Superlubricity Enabled by Pressure-Induced Friction Collapse - The

Letter Cite This: J. Phys. Chem. Lett. 2018, 9, 2554−2559

pubs.acs.org/JPCL

Superlubricity Enabled by Pressure-Induced Friction Collapse Junhui Sun,†,‡,⊥,#,▽ Yanning Zhang,∥ Zhibin Lu,*,† Qunyang Li,*,§ Qunji Xue,†,‡ Shiyu Du,⊥ Jibin Pu,‡ and Liping Wang*,†,‡ †

State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou 730000, China ‡ Key Laboratory of Marine Materials and Related Technologies, Zhejiang Key Laboratory of Marine Materials and Protective Technologies, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China § Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China ∥ School of Energy Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China ⊥ Engineering Laboratory of Specialty Fibers and Nuclear Energy Materials, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China # University of Chinese Academy of Sciences, Beijing 100049, China ▽ School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China S Supporting Information *

ABSTRACT: From daily intuitions to sophisticated atomic-scale experiments, friction is usually found to increase with normal load. Using first-principle calculations, here we show that the sliding friction of a graphene/graphene system can decrease with increasing normal load and collapse to nearly zero at a critical point. The unusual collapse of friction is attributed to an abnormal transition of the sliding potential energy surface from corrugated, to substantially flattened, and eventually to counter-corrugated states. The energy dissipation during the mutual sliding is thus suppressed sufficiently under the critical pressure. The friction collapse behavior is reproducible for other sliding systems, such as Xe/Cu, Pd/graphite, and MoS2/MoS2, suggesting its universality. The proposed mechanism for diminishing energy corrugation under critical normal load, added to the traditional structural lubricity, enriches our fundamental understanding about superlubricity and isostructural phase transitions and offers a novel means of achieving nearly frictionless sliding interfaces.

F

achieved when the interfacial pressure approaches critical threshold for pure graphene/graphene sliding system. The substantially reduced friction indicates vanishing of the potential corrugations between interacting atomic layers, which is attributed to quantum-mechanical-effects-induced energy crossings. Similar friction collapsing behavior is also revealed in other systems, for example, Xe/Cu, Pd/graphite, and MoS2/MoS2, which suggests a general and novel approach to realize superlubricity in sliding systems. As an unusual yet important surface/interface physical phenomenon, the behavior of pressure-induced friction collapse demonstrates the unique feature of nanoscale friction, which demonstrates its difference from the law of friction on the macroscopic scale. Pressure-Driven Flattening of Potential Corrugation in Sliding. To explore the frictional behavior of graphene/graphene mutual sliding system, we first calculate the sliding potential energy surface (PES) corrugation13 for various lateral configurations of the mutual surfaces at different perpendicular heights. Computational methods and the detailed high-

riction laws are of fundamental importance for understanding the sliding behavior in the fields of physics, engineering, geophysics, and biology.1−3 Our wisdom tells us that friction would increase with increasing normal load; however, a few counterintuitive examples have been recently reported. For example, friction experiments on chemically modified graphite showed that friction could unusually increase with decreasing load,4 resulting in an effectively negative coefficient of friction. A diversity of friction behavior was also observed in mutual sliding between graphene layers and polymer-coated silica surfaces.5,6 Despite distinct features shown on the nanoscale,2 friction still rises with increasing normal load7,8 if no extra physical processes or dissipations other than the sliding interfaces are involved.9 These studies3−10 enrich our understanding about the versatility of pressure-dependent friction. Interestingly, while the sliding friction may decrease with vertical pressure in the high load of repulsion regime,11 previous studies revealed that an attractioninduced friction collapse is also possible for the system.12 Despite the great efforts, the possible universal importance and the nature of the unusual friction collapse, which significantly deviate from the experience wisdom, remain yet unclear. In this work, using dispersion-corrected density functional calculations, an unusual pressure-driven friction collapse is © XXXX American Chemical Society

