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Wear resistance limited by step edge failure: The rise and fall of graphene as an atomically-thin lubricating material Yizhou Qi, Jun Liu, Ji Zhang, Yalin Dong, and Qunyang Li ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b12916 • Publication Date (Web): 06 Dec 2016 Downloaded from http://pubs.acs.org on December 10, 2016

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ACS Applied Materials & Interfaces

Wear Resistance Limited by Step Edge Failure: The Rise and Fall of Graphene as an Atomically-Thin Lubricating Material Yizhou Qi1, Jun Liu2, Ji Zhang1, Yalin Dong2, Qunyang Li1,3* 1

AML, CNMM, Department of Engineering Mechanics, Tsinghua University, Beijing

100084, China 2

Department of Mechanical Engineering, University of Akron, Akron Ohio 44325, USA

3

State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China

* To whom correspondence should be addressed. Email: [email protected].

KEYWORDS: Graphene; friction; wear; failure; rupture; step edge

1

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ABSTRACT Owing to its intrinsically lubricious property, graphene has a high potential to be an atomically-thin solid lubricant for sliding interfaces. Despite its ultra-high breaking strength at the nanoscale, graphene often fails to maintain its integrity when subjected to macroscale tribological tests. To reveal the true wear characteristics of graphene, a nanoscale diamond tip was used to scratch monolayer graphene mechanically exfoliated to SiO2 substrates. Our experimental results show that while graphene exhibited extraordinary wear resistance in the interior region, it could be easily damaged at the step edge under a much lower normal load (~ 2 orders of magnitude smaller). Similar behavior with substantially reduced wear resistance at the edge was also observed for monoatomic graphene layer on graphite surface. Using molecular dynamics simulations, we attributed this markedly weak wear resistance at the step edge to two primary mechanisms: i.e. atom-by-atom adhesive wear and peel induced rupture. Our findings shed light on the paradox that graphene is nanoscopically strong yet macroscopically weak. As step edge is ubiquitous for two-dimensional materials at the macroscale, our study also provides a guiding direction for maximizing the mechanical and tribological performance of these atomically-thin materials.

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INTRODUCTION Friction and wear-related problems have been one of the major failure mechanisms for mechanical systems 1. With miniaturization of devices to micro- and nanoscales, the tribological issues are becoming even more prominent due to the unprecedentedly high surface to volume ratio 2. Although continuous efforts have been devoted to search new materials and strategies that can help reduce friction and wear

3-6

, reliable and effective

lubrication remains scientifically challenging especially at the nanoscale

7, 8

. Recently,

with the emergence of two-dimensional (2D) materials, lubricating interface with atomically thin film has been proposed to be a promising resolution 9. Among the 2D materials, graphene is believed to be an ideal candidate. As the 2D carrier of graphite, graphene preserves a superior lubrication property at the nanoscale even with its thickness down to a few atomic layers

10-12

. Graphene is also super-strong

with an extremely high breaking strength of 130 GPa as measured by atomic force microscopy (AFM)

13

. Recently, nano-indentation test and MD simulations

14, 15

suggest

that graphene can withstand a relatively high normal load when slid by an indenter. In addition to the remarkable mechanical properties, graphene, when coated on a substrate, can effectively protect the underlying surface from oxidation or other chemical degradation, which is beneficial for lubrication applications 16. Despite the nearly “perfect” properties exhibited at the nanoscale, the tribological performance of graphene at the macroscale is often less satisfactory or even disappointing. Although pure graphene can reduce the friction coefficient of the covering surfaces to a 3



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limited extent (typically down to 0.03~0.3)

17-19

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, they are easily worn out in the

macroscale tests. Similar short life span is reported when graphene is used in form of ethanol or aqueous solution: the lubrication effect can only be sustained by continuously replenishing graphene 20. Besides the issue of wear, recent experiments also show that the lubrication performance of graphene is often very sensitive to environment. The lubricous state can easily break down due to changes in surrounding gas species or humidity 9, 21-23. The sharp disparity between the outstanding mechanical properties of graphene at the nanoscale and the poor tribological performance at the macroscale is scientifically puzzling and strongly invites a systematic interrogation. To better understand the mechanical properties of graphene and reveal the mechanisms that dictate this scale dependent tribological behavior, we performed a series of AFM scratch tests to characterize the wear resistance of graphene exfoliated on a SiO2 substrate. A substantially lower wear resistance was found when the tip slid over the step edge of a monolayer graphene sheet compared to that obtained within the interior region. Assisted with molecular dynamics simulations, we attributed the unexpectedly weak wear resistance to two primary mechanisms: i.e. atom-by-atom adhesive wear and peel induced rupture.

