain length, the alkane molecules transformed from a spherical oil droplet model to an ordered layered structure. At the same time, the interaction energy and the angle with the Z coordinate axis were further increased. The self-diffusion movement and the degree of molecular bending were reduced during the interaction, indicating that long-chain alkane molecules interact strongly with graphene, and a dense multilayer adsorption film was formed by horizontal adsorption on the surface of graphene, thus exerting a good lubricating effect. In addition, it was found that the increase in temperature was beneficial to the occurrence of the adsorption process, but high temperature is not conducive to the stable adsorption of alkane molecules on the surface of graphene.


Introduction
Efficient lubrication is one of the most effective ways to reduce energy consumption and carbon dioxide emissions during friction, the use of lubricant avoids direct contact of asperities on the surface of the friction pair, converts dry friction between friction pairs into internal friction between lubricants, thereby reducing friction and wear [1]. However, under extremely variable working conditions with ultra-high loads, a single liquid or solid lubricant cannot exert good tribological properties. For this reason, many scholars have proposed solid-liquid two-phase lubrication, which combined solid lubricants with liquid lubricants. Such as molybdenum disulfide, silicon dioxide, fullerene, graphene, etc., compounded with liquid lubricants, this avoided both cold welding adhesion to solid surfaces and dry friction under transient oil-starved conditions [2][3][4][5][6][7].
Among them, the excellent mechanical properties of graphene and the weak van der Waals force between layers make it easy to shear slip and have excellent friction reduction properties [8][9][10][11][12][13], which have attracted extensive attention in the field of tribology. Wu et al. [14,15] added graphene and graphene oxide nanosheets to 4010 aviation lubricating oil and studied the influences of load, rotational speed, etc., on tribological properties. The results showed that the adsorption of the two additives played a role in anti-shear, anti-tear, and filling, avoiding direct contact with the asperities. Ali et al. [16] investigated the tribological properties of graphene-containing lubricating oil through tribometer and bench tests, the results indicated that the addition of graphene improved friction reduction and anti-wear performance, reduced fuel consumption by 17%, and reduced the exhaust gas (CO, CO 2 , NO X ) emissions by 2.79-5.42%. Liu et al. [17] dispersed the modified graphene into a base oil, and the modified graphene formed a carbon-containing deposition film on the friction interface to avoid direct contact with the friction pair, thereby improving the tribological performance. Senatore et al. [18] dispersed 0.1% wt graphene oxide (GO) nanosheets into mineral lubricants by ultrasonic technology and found that GO can reduce the friction coefficient (average 20%) in boundary, mixed, elastohydrodynamic lubrication domains, and reduce the wear rate of friction pairs (the wear scare diameter was reduced by 12, 27, and 30%, respectively).
However, current research focuses more on the tribological properties and macroscopic properties exhibited by solid-liquid two-phase lubrication, and less on the micro-level interaction between solid-liquid two-phase lubricants, the interaction difference at the micro-level significantly affects the rheological properties, synergistic tribological effects and lubricant mechanism of the lubricant system. Molecular dynamics simulations can investigate micro-level interactions, which is an important complement to experiments [19][20][21][22][23][24][25]. Li et al. [26] explored the synergistic lubricant mechanism of graphene water-based lubricant system through molecular dynamics simulations, the results demonstrated that graphene enhanced the movement of water molecules, made it easier to move to the interface, and avoided direct contact of the asperities. Water molecules induced graphene to release lateral stress and played a good role in friction reduction. Zhang et al. [27] studied the interaction between alkane molecules with different chain lengths and palygorskite coatings, it was founded that short-chain alkanes had compatibility with palygorskite, and can stably adsorb on the surface of palygorskite to form a layered lubricating film, which played a good lubricating role. Wu et al. [28] investigated the rheological properties of graphene nanofluids by non-equilibrium molecular dynamics simulations, the results reflected that the addition of graphene increased the viscosity of base oil by 3 times under the conditions of 0.1 MPa, 500 K, and has a more important effect on increasing the viscosity of base oil at high temperature and pressure.
The interaction difference at the microscopic level between solid-liquid two-phase lubricants significantly affects the rheological properties, tribological properties, synergistic tribological effects, and lubrication mechanism of the lubricating system. This article aims to investigate the interaction of the solid-liquid two-phase lubrication system of graphene and alkanes with different chain lengths at the microscopic level by molecular dynamics simulations and to reveal the effect of the difference in molecular chain length of alkanes on the lubrication performance. This will provide insights into the compositional differences and base oil use, enabling graphene to exert better tribological properties in solid-liquid twophase lubrication systems.

