Multiscale Investigation of the Anti-Friction Mechanism in Graphene Coatings on Copper Substrates: Substrate Reinforcement via Microstructural Evolution

Abstract

Graphene exhibits great potential as an anti-friction coating material in MEMS. However, its underlying microscopic friction-reduction mechanism remains unclear. In this paper, the microstructural evolution and nanomechanical behavior of graphene coatings on copper substrates were systematically investigated by AFM friction experiments and MD simulations. MD simulations reveal that the anti-friction properties of graphene coatings primarily stem from microstructural regulation and load-bearing reinforcement of the substrate. The graphene coatings increase indentation diameter by forming transition radii at the indentation edges, and suppress the plowing effect of the substrate by restricting atomic upward movement, both of which enhance the dislocation density and load-bearing capacity of the substrate. Additionally, graphene coatings also reduce the scratch edge angle, weakening the interlocking effect between the substrate and tip, further lowering the friction force. Experimental results indicate that the tribological behavior of graphene coatings exhibits staged characteristics: graphene coatings show excellent ultrafriction properties under intact structural conditions, while showing a higher friction force in wear and tear states. This research provides a theoretical basis and technical guidance for the development of anti-friction and wear-resistant coatings for micro-nano devices.

1. Introduction

Friction and wear at material interfaces are the primary causes of energy loss and component failure in mechanical systems. According to statistics, approximately 20% of global energy consumption is used to overcome energy losses caused by friction and wear [1]. In particular, as mechanical systems continue to trend toward miniaturization, surface effects and size effects further exacerbate interface friction and wear issues [2,3,4]. Fortunately, the development of two-dimensional (2D) coating technologies in recent years has provided an effective solution to this challenge [5,6]. Among these, graphene stands out as the most representative 2D nanomaterial due to its exceptional mechanical, electrical, optical, and thermal properties [7,8,9,10]. It has been extensively applied in energy storage [11,12], surface engineering [13,14], electrical engineering [15,16], sensors [17,18], and biomedical applications [19,20,21]. Notably, graphene possesses an atomically smooth surface, ultra-high specific surface area, low friction coefficient, and strong chemical stability, making it an ideal 2D coating material. Graphene effectively reduces friction and wear on the surfaces of microdevices, offering an innovative solution to tribological issues in Microelectromechanical Systems (MEMS) [22]. For example, Lei et al. [23] proposed a planar spiral microinductor prepared by a graphene/copper composite film conductive coil based on MEMS technology. Compared to a pure copper microinductor with the same structure, this graphene/copper microinductor exhibited a 48.4% higher inductance value, with the quality factor rising from 26.2 to 30.3. Additionally, the thermal stability and gas barrier properties of graphene coatings effectively prevent metal oxidation in MEMS devices. These coatings can protect copper and copper-nickel alloy surfaces from oxidation for 3 h at 500 °C [24]. Research indicates that graphene-coated composite materials retain the inherent properties of graphene and the substrate, while synergistically enhancing the overall performance of the material [25,26,27,28]. Therefore, a deeper understanding of the friction-reducing mechanism of graphene coatings is crucial for improving the operational efficiency and component lifespan in MEMS.

In recent years, remarkable progress has been made in the tribological behavior of graphene coatings, and scholars have revealed the mechanisms of friction reduction of graphene coatings from multiple perspectives. In terms of substrate effects, Yao et al. [29] conducted atomic force microscope (AFM) friction experiments and found that rigid substrates enhance the load-bearing capacity and wear resistance of graphene by suppressing in-plane deformation. Zhao et al. [30] performed molecular dynamics (MD) simulations and demonstrated that strongly chemically adsorbed substrates weaken the C-C bond strength of graphene, leading to a reduction in the critical failure load. Regarding environmental factors, Li et al. [31] discovered that hydrogen atoms tend to adsorb around graphene wear cavities in the hydrogen environment, which accelerates graphene tensile fracture and alters the expansion direction of wear cavities. Additionally, Li et al. [32] revealed the synergistic lubrication mechanism between graphene- and water-based lubricants, where graphene promotes water molecule rolling, while water molecules protect the structure of graphene and enhance interfacial isolation. Fu et al. [33] further demonstrated that environmental humidity significantly improves the wear resistance of graphene step edges by isolating and passivating the sliding interface.

Beyond environmental influences, the intrinsic structure of graphene also significantly impacts its tribological behavior. Zhao et al. [34] found that the strain at graphene grain boundaries induces stress concentration, reducing wear resistance at the heterostructure interface of thin films; Huang et al. [35] confirmed that graphene wrinkles increase the contact area, and morphology variations degrade surface contact quality, resulting in elevated friction forces and reduced wear resistance of graphene. Chen [36] and Yin et al. [37] showed that both stacking and curling at graphene edge steps substantially enhance friction resistance. Yang et al. [38] observed cross-linking between multiple graphene layers during friction, and the friction coefficient decreases with an increasing number of graphene layers. Furthermore, Zhao et al. [39] compared the effects of different defects in graphene on friction characteristics, demonstrating that single vacancies and line defects weaken the load-bearing capacity of graphene, while Stone-Wales defects slightly enhance wear resistance. Li et al. [40] further proposed that hydrogen atom passivation suppresses chemical activity and out-of-plane deformation at single vacancy defects, leading to a notable enhancement of the critical normal load.