RESULTS AND DISCUSSION Graphene samples were prepared by mechanical exfoliation and their friction and anti-wear properties were examined by sliding and scratching them with silicon or 4


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diamond-like-carbon (DLC) coated silicon AFM tips (see Methods for details). Figure 1a shows an AFM lateral force (friction) image of a typical graphene flake (the corresponding optical image can be found in Figure S1). As implied by the high contrast in the lateral force image, covering the SiO2 substrate with few-layered graphene could substantially reduce surface friction. Particularly, the monolayer graphene could reduce friction ~25 times compared to the bare SiO2 (see inset of Figure 1a), which was qualitatively consistent with previous reports

10, 12, 14

. This result indicates that the

lubrication performance of graphene/graphite is likely an intrinsic property of sp2-bonded planar carbon atoms other than originating from slipperiness in adjacent graphene layers. 21, 24

5



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Figure 1. Results of scratch tests in the interior of monolayer graphene. (a) AFM lateral force image of a graphene sheet on SiO2/Si substrate. Bright color represents lower friction. Inset is a friction loop taken from the black line. The monolayer region is denoted as ML in the image and the AFM scan size is 50 µm 50 µm. (b) Friction variation on monolayer graphene under a normal load of 1726 nN during the scratch test. The friction coefficient is around 0.03. The inset shows a schematic of the scratch test. (c) Topographic and lateral force images after the test and the dash-dot squares mark the area where the scratch test was carried out. The squares are slightly enlarged to better show the boundary. A sink-in square is obvious in the topographic image and there is no distinct difference in the lateral force image between the inside and outside regions. (d) Schematics showing the deformation configurations before and after the scratch test. (e) Friction variations measured on a monolayer graphene sample with higher normal loads of 4159 nN, 6655 nN and 9150 nN respectively. Friction coefficients are typically around 0.01.

To examine the wear resistance of graphene, scratch tests were performed by repeatedly scanning the graphene samples with diamond-like-carbon (DLC) coated tips under high normal loads. Figure 1b shows friction variation as a function of scan cycles for a typical scratch test, where a squared region (1µm1µm) of monolayer graphene 6


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was scratched by a DLC tip under a normal load of 1726 nN. During the 512-line scratch test, friction force remained at a steady value near 50 nN giving a corresponding friction coefficient of 0.03. The scratched region was subsequently imaged with a larger scan size (5µm5µm) by the same DLC tip under a reduced normal load (43 nN). As shown by the zoom-out topographic image in Figure 1c, there existed an apparent sink-in region (averaged depth of 2 nm, see Figure S2) at the scratched region. Hypothetically, the formation of this crater could be due to wear of the graphene layer or plastic deformation of the SiO2 substrate, or both. However, we believe the graphene within the scratched region was likely intact, because the measured friction stayed rather low and stable throughout the scratch test. If graphene was broken during the scratch test, friction would increase abruptly at the onset of graphene damage due to exposure of the underlying SiO2 substrate, as demonstrated in Figure S3. The integrity of graphene was further supported by the fact that friction within the crater region was indistinguishable from that of the outside region, as shown by the lateral force image in Figure 1c. Considering the normal load of 1726 nN and the nominal radius of 100 nm of the DLC tip, the contact pressure due to the external load alone was estimated to be as high as 5.39 GPa from the Hertzian model 25. Although this level of stress might not be high enough to break graphene, it was large enough to cause plastic deformation of the amorphous SiO2 substrate

26

. As

schematically depicted in Figure 1d, our experimental results confirm that the monolayer graphene possesses a super high load carrying capacity, which is beyond the yielding stress of silica substrate. 7



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To further explore the robustness of graphene, we conducted a set of more aggressive scratch tests by scanning back-and-forth along a single line for a prolonged period (4096 cycles). These experiments were carried out at different locations on a sheet of monolayer graphene and the normal load was increased gradually (from 4159 nN to 9150 nN) until just before graphene failure. As shown in Figure 1e, variations of friction in three scratch tests all exhibited a similar trend, i.e., friction was slightly high at the beginning, and it then decreased rapidly in a few hundred cycles and became stabilized at a steady level. The initial friction evolution is likely due to progressive plastic deformation of the substrate and/or gradual removal of surface contaminants