Model Parameters
All models were established based on Materials Studio (MS) software. Firstly, linear alkane single molecule models with different carbon chain lengths were established, which were n-hexane (C 6 H 14 ), n-octane (C 8 H 18 ), n-decane (C 10 H 22 ), dodecane (C 12 H 26 ), tetradecane (C 14 H 30 ), and n-docosane (C 22 H 46 ), as shown in Fig. 1a. But the single molecule model cannot simulate a real lubricating system [20]. For this reason, the spherical oil models with a radius of 20 Å were constructed based on the Monte Carlo rule and the real density of each component for later molecular dynamics simulations. The final conformation of the model and the parameters of each component are shown in Fig. 1b and Table 1. Secondly, a lamellar structure with a size of 55.33 × 56.19 Å was constructed by supercell processing on the graphene crystal, and the unsaturated dangling bonds at the edge of graphene were functionalized to introduce H atoms to realize the graphene (abbreviated as Gra) model construction [29], as shown in Fig. 1c.  Thirdly, the spherical oil droplet model and the lamellar graphene structure were spliced together. To eliminate periodic effects, a vacuum layer of 60 Å was added in the Z direction [27,30]. The size of the simulation system was 60 × 60 × 100 Å, as shown in Fig. 1d.

Simulation Methods
Due to the unreasonable initial configuration, the energy of the system was at a high level. Therefore, geometry optimization and dynamic equilibrium were required to find the low-energy conformation that conforms to the real system [19]. All simulations were done based on the molecular mechanics and molecular dynamics methods of the Material Studio software Forcite module [31,32], the COMPASS force field suitable for polymer nanocomposite systems were selected [33][34][35], and the charge of each atom was automatically assigned by the force field parameters.
Step 2 The alkane molecules with different chain lengths were packed into cube boxes and the dynamic simulation of 50,000 step annealing and 1000 ps was carried out under the NPT ensemble [28], as shown in Fig. 2a, b. (The density change curves of other systems are shown in Fig. S1 of the supplementary material.) Fig. 2c shows that the experimental values of density are basically consistent with the calculated values, indicating the rationality of selecting COMPASS force field parameters.
Step 3 The dynamic equilibrium of 4000 ps was carried out under the NVT ensemble to eliminate the internal stress and to find a reasonable conformation at the global energy minimum [36]. The temperature was set to room temperature 298.15 K and controlled by the Andersen method [37]. The time step was 1 fs, the total number of dynamic simulation steps was 4 × 10 6 steps, and one frame was output every 1000 steps.

System Equilibrium and Conformational Evolution
To explore the interaction between the solid-liquid twophase lubrication system, the energy-temperature curves during the molecular dynamics simulations process and the output configurations of the six systems at four different times were extracted, which were 0, 500, 2000, and 4000 ps, respectively, as shown in Figs. 2d and 3. In Fig. 2d, the temperature of the system fluctuated around the target temperature of 298.15 K during the simulation process, the total energy and each energy component quickly reached Conformation of solid-liquid two-phase lubrication system at different times equilibrium and fluctuated around the stable value, manifesting that the system has reached a low-energy conformation with reasonable structure, which can be used for subsequent analysis and calculation of relevant properties. Based on the system equilibrium, the microstructure evolution during the solid-liquid two-phase interaction at different times was extracted, as shown in Fig. 3. At 0 ps, the layered graphene structure was fixed at the bottom of the box to simulate the solid lubricant during solid-liquid two-phase lubrication. A large number of tribological experiments also confirmed that graphene as a solid lubricant will be adsorbed on the surface of the friction pair to form a stable layered film [16,17]. Models of alkane oil droplets with different chain lengths were placed on the graphene surface with a preset distance of 14 Å to observe the dynamic process of the interaction [27], as shown in Fig. 3a. After 500 ps dynamics simulation, it is observed from Fig. 3b that alkane oil droplets with different chain lengths show different morphologies. In the Gra/ C 6 H 14 system, only a small amount of C 6 H 14 molecules were adsorbed to the surface of graphene, and the overall spherical oil droplet model was still maintained, indicating that the interaction between C 6 H 14 molecules and graphene was weak, and the short-time dynamics process cannot make C 6 H 14 molecules quickly adsorbed on the surface of graphene to form a layered structure. However, in the three systems of Gra/C 8 H 18 /C 10 H 22 /C 12 H 26 , it was found that alkanes formed a dense adsorption monolayer on the surface of graphene, and the spherical oil droplets gradually changed their original shape and transitioned to a layered oil film during the interaction process. It shows that the interaction between alkane molecules and graphene was enhanced, and it was easier to move to the graphene surface to form stable adsorption at the same time.