Although existing studies have extensively compared the friction characteristics of graphene under different substrate material, environmental, and defective structural conditions, the friction-reducing mechanism resulting from synergistic effects between graphene coatings and substrates remains unclear. To address this knowledge gap, this research systematically investigates the microscopic anti-friction mechanism of graphene coatings by combining AFM experiments and MD simulations. The study focuses on the influence of synergistic interactions between graphene coatings and substrates on load-bearing performance, particularly concerning the microstructure regulation of substrates by graphene coatings. The microstructural evolution of pure copper (Cu) and copper/graphene-coated (Cu/Gr) substrates was compared to analyze transition radii, indentation diameter, scratch edge angle, dislocation densities, and plowing effects, which ultimately revealed the anti-friction mechanism and substrate reinforcement effect of graphene coating. These findings provide significant reference for developing wear-resistant coatings for MEMS devices.

2. Materials and Methods

2.1. Experimental Section

As shown in Figure 1a, the CSPM5500 scanning probe microscope was used for sample characterization and tribological testing. This device integrates AFM, lateral force microscopy (LFM), and scanning tunneling microscopy (STM) functions, allowing for microscopic morphological characterization and tribological performance studies of samples. The Tap300DLC probe was selected for all experiments. This probe is a tapping-mode probe with a diamond-like carbon coating, featuring an elastic modulus of 40 N/m and a tip curvature radius of 15 nm. Before the friction experiments, the normal and lateral forces of the probe were calibrated via a non-contact method [22]. All testing devices are manufactured by Being Nano Instruments Co., Ltd, Guangzhou, China.

As shown in Figure 1b, the experimental samples included Cu and Cu/Gr, both procured from Nanjing Xianfeng Nanomaterials Technology Co., Ltd. (Nanjing, China). The Cu sample thickness was only 25 μm, with dimensions of 1 cm × 1 cm, prepared by multiple rolling processes from a pure copper plate. The Cu/Gr sample was prepared by depositing a single layer of graphene onto the Cu sample surface via chemical vapor deposition (CVD). The basic preparation steps are as follows: the Cu sample was first cleaned with deionized water and dried with nitrogen gas. Subsequently, the Cu sample was annealed for 30 min at 1000 °C in an H₂ atmosphere. Finally, a single-layer graphene was grown on the Cu sample surface for 15 min in a CH₄ and H₂ atmosphere. After shutting off the CH₄ gas, the Cu/Gr sample was naturally cooled to room temperature in the H₂ atmosphere. Cu samples are the most economical and effective substrates for preparing single-layer graphene via CVD [4,7]. Furthermore, Cu is also the most important and basic material in the MEMS due to its excellent electrical and thermal conductivity. Therefore, adopting Cu as the substrate is also the most practical choice in AFM experiments and MD simulations. Additionally, Raman spectroscopy was performed to ensure the high quality of the graphene on the Cu/Gr sample. The Raman spectroscopy exhibited a weak D peak (1350 cm⁻¹), a symmetric G peak (1580 cm⁻¹), a single 2D peak (2670 cm⁻¹), and a 4-fold intensity ratio of I(2D)/I(G) (Figure 1c). These results also confirmed that the graphene coating was a single-layer structure with high quality. Moreover, to ensure the stability of the sample position in testing, the Cu and Cu/Gr samples were placed on 304 stainless steel circular platforms and fixed with tape. AFM tapping mode was used for morphological characterization, with a scanning range of 10 × 10 μm and a scanning speed of 0.5 μm/s. Contact mode was applied for tribological experiments, with a scratch distance of 10 μm and a scratch speed of 500 nm/s. All experiments were conducted under ambient conditions of 20~23 °C and relative humidity of 40~60%.

2.2. MD Simulation

As shown in Figure 2, the MD simulation models of Cu and Cu/Gr substrate were constructed to compare the friction behavior of single-layer graphene. In Figure 2a, the Cu model comprises only the diamond tip and Cu substrate. The dimensions of the Cu substrate along the x, y, and z directions are 25 nm × 20 nm × 9 nm, with crystal orientation indices of [1 −1 0], [1 1 −2], and [1 1 1], respectively. A fixed layer (0.0–0.5 nm in thickness) was applied to the left and bottom regions of the substrate to prevent overall displacement under the tip scratch. An adjacent thermostatic layer (0.5–1.0 nm in thickness) was employed to maintain system temperature stability. The remaining region (1.0–9.0 nm) was designated as the Newtonian layer to simulate the dynamic response of the substrate under the tip action. The tip material was diamond with a radius of 2 nm, initially positioned 1.0 nm above the substrate. Additionally, the tip was treated as a rigid body to exclude its deformation effects on friction characteristics. In Figure 2b, the Cu/Gr model consists of the tip, Cu substrate, and single-layer graphene. The single-layer graphene was placed above the Newtonian layer on the substrate, with dimensions of 20 nm × 15 nm along the x and y directions, and the 0.5 nm edges on both sides of the graphene were fixed to ensure its positional stability.