27, 28

. Despite the high normal

loads (up to 9150 nN), friction coefficient on monolayer graphene in all three tests remained stable at a very low value (typically around 0.01) for thousands of scratch cycles without any sign of damage (see Figure S4). We have to note that graphene could still be impaired if the normal load was increased to a threshold value. It is noted that the critical normal load sensitively depended on the individual DLC tip that was used in our experiments. We attributed this variation of critical load primarily to the difference in radii of the DLC tips (see Figure S5 for more discussion). Because of the dependence of critical load on the tip radius, it is important to keep in mind that a same tip has to be used when quantitatively comparing the load carrying capacity of graphene. Although the exact critical load could not be determined unambiguously, our experiments clearly demonstrate that graphene, a monolayer of carbon atoms, indeed has an exceptional load carrying capacity far above the yielding point of the silica substrate. 8


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Our experimental results so far are qualitatively consistent with previous observations at the nanoscale

14, 15, 29

; yet they still seem to contradict with the poor lubrication

performance of graphene at the macroscale. We noticed that, in microscale frictional tests, the sliding distance was typically at the order of millimeter or above. The slider would inevitably slide across the step edges of single crystalline graphene. In order to get a comprehensive understanding of the wear resistance of graphene, we performed scratch tests by scanning across the step edge of a monolayer graphene flake under various normal loads.

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Figure 2. Results of scratch tests across the step edge of monolayer graphene. (a, b) Lateral force images of an edge of a graphene sheet before and after the scratch tests. White arrows indicate the locations where scratching was performed and the values above were the corresponding normal loads. (c) Schematics showing the configurations of graphene before and after the scratch test. (d) Lateral force image taken during the one-line scratch test across the step edge under normal load of 400 nN shown in (b). (e) Two friction traces extracted from (d) at the 3rd cycle and 141st cycle as indicated by the two dashed lines.

Figure 2a and b show the lateral force images of a graphene step edge before and after a series of scratch tests. One could clearly see that noticeable damage started to occur even when the normal load was as low as 160 nN. This normal load threshold was about 10


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60 times smaller compared with the load carrying capacity of 9597 nN when the same graphene flake was tested in the interior region using the same DLC tip (see Figure S6). The substantial reduction in wear resistance at the step edge of graphene was very reproducible for multiple graphene samples we tested (see Figure S7). It is worth mentioning that for each set of comparative experiments, we performed scratch test in the interior region first, then across the step edge, and finally back to the interior region again. By doing this, the possibility that the drastically different load carrying capacity between the interior and the step edge caused by tip changes during friction tests could be excluded. Careful examination on the after-test images suggests that the failure mode of graphene could be either adhesive wear likely via atom-by-atom removal

30-32

or peel induced

folding and rupturing as schematically depicted in Figure 2c and Figure S8. The peel-induced fold was recently observed during AFM manipulation

33

. To reveal the

detailed failure process, we recorded the lateral force evolution during the scratch test under 400 nN normal load, as shown in Figure 2d. Before graphene was worn, there was a clear friction contrast between the graphene region and the SiO2 region (see the lateral force trace at the 3rd cycle in Figure 2e). However, after graphene was worn, friction on both regions became similar in magnitude (see the lateral force trace at the 141st cycle in Figure 2e). As indicated by Figure 2d, friction of the graphene region barely changed initially, and at around the 72nd cycle, it increased instantaneously and then quickly evolved to a higher value close to that of the silica surface. This evolution behavior 11



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suggests that the observed wear behavior was an accumulative process and, once the process was initiated, it progressed very fast.

Figure 3. Comparative scratch tests of monolayer graphene on graphite. (a) Friction variation during an interior scratch test under a normal load of 15207 nN. Insets are the topographic images before and after the scratch test. There wasn’t any difference within the scratched location indicated by the white arrows in the topographic images before and after the test. The friction coefficient was around 0.004. (b) Topographic image of graphite after multiple scratch tests across the step edge; White arrows indicate the locations where one-line scratch tests were performed and the values above were the corresponding normal loads. Wear of graphene could be clearly observed when normal load was beyond 24 nN. (c) Topographic image taken during the one-line scratch test across the step edge under normal load of 290 nN shown in (b). (d) Height profiles extracted at the 78th, 139th and 196th cycles as indicated by the dashed lines in (c), showing evolution of the wear process.