In the Gra/C 14 H 30 /C 22 H 46 system, no obvious monolayer adsorption film was observed, which may be due to the strong interaction between the C 14 H 30 /C 22 H 46 alkane molecules themselves inhibited the adsorption with graphene, and this will be analyzed in the subsequent analysis. At 2000 and 4000 ps, compared with the long-chain alkane system, the Gra/C 6 H 14 system still maintained its original morphology and formed monolayer adsorption, the Gra/C 8 H 18 /C 10 H 22 /C 12 H 26 system formed a dense doublelayer adsorption film, while the Gra/C 14 H 30 /C 22 H 46 system formed a triple-adsorption layer over time. The relative atomic concentration in the following text will further quantitatively describe the formation of layered adsorption film. The above conformational evolution shows that with the increase of carbon chain length, alkane molecules are more likely to form a layered oil film on the surface of graphene during the simulation process.

Interaction Energy
To study the reasons for the obvious differences in the structural evolution of the alkane systems with different chain lengths interacting with the graphene surface, the energy changes of each system during the dynamics process were calculated. The adsorption energy between alkanes and   (1) and (2) [38]: where E adsorption is the adsorption energy between the alkanes and graphene. E total , E graphene , and E alkane are the total energy of the system, the energy of graphene alone, the energy of the alkanes system alone, and the energy of the alkanes system alone, respectively. E cohesive is the cohesive energy between alkane molecules, and E intramolecular is the internal energy of the alkanes system. The adsorption energy and cohesive energy are calculated based on the above formulas as shown in Fig. 4a, b.
According to the principle of thermodynamics, adsorption is an exothermic process, and energy is negative. The larger absolute value of the adsorption energy indicates the stronger adsorption between the alkanes system and graphene, and the formed adsorption film is more stable [39]. It can be seen from Fig. 4a that the adsorption energy of different systems gradually decreased during the first 500 ps of dynamics simulation, showing that alkane molecules are adsorbing on the graphene surface. Moreover, the absolute value of the adsorption energy of the Gra/C 8 H 18 /C 10 H 22 / C 12 H 26 system is larger than Gra/C 6 H 14 system at 500 ps, indicating that the interaction between long-chain alkanes and graphene is stronger, and short-chain alkanes are weak. However, the adsorption energy of the Gra/C 14 H 30 /C 22 H 46 system does not further increase with the increase of carbon chain length. The reasons for this will be further analyzed by the adsorption energy components and cohesive energy. In subsequent 3500 ps simulations, the adsorption energy of all the systems further decreased and tended to be stable, which is consistent with the adsorption film structure formed in Fig. 3c, d. At the same time, the adsorption energy in the final increases with the increase of carbon chain length, indicating that the longer the molecular chain is, the more stable the adsorption film will be. Why the adsorption energy does not further increase with the increase of carbon chain length at 500 ps? To further discuss the reasons for the above differences, the average van der Waals (vdW) and electrostatic interaction were calculated, as shown in Table 2.
On the one hand, the adsorption energy is contributed by van der Waals energy and electrostatic energy [40]. It can be seen from Table 2 that the adsorption energy of each system mainly comes from the vdW interaction, and the electrostatic interaction can be ignored, which is due to the weak polarity of linear alkanes, resulting in less electrostatic interaction. The vdW energy is related to the interaction site [41]. The more interaction sites between alkane molecules and the graphene surface, the greater the vdW energy. On the other hand, the interaction between the alkanes system and graphene is not only affected by the adsorption, but also by the interaction between the alkane molecules themselves. Cohesive energy is a parameter to measure the force between substances, which can effectively reflect the bonding strength of the system. From Fig. 4b we can see that the cohesive energy of each alkanes system changes relatively little during the dynamics simulation process beside Gra/C 6 H 14 system, and the absolute value of the cohesive energy increases with the increase of the carbon chain length. It shows that the longer the alkane chain is, the stronger the bonding between the alkane molecules is, and it is more difficult to interact with graphene during the simulation process, resulting in the Gra/C 14 H 30 /C 22 H 46 system in Fig. 3b not forming a dense monolayer adsorption film in short time. The absolute value of the average energy and energy difference was further calculated, as shown in Fig. 5. We can find from Fig. 5a and b that the adsorption energy of different chain length alkane systems and graphene are all smaller than the cohesive energy between alkane molecules, indicating that it is difficult for alkane molecules to overcome their interactions in a short time and stably adsorb on the graphene surface. Besides, to better understand the influence of energy difference on system interaction and conformational evolution, we choose 300 kcal/mol as the threshold to evaluate the relative relationship of different systems, as shown in Fig. 5c. The energy difference of the Gra/C 6 H 14 /C 14 H 30 /C 22 H 46 system is larger than the Gra/C 8 H 18 /C 10 H 22 /C 12 H 26 system, which shows that the adsorption process in the Gra/C 6 H 14 /C 14 H 30 /C 22 H 46 system is more difficult to occur, which is consistent with the structural evolution of Fig. 3b and the adsorption energy change of Fig. 4a, reasonable explanation for the obvious differences in the structural evolution of alkane systems with different chain lengths when interacting with the graphene surface.