First, the model was subjected to energy minimization to obtain the lowest energy equilibrium configuration. Subsequently, the model was relaxed under the microcanonical ensemble (NVE) for 50 ps to eliminate the interference of atomic thermal vibrations. Finally, the model was performed under an isothermal-isobaric ensemble (NVT) for 50 ps to maintain its temperature at 27 °C. Moreover, to explore the impact of graphene coatings on the load-bearing properties of the substrate, nanoindentation simulations were first conducted with an indentation speed of 2 × 10¹⁰ nm/s and an indentation depth of 3 nm. Following this, scratch simulations with different depths were performed to investigate the effect of graphene coatings on friction properties, with a scratch speed of 5 × 10¹⁰ nm/s and a distance of 3 nm. Periodic boundary conditions were applied in both the x and y directions to simulate an infinitely extended structure, while free boundary conditions were applied in the z direction to allow for free relaxation in the vertical direction. All molecular dynamics computations were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS-64bit-2Aug2023), and the simulation results were visualized and analyzed using the Open Visualization Tool (Ovito 3.5.2) software. The loading information of AFM experiments and MD simulations is listed in

Table 1. Loading information on AFM experiments and MD simulations.

Parameter Types	AFM Experiments	MD Simulations
Sample dimensions (nm)	107 × 107	25 × 20
Probe radius (nm)	15	2
Normal force (nN)	150/350/450	50 (1.5 nm)/70 (2.0 nm)/ 110 (2.5 nm)/135 (3.0 nm)
Scratch speed (nm/s)	5 × 102	5 × 1010
Scratch distance (nm)	104	3
Temperature (℃)	20~23	27
Humidity	40~60	—
Probe material	Diamond	Diamond

.

The accurate selection of potential functions is critical to the reliability of simulation results. The Cu substrate exhibits weak chemical adsorption capacity to graphene [41,42]. Therefore, in the MD simulations, only the van der Waals forces were considered between the Cu substrate and graphene coating interfaces, while the chemical adsorption of the Cu substrate on the graphene coating was neglected. In this study, widely validated potential functions were employed to describe interatomic interactions. Specifically, the interactions between carbon atoms (C_G) within the graphene layer were described by the Adaptive Interreactive Bond Order (AIREBO) potential [43], while the interactions between Cu atoms in the substrate were described by the Embedded Atom Method (EAM) potential [44]. In addition, the 12–6 Lennard–Jones potential was applied to describe the interface interactions between the diamond tip (C_T), graphene (C_G), and the substrate (Cu) [45], which is expressed as follows:

$$E=4\epsilon \left[{\left({\displaystyle \frac{\sigma }{r}}\right)}^{12}-{\left({\displaystyle \frac{\sigma }{r}}\right)}^6\right]$$

(1)

where E represents the potential energy, r denotes the atomic distance, ε indicates the potential depth, and σ signifies the equilibrium interatomic distance. The specific values of these parameters are listed in

Table 2. Potential parameters for interactions between the tip, graphene, and substrate.

Atom	ε (eV)	σ (nm)
CT-CG	0.00286	0.347
Cu-CG	0.01170	0.300

.

3. Results and Discussion

3.1. Surface Morphology of Samples

Before the friction experiment, the surface morphologies of Cu and Cu/Gr samples were characterized using AFM tapping mode. As shown in Figure 3a, the Cu sample exhibits a rough surface with multiple continuous peaks and valleys. Furthermore, numerous grain protrusions are observable on the Cu sample surface, which are directly linked to the crystal structure of the Cu substrate. In contrast, the Cu/Gr sample exhibits a flatter surface morphology due to the graphene coatings on the Cu substrate, without continuous peaks and valleys or prominent grain protrusions (Figure 3b). However, the Cu/Gr sample surface features extensive waves and wrinkles, which are typical characteristics resulting from thermal stress and lattice mismatch during graphene growth.