The above experimental results have shown that the step edge of graphene is very 12


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fragile during contact sliding, which can be the key mechanism that limits the overall wear resistance of graphene. In order to check whether this behavior is universal and not specific to the particular substrate material we used, we carried out similar comparative tests for monolayer graphene on freshly cleaved graphite surface. As shown in Figure 3a, friction during the scratch test performed in the interior region of graphene remained low (µ=0.004) and stable even at very high normal load (up to 15207 nN). The before- and after-test morphologies of the scratched region confirmed that graphene was intact. However, scratch tests across the step edge using the same DLC tip again demonstrated that the monolayer graphene could be easily worn when the normal load was as low as 24 nN, as shown in Figure 3b. This sharp contrast in load carrying capacity confirmed that step edge was indeed a weak spot for graphene despite its ultra-strong interior strength. We also monitored the height evolution of the step edge during the scratch test under the load of 290 nN. As is evident in Figure 3c and d, for the first 110 scratch cycles, the monoatomic step edge seemed to be undamaged and its location was essentially stationary. Starting from the 111th scratch cycle, the step was suddenly knocked down and its location was pushed rightward for ~200 nm within 10 cycles. After the first knock-down, the new step survived for another 21 scratch cycles before it was completely worn out at about the 165th cycle. The characteristics of the wear process for graphene on graphite were qualitatively similar to those for graphene on SiO2. Although the load carrying capacity of graphene when slid in the interior region has been studied by Molecular Dynamics (MD) simulations 14, the wear characteristics across 13



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the step edge have not been systematically explored. Since the edge of graphene is relatively active with high formation energy on the order of ~10 eV/nm

34

, it is possible

that strong interactions may occur between the sliding tip and the atoms along the edge 35, 36

. To provide more atomic-level insights, we carried out comparative MD simulations by

sliding a nanoscale diamond tip in the interior of graphene and across the step edge (see Methods and more in Figure S9). In the simulations, the Lenard-Jones potential (bond formation forbidden) and the reactive empirical bond order (REBO) potential 37 (bond formation allowed) were used to simulate the non-reactive and reactive interactions between tip and graphene, respectively. Because the experiments were performed in ambient conditions, the carbon atoms on the surface of the tip were fully passivated and at the step edge were partially terminated by hydrogen when reactive interaction was used 38.

14


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Figure 4. MD simulations of sliding and scratching in the interior region and across the step edge of graphene. (a) Breaking due to in-plane tension limits the ultimate load graphene can withstand when scratched in the interior region if bond formation is prohibited between tip and graphene. (b) Adhesive wear becomes the dominant failure mode of graphene when scratched in the interior region if bond formation is allowed between tip and graphene. (c) Two primary damage mechanisms occurring at the step edge: adhesive wear via atom-by-atom removal and peel induced rupture. (d) Typical critical normal loads required to initiate graphene damage for different scenarios.

When bond formation between the tip and graphene was prohibited, which was the assumption of most previous simulations

14, 39-41

, graphene could withstand a very high

normal load (2500~3000 nN) when the tip slid in the interior region as depicted by the scenario Interior-1 of Figure 4a. In this case, our simulations revealed that, if the normal load kept increasing, graphene would eventually break due to the in-plane stretching (Figure S10). Therefore, the critical load carrying capacity for this scenario is essentially limited by the intrinsic strength of graphene, as previously discussed 14. 15



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When bond formation was allowed between the tip and graphene, the load carrying capacity of graphene reduced significantly though the silica substrate could still have significant plastic deformation before graphene failed. With an external normal load of 150 nN, graphene remained intact after several cycles of scratching despite the plastic deformation in the SiO2 substrate. However, when the normal load exceeds 200 nN, C-C bond formation occurred between the tip and graphene and the bonded interface was torn apart upon subsequent sliding, as shown in scenario Interior-2 in Figure 4b. The failure mechanism of adhesive wear is distinctively different from scenario Interior-1. In this case, the load carrying capacity is dictated by the critical normal load that induces bond formation between the tip and graphene (see Figure S11 for more discussions). In contrast to the interior cases, scratching across the step edge easily led to large deformation and damage of graphene, even under substantially smaller normal loads. As shown in the lower right panel of Figure 4c, after one scratch cycle at 5 nN normal load, some carbon atoms at the step edge of graphene have been removed by the sliding tip. Because the carbon atoms along the step edge contained dangling bonds, the tip-graphene bond formation could occur at relatively low loads (see Figure S12). In comparison, when there are no dangling bonds at the edge of the graphene, the adhesive wear can be significantly suppressed (see Figure S13). Shearing of the strong C-C covalent bonds formed between the tip and the edge of graphene would cause removal of graphene atoms leading to adhesive wear. The simulation results confirm our early hypothesis that the adhesive wear is via the atom-by-atom removal fashion