Mean Square Displacement and Centroid Distance
In molecular dynamics simulations, the diffusion coefficient (D) is often used to evaluate the dynamic behavior of molecules in the system. The larger the diffusion coefficient, the stronger the molecular movement ability. It needs to be obtained by linearly fitting the mean square displacement (MSD) curve according to the Einstein equation. The specific calculation formula is as follows [26,28].
where n represents the total number of atoms, r i t + t 0 and r i t 0 represent the position of the i particle at time t + t 0 and  t 0 , respectively. In order to accurately evaluate the movement ability of alkane systems with different chain lengths, the MSD of 200, 700, and 900 ps in the three stages and centroid distance during the simulations were extracted, and one-sixth of the slope of the MSD linear fitting represents D, as shown in Fig. 6, (Detailed liner equations are shown in Tables S1-S3 in the supplementary material). According to Fig. 6a and Table S1, the slope of the first 200 ps fitting line decreases with the increase of alkane chain length, indicating that the carbon chain length significantly affects the movement ability of alkane molecules, and the diffusion coefficient decreases with the increase of alkane chain length. This phenomenon was also found in the study of Zhang et al. [27] that the movement ability of alkane molecules weakened with the increase of carbon chain length. Combined with the above energy changes and difference in molecular weight, this may be due to the fact that long-chain alkanes with a large molecular weight are more likely to adsorb on the surface of graphene to form a lubricating film, the attraction of graphene to long-chain alkane molecules inhibits its own diffusion, resulting in a relatively low diffusion coefficient. Therefore, graphene has a weak attraction to short-chain alkane C 6 H 14 , resulting in a relatively high diffusion coefficient, which shows a trend of decreasing diffusion coefficient with the increase of alkane chain length. In the subsequent 700 ps of Fig. 6b, the movement ability of alkane molecules still maintains this rules. The greater MSD of Gra/C 14 H 30 / C 22 H 46 than Gra/C 12 H 26 can be attributed to the energy difference is large, which makes it difficult to stable adsorb on the surface of graphene quickly. It can be confirmed by the change of centroid distance in Fig. S2 b in the second stage. Combined with the energy change at 500-2000 ps in Fig. 4a, the adsorption energy is further reduced, the alkane molecules continue to adsorb with graphene, and we can see that from Fig. 3b, c the alkane molecules transition to an ordered layered structure, from a single-layer adsorption film to a double-layer adsorption film. But in the final 900 ps of the third stage, shown in Fig. 6c, compared with the initial 200 ps and subsequent 700 ps, the diffusion coefficients of each system decreased to varying degrees, indicating that the movement ability of alkane molecules was relatively weakened over time. The strong interaction of the graphene surface with alkane molecules further inhibited the movement of alkane molecules, and finally a dense double-layer adsorption film was formed in the Gra/C 8

Curvature and Inclination
According to the conformational evolution of each system at different times in Fig. 3, it can be observed that some alkane molecules transform from the initial spherical oil droplet model to the layered ordered structure. For this reason, the changes in the microstructure were further studied through the curvature χ and inclination angle θ of the alkane molecules. The curvature χ is defined as the change in the relative distance between the first and last carbon atoms, which reflects the bending degree of alkane molecules. The calculation formula is as follows.