To quantify the surface flatness of Cu and Cu/Gr samples, surface roughness parameters such as arithmetic mean roughness (R_a), root mean square roughness (R_q), maximum height difference (S_y), and ten-point height roughness (S_z) of the surface profile were analyzed. As shown in Figure 4, the Cu sample exhibits an R_a of 20.5 nm, while the Cu/Gr sample shows a significantly lower R_a of only 3.1 nm, indicating a smoother overall surface of the Cu/Gr sample. The R_q values follow a similar trend, with 27.3 nm R_q for the Cu sample and 4.2 nm R_q for the Cu/Gr sample, reflecting more pronounced fluctuations between peaks and valleys on the Cu substrate. Additionally, the S_y and S_z values of Cu are notably higher than those of Cu/Gr, further demonstrating pronounced height differences between peaks and valleys on the Cu substrate. These quantitative measurement results confirm that the introduction of graphene coatings effectively improves the surface roughness of the Cu substrate.

3.2. Nanoindentation Characteristics in Experiments

To investigate the effect of graphene coatings on the normal load-bearing characteristics of the substrate, nanoindentation experiments were conducted on Cu and Cu/Gr samples. Under constant-force loading, Figure 5a shows the relationship between the normal force F_z and the vertical displacement z of the probe. When the vertical displacement z is less than 28 nm, the normal force F_z is close to 0 nN due to no contact between the probe and the samples. As the vertical displacement z increases, the probe gradually indents into the sample, leading to an increase in the normal force F_z on both Cu and Cu/Gr samples (dashed lines). Notably, at the same vertical displacement z, the normal force F_z on the Cu/Gr sample is always higher than that on the Cu sample, indicating that the graphene coatings enhance the compressive strength of the substrate. Additionally, when the probe is lifted, the regression curve exhibits a unique characteristic of nanoindentation, with a small valley appearing at a vertical displacement z of 25 nm (solid line). During the gradual lifting of the probe, the sample exhibits an attractive force to resist the lifting motion of the probe when the probe and sample separate. Therefore, a negative normal force appears at a vertical displacement z of 25 nm. When the attractive force of the sample fails to resist the lifting motion of the probe, the probe rapidly separates from the sample, resulting in a normal force of 0 nN, which also leads to a small valley at vertical displacement z of 25 nm. Figure 5b quantitatively compares the indentation profiles under the same normal force F_z of 800 nN. Both Cu and Cu/Gr samples exhibit indentations, and the indentation on the Cu sample surface is more distinct compared to that on the Cu/Gr sample. The maximum indentation depth H reaches 37 nm on the Cu sample, whereas the Cu/Gr sample exhibits a maximum depth of only 23 nm. Nanoindentation experiments demonstrate that Cu/Gr samples exhibit shallower indentation depths under the same normal forces; or at the same indentation depth, Cu/Gr samples display higher compressive strength. The graphene coating enhances the load-bearing capacity of the Cu substrate, effectively suppressing plastic deformation under identical normal forces, which is also confirmed in the MD simulation.

To minimize the influence of probe vertical motion on analyzing the anti-friction mechanism of graphene coatings, a constant-depth loading mode is commonly adopted in MD scratch simulations. To validate the equivalence of loading protocols between constant force and constant depth, different normal forces were applied to the Cu/Gr sample surface. Figure 5c displays the surface morphology of the Cu/Gr samples under normal forces of 400 nN, 800 nN, 1200 nN, and 1600 nN. When the probe normal force F_z is 400 nN, no indentation is observed on the Cu/Gr sample surface. However, triangular indentations appear on the Cu/Gr sample surface when normal force F_z exceeds 800 nN. Furthermore, as the probe normal force increases, the indentation morphology becomes clearer with larger indentation openings. Figure 5d shows the indentation depth curves of the Cu/Gr samples at corresponding normal forces. When the probe normal forces are 400 nN, 800 nN, 1200 nN, and 1600 nN, the maximum indentation depths H of the Cu/Gr sample are 0 nm, 26 nm, 36 nm, and 41 nm, respectively. The indentation depth increases with the probe normal force. Therefore, it is relatively reasonable to replace constant-force loading with constant-depth loading in the MD simulations.

3.3. Friction and Wear Characteristics in Experiments

To investigate the friction and wear characteristics of the graphene coatings under different normal forces, friction and wear experiments were conducted on Cu and Cu/Gr samples using the AFM contact mode. Figure 6a shows the relationship between the friction force F_x and the normal force F_z. As the normal force increases, the friction force F_z on both the Cu and Cu/Gr samples increases. Among these, the friction force F_x on the Cu sample increases linearly with the normal force F_z. This is because the scratch state remains constant, with only the plowing depth and atomic stacking number increasing linearly with the normal force [22]. However, the friction force F_x on the Cu/Gr sample exhibits three distinct stages. When the normal force F_z is below 450 nN, the friction force F_x on the Cu/Gr sample remains small and stable at 5.21 nN, which is significantly lower than that on the Cu sample. Combining the surface morphology of the Cu/Gr sample shown in Figure 6b, no scratches are observed on the graphene coatings during this stage, and the surface morphology of the Cu/Gr sample remains intact. This result indicates that graphene exhibits superior anti-friction and lubrication properties in its intact state. At this phase, this state is also regarded as the friction and lubrication stage.