Received: March 22, 2018 Accepted: May 1, 2018 Published: May 1, 2018 2554

DOI: 10.1021/acs.jpclett.8b00877 J. Phys. Chem. Lett. 2018, 9, 2554−2559

Letter

The Journal of Physical Chemistry Letters

Figure 1. Pressure-driven flat and inversed PES corrugation for graphene/graphene. By decreasing interlayer separation, z, emulating infliction of external load, in principle, the corrugation of PES (meV/atom) becomes (a) corrugated (z = 2.7 Å, minima at H sites), (b) enhanced corrugated (z = 2.2 Å), (c) theoretically flat (zc1 = 1.825 Å), and (d) anticorrugated (z = 1.692 Å, minima at top sites). The lattice parameter of graphene a = 2.46 Å.

Figure 2. Load dependence of atomic-scale friction. (a) Normal pressure σN and (b) frictional shear strength τf as a function of graphene interlayer spacing z. (c) τf versus σN based on panels a and b. The black line refers to τf of corrugated PES, while the red line refers to τf of counter-corrugated PES in the repulsive region. The red arrow represents critical frictionless sliding in the high loading regime.

Figure S4a−c, giving similar features as those from PBE functional calculation (Figure S3). This clearly demonstrates that the general characteristics of the interfacial pressure-driven planarization of PES are not sensitive to the choice of the DFT functional. Pressure-Induced Friction Collapse. To evaluate how the atomic-scale friction evolves under the interfacial pressure, we discuss the pressure dependence of friction for the interfacial pressure in the compressive regime. The lateral force that has to be applied to move the upper surface could be estimated from the sliding potential along the minimum energy pathway, in which the potential corrugation is lower than others. Thus the key to accounting for friction about graphene/ graphene is the energy height between saddle and hollow sites in PES (Figure 1a). Following the method by Zhong and Tománek,22 we obtained the normal pressure and the averaged lateral friction from Fn = −dEb/dz and Ff = |ΔEb|/Δr based on the hollow site, where ΔEb and Δr are the energy barrier and the displacement along the minimum energy pathway between saddle and hollow sites, respectively. Then, divided by the studied cell area of atomic contact, A, we obtain the normal pressure, σN, and frictional shear stress, τf, namely, σN = Fn/A and τf = Ff/A. Although Ff (thereby τf) is obtained at fixed interlayer spacing (instead of fixed pressure), the dependence of friction on the interfacial pressure reveals the key features relevant to atomic-scale friction. The normal pressure and frictional shear results for graphene/graphene are shown in Figure 2a,b, respectively. The correlation between the normal pressure and lateral friction is shown in Figure 2c. As shown in Figure 2c for the bilayer sliding system, the lateral shear stress τf mainly increases with normal pressure for σN < 160 GPa, indicating the Amonton-like laws feature. Hence, this suggests that for moderate loading range the macroscopically observed proportional relationship between friction force and normal load seems to be extended to the nanoscale.8 However, the situation is completely altered when

symmetry structures (Figure S1) for interlayer sliding are shown in the Supporting Information. We show in Figure 1a−d the calculated the variation of the PES corrugation with the interlayer spacing z = 2.7, 2.2, 1.825, and 1.692 Å, corresponding to different levels of normal pressure. By decreasing the interlayer spacing, z, the PES initially becomes corrugated (Figure 1a, z = 2.7 Å) and the corrugation gradually enhances (Figure 1b, z = 2.2 Å). When the interlayer spacing z is decreased to zc = 1.825 Å, however, the PES abnormally becomes smooth, resulting in a nearly vanishing energy corrugation (Figure 1c). Further decrease in interlayer spacing will lead to an increase in the PES corrugation (but with a different phase distribution, i.e., inverse-corrugation) (Figure 1d, z = 1.692 Å). It is worth noting that the flattened PES signifies vanishing phonons dissipation for sliding along adjacent positions,14,15 leading to minimized friction under the critical pressures. The approach disclosed by the first-principle calculations sufficiently reduces the total dissipation,13−17 although it does not rule out frictional dissipation through other mechanisms.18−21 To better understand the evolution of the total energy with normal load, we calculate the variations of the binding energy Eb(z) with the interlayer spacing z for different stacking configurations and show them in Figure S3. Obviously, Figure S3 demonstrates the remarkable energy crossing between neighboring stacking sites at critical spacing zc ≈ 1.825 Å. This suggests that the corrugation feature of PES can be inversed when normal pressure goes across this point, which is consistent with the results shown in Figure 1. Consequently, a flattened potential corrugation along the minimum energy path with nearly frictionless sliding may appear under the critical interlayer distance (as proved later). We also perform additional functional calculations (PW91, PBESOL, and LDA) to reproduce the unusual pressure-driven flattening of PES (Figure 1) and the potential crossings in Figure S3 in the region of compressive stress. The calculated results are shown in 2555