30-32

. Further simulations also 16


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suggested that the newly exposed carbon atoms within the worn region might facilitate bond formation for subsequent scratch tests leading to more severe wear (see Figure S14). This is also qualitatively consistent with our experimental observation that during reciprocal sliding damage process was initially gradual and the damage zone was relatively local within the sliding track, and then became accelerated after accumulating certain number of sliding cycles at the later stage, as shown in Figure 2d, e and Figure 3c, d. In addition to the adhesive wear, we also noticed that the graphene sheet was folded up appreciably when the normal load increased to a relatively high level (50 nN in our case), as shown in the lower left panel of Figure 4c. The fold-up configuration could propagate laterally from the contact region to certain distance depending on the competition among the graphene-substrate adhesion, the tip-graphene adhesion and the intrinsic tearing strength of graphene (see Figure S15). However, if there were any pre-existing defects in graphene along the step edge, then during the fold-up process, stress concentration would occur at those defects resulting in local peel-induced rupture of graphene (see Figure S16). Recently, it was reported that the folded graphene could even tear itself via thermally activated process if the substrate adhesion is relatively weak 42. However, when there is much stronger interfacial strength between graphene and substrate, our simulation suggests that both peeling and folding of graphene sheet from substrate are suppressed (see Figure S17). Regardless of the detailed failure mechanisms, our simulations suggest that the load 17



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carrying capacity of graphene when being slid across the step edge is largely determined by the critical load that induces bond formation between the tip and graphene edge. The active carbon atoms along the step edge can substantially lower the energy barrier for bond formation. Moreover, the fold-up motion and associated peel induced rupture at the edge of graphene can further expedite the wear process especially when graphene is loosely adhered to substrates. Therefore, passivating the edge of graphene and laying it on a more adhesive substrate may effectively suppress wear at the edge leading to substantial increased load carrying capacity.

CONCLUSIONS In conclusion, wear characteristics of graphene were systematically studied using AFM scratch tests. For the first time, our experiments showed that, although graphene was extraordinarily strong in the interior region, it was very fragile at the step edge. Compared with the interior case, the load carrying capacity of graphene when scratched across the step edge could be two orders of magnitude lower. Assisted by atomistic simulations, we identified distinct physical mechanisms underlying the drastically different wear behavior. The substantially weaker strength at the step edge is attributed to the easy bond formation between the tip and the edge of graphene as well as the rich failure modes, i.e. adhesive wear and peel-induced rupture. Because step edges are ubiquitous in macroscale samples, our findings successfully resolve the paradox that graphene is nanoscopically strong yet macroscopically weak. More importantly, the 18


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mechanisms revealed in our study also help provide general strategies for maximizing the tribological performance of graphene and other two-dimensional materials.

METHODS Experimental Measurements: Graphene sheets separated from Kish-graphite were deposited onto a Si substrate with a 300 nm SiO2 layer by Mechanical Exfoliation (ME) method

43

. The typical root-mean-square roughness of the bare SiO2 substrate and the

monolayer graphene covered surface are 0.55 nm and 0.45 nm respectively, calculated from 1µm × 1µm topographic images. The thickness of the graphene samples was first identified with AFM (Ntegra, NT-MDT Inc.) and further confirmed with Raman spectroscopy (Horiba HR800 with a laser wavelength of 514 nm). For initial identification of graphene samples (e.g. Figure 1a), silicon probes (MicroMasch, CSC37/Al BS, Cantilever B) were used. The normal spring constants of silicon probes are typically around 0.3 N/m, calibrated with Sader’s method 44, and the lateral force constants were calibrated using a diamagnetic lateral force calibrator 45. The friction and scratch tests were conducted in ambient conditions (temperature 20 ºC to 25 ºC, relative humidity 40% to 60%) using diamond-like-carbon (DLC) coated AFM probes (NT-MDT, DCP20). The normal spring constants of these DLC probes cantilevers are typically around 48 N/m, as calibrated via the reference cantilever method

46

. The lateral force

constants were calibrated again using a diamagnetic lateral force calibrator

45

. The

nominal radius of the DLC probe tip is 100 nm as provided by the manufacturer. We also 19