However, when the normal force F_z ranges between 450 nN and 750 nN, the friction force F_x on the Cu/Gr sample increases sharply with the normal force, eventually stabilizing at a maximum friction force F_x of 624.42 nN. Notably, the friction force F_x of the Cu/Gr sample exceeds that of the Cu sample during this stage. Meanwhile, the graphene coating on the Cu/Gr sample exhibited slight wear in Figure 6b. This result indicates that localized damage of the graphene coating enhanced the interlocking effect on the probe, resulting in a new increase in the friction force of the probe [29]. This stage is also referred to as the wear stage. When the normal force F_z exceeds 750 nN, the friction force increases dramatically. The friction force F_x reaches 1439.83 nN when the normal force F_z is 780 nN. As shown in Figure 6b, the graphene coatings on the Cu/Gr sample exhibit crack expansion, forming a wider scratch groove. Additionally, the graphene coatings suffer from large-area tearing, with numerous wrinkles and piles forming ahead of the probe. This result indicates that severe structural damage of the graphene coating leads to a further increase in probe friction force [32,41]. This stage is also referred to as the tearing stage.

Figure 7 shows the relationship between the friction force F_x and the scratch distance L. Under normal forces F_z of 150 nN, 350 nN, and 450 nN, the average friction forces on the Cu sample are 112.23 nN, 163.24 nN, and 205.39 nN, respectively, while the corresponding friction forces on the Cu/Gr sample are 2.43 nN, 7.98 nN, and 80.68 nN, respectively. Notably, due to the high surface roughness of the Cu sample, significant height variations exist between peaks and valleys, inducing strong interlocking effects on the probe, which results in considerable fluctuations in friction force F_x. In contrast, the flatter surface of the Cu/Gr sample weakens the interlocking effect, resulting in lower fluctuations in friction force F_x. During the anti-friction and lubrication stage, the graphene coatings reduce the friction force F_x on the Cu/Gr sample by 60.72%, and minimize the fluctuation amplitude of the friction force F_x. This phenomenon indicates that the graphene coatings exhibit excellent anti-friction performance and enhance the stability of the friction process. Notably, in Figure 7c, when the normal force F_z reaches 450 nN, the friction force F_x of the Cu/Gr sample increases, accompanied by higher fluctuation amplitudes. Since 450 nN is the dividing point of the normal force between the lubrication stage and the wear stage according to Figure 6, the friction state of graphene is transforming from the lubrication stage to the wear stage at this normal force, which increases the interlocking effect between graphene and the probe as graphene undergoes wear, resulting in a higher and more unstable friction force F_x.

3.4. Nanoindentation Characteristics in MD Simulation

To reveal the intrinsic mechanism of substrate reinforcement by graphene coatings, the nanoindentation behavior of Cu and Cu/Gr substrates was simulated using MD simulations. Under constant-depth loading conditions, Figure 8a shows the relationship between the normal force F_z and the indentation depth H. As the indentation depth H increases, the normal force F_z increases on both Cu and Cu/Gr substrates. Notably, the normal force increase rate on the Cu/Gr substrate is higher than that on the Cu substrate. This indicates that the Cu/Gr substrate exhibits shallower and smaller indentation depths H under the same normal force F_z; or the Cu/Gr substrate exhibits a higher normal force F_z at the same indentation depth H, which is consistent with nanoindentation experimental results. Additionally, when the indentation depth H exceeds 2.2 nm, the normal force F_z on the Cu substrate stabilizes at 192.94 nN, indicating that the nanoindentation behavior on the Cu substrate has reached a mechanical saturation stage. In contrast, the normal force F_z on the Cu/Gr substrate continues to increase with the indentation depth H. The normal force F_z reaches 487.06 nN when the indentation depth is 2.2 nm. These simulation results demonstrate that the graphene coatings enhance the load-bearing capacity of the substrate and improve the mechanical saturation state.

Figure 8b shows the relationship between the dislocation density ρ and the indentation depth H. As the indentation depth H increases, the dislocation density ρ of Cu and Cu/Gr substrates both exhibit an upward trend. Notably, the dislocation density ρ on the Cu/Gr substrate is higher at the same indentation depth compared to the Cu substrate. This result, which seems to contradict the view that graphene suppresses plastic deformation of the substrate, stems from different loading modes. Under constant-force loading, Cu/Gr samples exhibit shallower and smaller indentations because the graphene coating enhances substrate hardness. However, under constant depth loading, the tip is enforced to reach the same indentation depth regardless of the Cu/Gr substrate stiffness. This effect also induces a higher normal force and a denser dislocation network, which can be seen in Figure 9.