DOI: 10.1021/acs.jpclett.8b00877 J. Phys. Chem. Lett. 2018, 9, 2554−2559

Letter

The Journal of Physical Chemistry Letters

Figure 3. Pressure-dependent redistribution of electronic density and the PDOS of compression-stabilized graphene/graphene stacking. Electron density differences and PDOS of (a,e) z = 2.7 Å, (b,f) z = 2.2 Å, (c,g) z = 1.825 Å, and (d,h) z = 1.692 Å, respectively. Red and blue represent electron accumulation and depletion within the range of ±0.01e/Å3, respectively. The yellow or black spheres indicate the layer of carbon atoms. The Fermi level is set at zero energy and marked by blue lines.

difference24 shown in Figure 3a−d, Δρ = ρbilayer − ρgraphene1 − ρgraphene2, obtained from electron densities of the bilayer and corresponding isolated monolayer, respectively. For convenience, we studied the pressure-induced charge feature of the bilayer for T and H sites. As shown in Figure 3a (z = 2.7 Å), the interlayer interaction induces charge depletion between the two layers.25 The higher the normal pressure, the more the charge polarization in the interacting electrons system of the bilayer (Figure 3b, z = 2.2 Å). In particular, Figure 3a shows that under moderate pressure of z = 2.7 Å, for top stacking, the charge accumulates around “on-top” carbon atoms and depletes at sixfold hollow core points. For hollow stacking, the electronic charge accumulates around “hollow” carbon atoms and depletes around “on-top” ones.24,25 Interestingly, under gradually increased interfacial pressure, the interlayer interaction induces the translation and the inversion of electronic density for the stacking sites. In contrast, with the load increasing to z = 2.2, 1.825, and 1.692 Å (Figure 3b−d), the electronic charges gradually laterally shift, and then inverse charge distributions appear. The contrast between z = 2.2 (Figure 3b) and z = 1.692 Å (Figure 3d) suggests that for top and hollow sites, with increased interfacial pressure, the charge distributions exhibit distinct behavior. The pressure-induced inversion of charge density indirectly indicates that the PES of the bilayer undergoes a transition from corrugation (Figure 1b, z = 2.2 Å) to almost flat at zc (Figure 1c, zc = 1.825 Å) and to countercorrugation (Figure 1d, z = 1.692 Å) with the interfacial pressure.