(5) = L−L 0 L 0 Fig. 9 The angle between the alkane molecules and the coordinate axis a X axis b Y axis c Z axis Here χ represents the curvature of alkane molecules, L is the distance between the first and last carbon atoms of the alkane molecules at any time, and L 0 is the distance between the first and last carbon atoms when the alkane molecules are free to stretch, as shown in Fig. 7a. The inclination θ is defined as the angle between the alkane molecules and coordinate axes of X, Y, and Z, as shown in Fig. 7b.
Based on the above definitions, the curvature of alkane molecules at different time intervals during the dynamics process was calculated, as shown in Fig. 8, which is the result of statistical averaging of all the molecules in the system. The curvature is less than 0, indicating that the alkane molecules are relatively curved, while the curvature is close to 0, indicating that the alkane molecules are free to stretch. It can be seen from Fig. 8a that during the initial 500 ps dynamics simulations, the alkane systems with different carbon chain lengths have a peak near 0, and the intensity of the peaks decreases with the increase of alkane chain lengths, C 14 H 30 /C 22 H 46 has no peaks near the curvature of 0. This shows that most short-chain alkanes are relatively stretched, while long-chain alkanes are relatively curved. With the increase of alkanes chain length, the degree of bending of alkane molecules increases. In addition, it can also be found that with the increase of alkane chain length, the number of peaks in each system decreases in turn. It shows that the short-chain alkane molecules are in the form of mostly stretching and few bending, while the long-chain alkanes are on the contrary. And when the carbon chain length continues to increase to the C 14 H 30 /C 22 H 46 , all alkane molecules are in a bent state. During the subsequent 3500 ps dynamics simulations, as shown in Fig. 8b, c, the curvature of the C 6 H 14 system remained unchanged, which means that the C 6 H 14 alkane molecules have strong rigidity and still maintain the original shape during the dynamics process. However, the Gra/C 8 H 18 /C 10 H 22 /C 12 H 26 /C 14 H 30 /C 22 H 46 system has a trend of increasing the peak value near 0, decreasing the peak value below 0 and shifting the peak value to the right. This indicates that the alkane molecules in the system are further stretched during the simulation, and the distance between the first and last carbon atoms is transitioned from L to L 0 , as shown in Fig. 7a.
The angle between the alkane molecule and the XYZ coordinate axis during dynamics simulations were calculated, and the result of statistical averaging of all the molecules in the system is shown in Fig. 9. The angle between the C 6 H 14 molecule and XY coordinate axis decreases slightly, and the angle with the Z coordinate axis increases slightly, indicating that most of the molecules in the C 6 H 14 alkane system still retain the original spherical oil droplet shape, and some molecules are adsorbed to the surface. However, it can be found from Fig. 9a, c, as the chain length of the alkanes increases, the inclination angle between alkane systems and the X coordinate axis decreased continuously, and Besides, the angle between alkane molecules and the Y coordinate axis has no obvious rule from Fig. 9b, indicating that long-chain alkane molecules tend to be perpendicular to the Z coordinate axis and tilt to the X coordinate axis. Due to the weak adsorption of graphene on short-chain alkane molecules, most C 6 H 14 molecules still retain their original spherical oil droplet shape, the strong adsorption with longchain alkane molecules makes alkane molecules move to the surface of graphene and tend to be horizontally adsorbed on the surface to form a stable layered film.

Relative Atomic Concentration
There are obvious differences in the layered adsorption films formed during the interaction. Figure. 10 shows the relative concentration changes along the Z direction for different systems at different times. According to Fig. 10a, the relative concentration curves of different alkane systems have two peaks around 7 and 37 Å, respectively, indicating that most of the atoms gather here. Besides, C 8 H 18 /C 10 H 22 /C 12 H 26 system has higher peaks than C 6 H 14 /C 14 H 30 /C 22 H 46 system at around 7 Å, and the opposite trend appears at 37Å. 7 Å corresponds to the centroid position of the first layer of adsorption film, and 37 Å corresponds to the centroid position of the alkane oil droplet. It shows that in the first 500 ps simulation process, the alkane molecules in C 8 H 18 /C 10 H 22 /C 12 H 26 system are more likely to form a dense monolayer adsorption film on the graphene surface, while in C 6 H 14 /C 14 H 30 / C 22 H 46 system only a small amount of alkane molecules are adsorbed on the graphene surface to form a loose adsorption film, a large number of alkane molecules are still located at the centroids of the initial alkane oil droplets, as shown in the conformational evolution of Fig. 3b. In Fig. 10b, the peak value of C 6 H 14 near 37 Å decreases, and the peak near 7 Å increases, indicating that the interaction between C 6 H 14 and graphene was enhanced, and the first layer of adsorption film was gradually formed. In the Gra/C 8 H 18 /C 10 H 22 /C 12 H 26 / C 14 H 30 /C 22 H 46 system, the peak near 37 Å disappeared, the peak near 7 Å was enhanced, and a new peak appeared near 10 Å, which shows that a dense double-layer adsorption film is further formed based on the single-layer adsorption film. During the final 2000 ps dynamics simulation, we can see from Fig. 10c that the peak near 7 and 10 Å was further enhanced and over 16 and 12, respectively. A new peak obviously appeared near 15 Å in Gra/C 14 H 30 /C 22 H 46 system, it shows that the long-chain alkane system forms a denser adsorption film and exerts a better lubricating effect, which is consistent with the conformational evolution of Fig. 3d.