Figure 9 shows the dislocation distribution of the Cu and Cu/Gr substrates. The indentation depths H of 1.5 nm, 2.2 nm, and 3.0 nm were applied on Cu and Cu/Gr substrates. As shown in Figure 9, as the indentation depth H increases, more substrate atoms are pressed into the substrate, forming a density dislocation network to resist the downward pressure of the tip. Additionally, the indentation diameter D on both Cu and Cu/Gr substrates increases with increasing indentation depth H. Notably, at the same indentation depth, the indentation diameter D and dislocation density ρ of Cu/Gr substrates are higher than those of Cu substrates. For example, when the indentation depth is 2.2 nm, the graphene coatings increase the indentation diameter D of the Cu substrate from 4.6 nm to 8.2 nm, the dislocation density ρ from 0.065 nm⁻² to 0.104 nm⁻², and the normal force also increases by 294.12 nN. Lei et al. [25] also observed consistent indentation diameter and dislocation behavior in nanoindentation of graphene-coated aluminum substrates.

The indentation morphology at corresponding indentation depths H was analyzed in Figure 9. A transition radius R is formed at the indentation edge of the Cu/Gr substrate, which increases the indentation diameter and indented atom count, forming a denser dislocation network and enhancing the load-bearing capacity of the substrate. However, no transition radius R was observed at the indentation edge of the Cu substrate, and its indentation diameter was approximately the maximum contact diameter between the tip and substrate. A low-density dislocation network is formed inside the Cu substrate, which results in a weaker load-bearing capacity than the Cu/Gr substrate. Therefore, graphene modifies the indentation behavior of the substrate by the transition radius, effectively enhancing its load-bearing capacity. Additionally, the transition radius also reduces the scratch edge angle θ. For example, when the indentation depth H is 2.2 nm, the scratch edge angles θ of the Cu and Cu/Gr substrates are 82° and 73°, respectively, which is beneficial for the reduction in friction force, and this is discussed in Section 3.5.

3.5. Friction and Wear Characteristics in MD Simulation Under Constant-Force Loading Mode

To explore the effect of graphene coatings on the friction behavior of Cu substrates, constant-load scratch simulations were conducted on Cu and Cu/Gr substrates. Additionally, in order to study the influence of transition radius R and scratch edge angle θ on friction force, different tip radius r values were applied to adjust transition radius R and scratch edge angle θ. Figure 10a shows the scratch morphology under different substrates and tip radii. When the normal force F_z is 150 nN, no transition radius R is formed at the indentation edge on the Cu substrate, the scratch edge angle θ is 90°, and the indentation depth H is 1.8 nm. Moreover, a large number of substrate atoms accumulate in front of the tip, indicating that internal atoms are stripped to the substrate surface, exhibiting a plowing effect on the Cu substrate. However, a transition radius R is formed at the indentation edge on the Cu/Gr substrate, with a cutting edge angle θ of only 32° and an indentation depth H of only 1.0 nm. Cu/Gr exhibits shallower and smaller nanoindentations at the same normal force, which is consistent with the results of nanoindentation simulations. This indicates that graphene enhances the load-bearing capacity of the Cu substrate, effectively suppressing plastic deformation under identical normal forces. Furthermore, no substrate atoms accumulate in front of the tip during the scratch process; the graphene coatings suppress the upward deformation and weaken the plowing effect of the substrate.

Figure 10b shows the variation in the transition radius R and scratch edge angle θ with different tip radii r. As the tip radius increases, the transition radius R increases on the Cu/Gr substrate, while the scratch edge angle θ decreases. When the tip radius r is enlarged to 4.0 nm, the transition radius R increases to 5.3 nm, while the scratch edge angle θ decreases to 17°, which indicates that the increasing tip radius enlarges the transition radius R while reducing the scratch edge angle θ. Figure 10c shows the relationship between the friction force F_x and the scratch distance L. When the normal force F_z is 150 nN, the average friction force F_x on the Cu substrate is 75.72 nN, while the average friction force F_x on the Cu/Gr substrate is only 24.68 nN, which means that graphene reduces the friction force by 67.41%. This result is consistent with the AFM friction experiment. Additionally, the friction force on the Cu/Gr substrate decreases continuously as the tip radius r increases. For example, when the tip radius r increases to 4.0 nm, the friction force F_x on the Cu/Gr substrate is only 9.08 nN, which indicates that the lower scratch edge angle θ weakens the interlocking effect between the substrate and the tip, leading to a further reduction in friction force F_x.

3.6. Friction and Wear Characteristics in MD Simulation Under Constant-Depth Loading Mode

To investigate the underlying anti-friction mechanism of graphene coatings on Cu substrate, different indentation depths H were applied in scratch simulations on Cu and Cu/Gr substrates. Figure 11 shows the relationship between the friction force F_x and scratch distance L at the same indentation depth H. The friction force F_x increases with indentation depth H on both Cu and Cu/Gr substrates, which is consistent with the friction force trend reported by Ran et al. [46]. Additionally, at the same indentation depth H, the friction force F_x on the Cu/Gr substrate is higher than that on the Cu substrate. For example, when the indentation depth H is 2.5 nm, the friction force F_x on the Cu substrate is 75.83 nN, while it reaches 93.89 nN on the Cu/Gr substrate. This phenomenon appears to contradict the anti-friction properties of graphene, which is attributed to the constant-depth loading mode. At the same indentation depth H, the Cu/Gr substrate obtains a higher dislocation density ρ and normal force F_z, which also leads to a higher friction force F_x. This is discussed below.