the pressure increases beyond 200 GPa, where lateral friction decreases and passes through a nearly zero value (red arrow) before it increases again (red lines), as shown in Figure 2c. In particular, the friction τf decreases to nearly zero (red arrow) with increasing the normal pressure σN (between 200−280 GPa), leading to friction decreasing with pressure in the highload regime. These results can be expected from the above pressure-induced inversion of PES corrugation (Figure 1) and the energy crossing (Figure S3) under the critical pressure of zc ≈ 1.825 Å. The pressure−friction trends observed suggest that friction on the atomic scale may be collapsed to nearly zero with increasing interfacial pressure to the critical value, which considerably departs from the classic Amonton’s laws. Detailed Analysis of the Pressure-Modif ied PES Corrugation for the Friction Collapse. The corrugation of sliding potential is a result of the interfacial energy variation due to the nonuniform charge density nature of the discrete atoms within the interfaces. To understand the mechanism underlying the pressure-induced flattening of the PES for friction collapse and the potential crossings in the of the near-surface region, we discuss the main role of electrostatic and dispersion interactions for the sliding systems within the regions. In the high-load regime, the electronic density is determined by the electrostatic interactions through Pauli repulsion.23 The negligible difference between the total energy (Figure S5a) and electrostatic energy (Figure S5b) illustrates that electrostatic interaction mainly determines the interlayer interactions of the bilayer in the high-load regime. Therefore, the interlayer bonding mechanism is further analyzed by the electron density 2556

DOI: 10.1021/acs.jpclett.8b00877 J. Phys. Chem. Lett. 2018, 9, 2554−2559

Letter

The Journal of Physical Chemistry Letters

GPa). As a result, the interfacial pressure-driven friction collapse for nearly zero friction emerges as interfacial pressures σN approach the critical pressure for corresponding sliding systems. Because the relatively low critical normal pressures are potentially achievable in experiments,33 future experiments are invited to validate the superlubric friction behavior predicted by our simulations. We now address the experimental feasibility of realizing the pressure-induced nearly frictionless sliding. The results may call for careful examination of the role of critical pressure in potential corrugation/friction. Specific experiments about atomic force microscopy (AFM) or quartz crystal microbalance (QCM) measurements may be performed. For the graphene/ graphene sliding system, a capped carbon nanotube tip could be used to probe the pressure-driven friction measurement on the graphene surface. To avoid the negative affection of wrinkling or deformation of graphene4,34,35 in front of the scanning tip, binding the film sample strongly to a rigid surface may be necessary. The role of wrinkling and buckling of graphite is discussed in detail in S4 of the Supporting Information. For the Xe/Cu sliding system,36 Xe-terminated tip could be used as the probe for AFM friction measurements of planar geometry of Cu(111), in which the atomic particles allow the AFM to resolve the atomic structures of the surface.37 The pressuredependent potential corrugation for friction36 should be studied with varying amplitudes of tip height. For the QCM study of sliding friction about the Xe/Cu sliding system,36 the normal force for Xe layer could be tuned by depositing/adsorbing Cu(111). Meanwhile, the pressure-induced friction collapse could be observed when using an atomic-scale Pd tip for friction experiments on graphite, avoiding obvious wrinkle. The principle of pressure-induced collapse of atomic-scale friction may be extended to understand the sliding of crystal surfaces under compression. Our calculations suggest that a pressure-induced interlayer slippage could take place around 30.1 GPa in 2H-MoS2 (Figure S13). The structural transition from initial 2Hc-MoS2 to final 2Ha-MoS2 is thus triggered. This prediction is in agreement with the recent experimental observations, where structural transition occurs almost completely at 28−30 GPa in 2H-MoS2 crystals.29,38 The observed transition could arise from the interfacial friction collapse in MoS2 compression, resulting in the interlayer sliding.29 The detailed discussions about the normal-pressureinduced interlayer sliding in MoS2 are given in S5 of the Supporting Information. Similar pressure-induced atomic-scale friction collapse of interlayer sliding has been indirectly observed in various systems (structures),29,30,39−42 triggering the electronic responses. The strain-induced translational or rotational slides in the interfaces of nanocrystals could result from the strain-driven evolutions of the potential energy landscape.30 The present result of the critical state of nearly zero sliding resistance, which results from the possible elimination of potential corrugation under critical pressure, may provide a new perspective on the term “superlubricity”. In addition to the well-known structural lubricity43 and the ultralow friction,44,45 the concept of superlubricity may be further enriched in terms of the interlayer interaction-induced superlubric state, thereby enabling a unique strategy for frictionless sliding. In summary, in contrast with the common wisdom that friction of a sliding interface increases with normal load, firstprinciple calculations suggest that the friction of a graphene/ graphene sliding system may decrease with increasing pressure