Influence of Temperature and Preset Distance
The interaction between alkane molecules and graphene is affected by many factors such as molecule structure, surface morphology, and ambient temperature. The effect of temperature is particularly significant, and Fang et al. extensively studied the effect of temperature on molecular orientation [42,43]. In this paper, the effects of temperature and preset distance on the interaction between alkane molecules and graphene were further studied, and the interaction energy of the Gra/C 6 H 14 /C 14 H 30 /C 22 H 46 system during the dynamics simulation was extracted. According to Fig. 11a, for Gra/ C 6 H 14 system, the adsorption energy drops sharply with the increase in temperature and tends to be stable. It shows that high temperature is benefit to the occurrence of adsorption process, the increase in temperature increases the thermal motion of molecules and enhances the interaction between alkane molecules and graphene. However, over time, the absolute value of adsorption energy of the Gra/C 6 H 14 system did not increase further with the increase of temperature, as shown by the solid blue and red lines in Fig. 11a, showing a trend that the adsorption energy at a stable period decreases with the increase in temperature. This phenomenon is more obvious in the system of Gra/C 14 H 30 /C 22 H 46 , as shown in Fig. 11b, c, the blue curve in the stable stage is higher than the red curve. This suggests that the increase in temperature enhances the thermal movement of molecules, which is benefit to the occurrence of the adsorption process. But it is not conducive to the stable adsorption of alkane molecules on the graphene surface, making the stability of the layered oil film formed on the graphene surface worse.
Generally speaking, the actual structure of graphene should be a corrugated surface, there are obvious height differences between the peaks and troughs on the surface. To further explore the influence of surface morphology differences on the interaction, reduced the initial preset distance of the oil droplet from 14 to 10 Å to simulate the height difference, and the calculation results in 298.15 K are shown in Fig. 12. Compared with Fig. 4a, the reduction of distance makes the adsorption energy of each system drop faster and reach equilibrium quickly, especially for the Gra/C 6 H 14 system shown in Fig. 12a. This indicates that the decrease of the preset distance between alkane oil droplet and graphene is conducive to the occurrence of interaction so that the alkane molecules can adsorb to the graphene surface faster to form a stable oil film. In addition, compared with Figs. 12 and 4 we can see that no matter whether the preset distance is 14 or 10 Å, the adsorption energy and cohesive energy at the stable stage increase with the increase of alkane molecular chain length after 4000 ps dynamics simulation. Further confirmed that the interaction between alkane molecules and graphene and the bond strength between alkane molecules was enhanced with the increase of carbon chain length, and the adsorption film formed by long-chain alkanes on the surface of graphene was more stable.

Conclusions
The interaction difference between graphene and alkane lubricating oil molecules with different chain lengths was investigated by molecular dynamics simulations, which is helpful for the application of graphene as a solid lubricant in a solid-liquid two-phase lubrication system. The result shows that the carbon chain length significantly affects the interaction between alkane molecules and graphene. The interaction energy and the angle with the Z coordinate axis at the stable stage increase with the increase of alkane molecular chain length, and the self-diffusion movement is weakened with the increase of chain length, which is attributed to the strong attraction of graphene to long-chain alkane molecules inhibiting its self-diffusion motion so that the alkane molecules are horizontally adsorbed on the graphene surface to form a dense double-layer adsorption film, playing a good lubricating effect. Besides, it was found that the increase in temperature and decrease of the distance between alkane oil droplet and graphene was beneficial to the occurrence of adsorption process, but high temperature is not conducive to the stable adsorption of alkane molecules on the surface of graphene.