Figure 12a shows the variation in the normal force F_z with scratch distance L at the same indentation depth H. At the same indentation depths H, the normal force F_z on the Cu/Gr substrate is higher than that on the Cu substrate. For example, when the indentation depth H is 2.5 nm, the normal force F_z on the Cu/Gr substrate is approximately 455.75 nN, while it is only approximately 92.31 nN on the Cu substrate, which is consistent with the results of Lei et al. [25]. Notably, the normal force F_z increases with indentation depth H on the Cu/Gr substrate, whereas it remains constant on the Cu substrate. This is because the plowing effect on the Cu substrate is obvious, with a large number of substrate atoms being pushed to the substrate surface rather than pressed into the substrate interior, which results in a lower dislocation density. Furthermore, as the indentation depth H increases, more atoms are displaced to the substrate surface by the tip, and the dislocations are released at the substrate surface. Therefore, with the increasing indentation depth H, the normal force F_z on the Cu substrate remains stable during the scratch process. In contrast, graphene coating suppresses the plowing effect on the Cu/Gr substrate, which prevents upward migration of substrate atoms and presses more atoms into the substrate interior, resulting in a higher dislocation density. In addition, as the indentation depth H increases, more atoms are pressed into the substrate interior due to the restriction of the plowing effect by graphene. Therefore, in the scratch process, the normal force F_z on the Cu/Gr substrate continuously increases with increasing indentation depth H. The restriction of the plowing effect by graphene can be seen in Figure 13.

Figure 12b shows the variation in the friction coefficient f with the indentation depth H and scratch distance L. The friction coefficient f reaches 0.82 on the Cu substrate at an indentation depth of 2.5 nm. Furthermore, the friction coefficient f increases with increasing indentation depth H, exhibiting poor stability on the Cu substrate. In contrast, on a Cu/Gr substrate, the friction coefficient f remains relatively stable during the scratch process, and there is no significant variation in the friction coefficient with increasing indentation depth H, remaining at 0.21 at an indentation depth of 2.5 nm. This is because the friction force F_x increases with increasing indentation depth H on the Cu substrate, while the normal force F_z remains stable, causing a sensitive friction coefficient f to the variation in indentation depth H. On the Cu/Gr substrate, the friction force F_x and normal force F_z both increase with increasing indentation depth H, and their increments counteract each other, resulting in a lower and more stable friction coefficient f for the Cu/Gr substrate. During the scratch process, the friction coefficient f of the Cu/Gr substrate remains lower than that of the Cu substrate, reducing the friction coefficient f of the Cu substrate by 74.39%. The graphene coatings demonstrate excellent friction stability and anti-friction properties, which are consistent with the friction experiment results in Section 3.3.

Figure 13 shows the substrate morphology during the scratch process. When the indentation depth H is 2.5 nm and the scratch distance L is 2.0 nm, the dislocation distribution of the Cu and Cu/Gr substrates is shown in Figure 13a. On the Cu substrate, the dislocation extension depth and length are 5.4 nm and 5.5 nm, respectively, and the dislocation density ρ is only 0.09 nm⁻². In contrast, the dislocation extension depth and length on the Cu/Gr substrate are 6.2 nm and 9.6 nm, respectively, with a dislocation density ρ of 0.22 nm⁻². The graphene coatings enhance the dislocation density of the substrate by 2.4 times, which explains the higher friction force and normal force of the Cu/Gr substrate at the same indentation depth. Figure 13b shows the displacement distribution of substrate atoms. Grooves are formed on the surfaces of the Cu and Cu/Gr substrates after scratching. The groove width of the Cu substrate is 4.6 nm, and a large number of substrate atoms pile up at the front and sides of the scratch groove, with an accumulation height of 1.9 nm. These results indicate that a large number of substrate atoms are stripped to the surface, and the Cu substrate exhibits a plowing effect. On the contrary, the groove width of the Cu/Gr substrate reaches up to 8.2 nm, with no accumulated atoms at the front and side of the scratch groove, and the maximum accumulation height is only 0.2 nm. This indicates that graphene coatings expand the indentation diameter and restrict the upward movement of substrate atoms, suppressing the plowing effect, further improving the load-bearing capacity of the substrate. Chen et al. [47] investigated the influence of tensile and compressive strain graphene coatings on the friction characteristics of NiCoCr entropic alloys, and they also reached similar conclusions. However, because of the constant-force loading mode employed in their MD simulations in their study, the bare NiCoCr entropic alloy exhibited deeper indentation depths and denser dislocation densities, while the graphene-coated NiCoCr entropic alloy showed shallower indentation depths and lower dislocation densities. Furthermore, they focused more on the dislocation density variations in the substrate, neglecting the microstructure variations such as transition radii and bearing diameters. Nevertheless, these two studies both indicate that graphene coatings suppress the plowing effect on the substrate surface.