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inspected the tip shapes by scanning electron microscopy (Quanta FEG 450). Scratch tests were performed by scratching the graphene samples surface within a square region or repeatedly over a single line (one-line mode). The scratch size/length was 1 µm and the scan speed was 2 µm/sec for 512-line tests or 4 µm/sec for 4096-line tests. MD Simulation: A schematic of MD simulation setup is presented in Figure S9. In the model, a hemispherical diamond tip apex with a radius of 3 nm was used to slide against a monolayer graphene supported on (111) surface of SiO2 (α-quartz). The oxygen and silicon atoms in the bottommost layer of α-quartz were fixed. Frictional sliding both in the interior region and across the step edge were simulated. For the step edge sliding case, the size of the graphene layer was 17.2 nm × 39.8 nm in x- (sliding) and y- directions. The dimension of the α-quartz substrate was 24.5 nm × 40.7 nm × 3.2 nm in the x, y and z (out of plane) directions. For the interior sliding case, the size of graphene was 15.9 nm × 13.0 nm in the x, and y directions, respectively. To avoid the collective motion of the whole graphene layer, the atoms at the side boundaries (boundaries perpendicular to the free step edge) were fixed along the x and y directions but free to move along z direction. The surface of the tip as well as the graphene edge were passivated using hydrogen atoms through C-H bonding. In our simulations, the tip surface was fully passivated by hydrogen, while only 80% of the carbon atoms along the graphene step edge were passivated. The atoms in the topmost six layers of the tip were treated as rigid and subjected to an external normal force along the z direction 47. The rigid portion of the tip was linearly coupled to a virtual atom, which moved at a constant speed of 10 m/s along 20


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the x direction. The linear spring with a stiffness of 64 N/m was used to mimic the compliance associated with the AFM cantilever. Periodic boundary conditions were imposed in the x- and y- directions, while free boundary conditions were used in the z direction. A canonical (NVT) ensemble was applied to the free atoms to maintain a target temperature of 300 K. The 2nd-generation REBO potential was used to describe the inter-atomic interactions (C-C and C-H) within tip, as well as graphene 37. The interactions (Si-Si, Si-O and O-O) within the α-quartz substrate were modeled using Tersoff potential

48

whose parameters

were taken from Munetoh et al. 49. In the non-reactive case (bond formation not allowed), we adopted the 12-6 Lennard-Jones (LJ) potential to describe the interactions among tip, graphene and silica substrate. The LJ parameters for C-O, C-Si, H-O and H-Si were derived based on the Universal Force Field (UFF) model 50 and Lorentz-Berthelot mixing rules 51, resulting in the following parameters: εC-O = 3.442 meV, εC-Si = 8.909 meV, εH-O = 2.2 meV, εH-Si = 5.8 meV, σC-O = 3.001 Å, σC-Si = 3.326 Å, σH-O = 3.193 Å and σH-Si = 3.5905 Å. The work of adhesion between the graphene layer and the silica substrate based on these LJ parameters is 0.0933 J/m2 which lies in the lower limit of experimental data reported in literature (0.096~0.45 J/m2)

52-54

. In the reactive case (bond formation

allowed), except for the interaction between tip and graphene that was described by the 2nd-generation REBO potential, other interactions remained the same.

ASSOCIATED CONTENT 21



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Supporting Information The Supporting Information is available free of charge on the ACS Publications website at http://pubs.acs.org: Optical and Raman characterization of graphene, more experimental details and results, more simulation details and results (PDF)

AUTHOR INFORMATION Corresponding Author ‡E-mail: [email protected] ORCID Qunyang Li: 0000-0002-6865-3863 Author Contributions Y.Q. performed experiments and obtained the experimental data, and analyzed the data with input from all other authors. J.Z. prepared some of the graphene samples. J.L. performed all simulations. Y.D. supervised the simulation work and Q.L. supervised the experimental work. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS We thank Prof. Xi-Qiao Feng for his helpful and critical comments on our work. Q.L., 22


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Y.Q. and J.Z. gratefully acknowledge the support from the National Natural Science Foundation of China (11272177, 11422218 and 11432008), the National Basic Research Program of China (2013CB933003, 2013CB934201 and 2015CB351903), the Cyrus Tang Foundation (Grant No. 202003), the Tsinghua University Initiative Scientific Research Program (2014Z01007) and the Initiative Program of State Key Laboratory of Tribology (SKLT2015D01). Y.D. and J.L. would like to acknowledge the support from the startup fund of the University of Akron. The simulation work was supported in part by an allocation of computing time from the Ohio Supercomputer Center.

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Wear Resistance Limited by Step Edge Failure - ACS Publications

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