3.7. Microscopic Substrate Reinforcement Effect and Anti-Friction Mechanism of Graphene Coatings

The microstructure of Cu and Cu/Gr substrates was observed by MD simulation. Figure 14a shows a schematic diagram of the scratch morphology to reveal the reinforcement effect of the graphene coatings on the substrate. When the pressing depth is the same, scratch grooves form on both Cu and Cu/Gr substrates. At this moment, the indentation diameter D₁ on the Cu substrate is approximately equal to the maximum contacting diameter between the tip and the substrate, and the indentation depth H₁ is approximately equal to the pressing depth of the tip. When the tip scratches the substrate surface, a large number of substrate atoms are stripped to the substrate surface, accumulating at the front and sides of the scratch groove. This phenomenon releases dislocations on the substrate surface, weakening the load-bearing capacity F_z1 of the substrate. However, when graphene is coated on the Cu substrate surface, a deeper indentation depth H₂ is obtained on the Cu/Gr substrate under the same pressing depth due to the additional layer of graphene atoms. The graphene is also subjected to tensile forces F_a and F_b from the tip, and a transition radius R is formed at the indentation edge, which increases the indentation diameter D₂. In addition, due to the covering effect of the graphene coatings, the original atoms moving upward are squeezed into the substrate, suppressing the plowing effect. Therefore, the graphene coatings increase the dislocation density of the substrate by enlarging indentations and suppressing plowing effects, which effectively enhances the load-bearing capacity of the substrate. Although the normal force F_z2 on the Cu/Gr substrate combines the normal forces of the substrate and graphene, single-layer graphene only provides a normal force of 120 nN at a 2.5 nm nanoindentation [48]. Therefore, the microstructure regulation of the substrate by the graphene coating is the key factor in enhancing the load-bearing capacity of the Cu/Gr substrate.

Figure 14b shows the schematic diagram of friction. At the same normal force F_z, due to the plowing effect of the Cu substrate, a large number of substrate atoms accumulate at the tip front, increasing the scratch edge angle θ₁, which enhances the interlocking effect between the Cu substrate and the tip. Conversely, on the Cu/Gr substrate, graphene suppresses the plowing effect and forms a transition radius R at the indentation edge, reducing the scratch edge angle θ₂, which also weakens the interlocking effect between the Cu/Gr substrate and the tip. The friction force is expressed as follows:

$$F_x=F_z\times \tan \theta$$

(2)

where F_x and F_z are the friction force and normal force of the tip, respectively, and θ is the scratch edge angle. As shown in Formula (2), when the normal force is the same, a smaller scratch edge angle θ results in a lower friction force F_x on the tip. Therefore, the graphene coatings reduce the interlocking effect between the substrate and the tip by modifying the scratch morphology of the substrate, which further reduces the friction force of the tip.

4. Conclusions

In this study, the microstructural evolution and nanomechanical behavior of Cu and Cu/Gr were systematically investigated by AFM experiments and MD simulations, revealing the microscopic anti-friction mechanism of graphene. There was a particular focus on the microstructure regulation and load-bearing property modification of the substrate by the graphene coating. The conclusions are as follows:

(1) The graphene coating modifies the load-bearing properties of Cu/Gr by regulating its microstructure. A transition radius R is formed at the indentation edge on the Cu/Gr substrate, increasing the load-bearing diameter D, and leading to a higher dislocation density ρ in the substrate. Additionally, the graphene coatings inhibit the upward movement of substrate atoms, suppressing the plowing effect. More atoms are compressed into the substrate, forming a dense dislocation network. These two effects both strengthen the normal load-bearing capacity of the substrate.

(2) At constant-depth loading conditions, the friction force F_x increases on both Cu and Cu/Gr substrates as the indentation depth increases. Furthermore, the normal force F_z2 on the Cu/Gr substrate increases with indentation depth H due to suppression of the plowing effect, whereas the normal force F_z1 on the Cu substrate remains stable owing to an obvious plowing effect. This phenomenon results in a lower and more stable friction coefficient f₂ for the Cu/Gr substrate, while the Cu substrate exhibits a higher and fluctuating friction coefficient f₁.

(3) The graphene coating reduces the scratch edge angle θ₂ of the Cu/Gr substrate, weakens the interlocking effect between the substrate and probe, and decreases the friction force F_x2 at the same load conditions F_z. Furthermore, the tribological behavior of the graphene coatings exhibits staged characteristics: the graphene coating exhibits anti-friction and lubricating properties in its intact structure, whereas the friction force increased significantly in the wear state.