To gain further insight into the pressure-induced the collapse and inversion of PES corrugations (Figure 1) in the high-load regime, we examine the behavior of partial density of states (PDOS) for the pressure-driven structure instability (Figure S3) within the compressive region shown in Figure 3e−h. Under the moderate interfacial pressure of z = 2.7 Å shown in Figure 3e, PDOS of Top stacking shows more electrons around the Fermi level than the Hollow stacking, rendering Top stacking more energetic and unstable than Hollow stacking.26 When the interfacial pressure further increases to z = 2.2 Å, as shown in Figure 3f, the energy for T site and H site is enhanced with Hollow stacking still more stable than Top stacking. These are in agreement with the enhanced PES corrugation between T stacking and H stacking under the pressure of z = 2.2 Å in Figure 1b. In contrast, under the interfacial pressures above z = 2.2 Å, we find that under the pressure of z = 1.825 Å (Figure 3g) and z = 1.692 Å (Figure 3f) the Top stacking is more stable than Hollow stacking due to the enhanced electronic interaction around the Fermi level for Hollow stacking compared with Top stacking. Thus these results further prove that the interfacial pressure induced the collapse and inversion of PES (Figure 1a−d, respectively) and energy crossing (Figures S3 and S4) in the repulsive regime. Although the critical pressure needed to observe the effects in the high-pressure regime is rather large, we speculated that a decreased critical pressure may be possible through the growth of graphene on a metal or ceramic substrate owing to the graphene−substrate interaction.16,27,28 The substantial interaction between the substrates and graphene through hybridization of the electronic states and charge transfer could cause the reduction of the chemical interaction between the graphene layers.27,28 The relatively low critical pressure could thus be achieved. Generality of the Pressure-Induced Friction Collapse. Considering that the present pressure-induced friction collapse is an unusually interfacial phenomenon between interaction surfaces, we have wondered whether one can generate a similar friction collapse in other sliding systems, in view of the fact that the pressure-induced interlayer slipping29,30 has been known for a long time. To test this idea, the sliding systems of Xe/Cu and Pd/graphite are also calculated and are shown in the Supporting Information. The pressure-driven collapse of PES corrugation for Xe/Cu (critical separation zc ≈ 2.87 Å)11,12,31,32 and Pd/graphite (critical separation zc ≈ 2.82 Å) systems is shown in Figures S7 and S11, respectively. Consequently, the load-driven collapses of friction occur in correspondingly sliding systems, Xe/Cu (Figure 4a, critical pressure σc ≈ 7.5 GPa) and Pd/graphite (Figure 4b, critical pressure σc ≈ 3.1

Figure 4. Pressure-induced friction collapse for (a) Xe/Cu and (b) Pd/graphite sliding systems. The arrows represent the respective critical distances (pressures). 2557

DOI: 10.1021/acs.jpclett.8b00877 J. Phys. Chem. Lett. 2018, 9, 2554−2559

The Journal of Physical Chemistry Letters and even become nearly zero at a certain critical load. The nearly frictionless state originates from the pressure-driven transition of the potential energy surface, that is, from a corrugated state to a flattened state and to a counter-corrugated state. The energy dissipation underlying the sliding is thus sufficiently suppressed under the critical pressure. Similar behavior is also observed in sliding systems, such as Xe/Cu and Pd/graphite, suggesting its generality. The pressure-induced friction collapse may also account for the previously reported abnormal layer sliding for structural transition from 2Hc-MoS2 to 2Ha-MoS2 in high-pressure MoS2 experiments. Our proposed mechanism enriches the concept of superlubricity, which has a potential impact on a broad range of engineering applications.

■

■

ACKNOWLEDGMENTS

■

REFERENCES

We thank Virginio Bortolani and Yanqing Feng for useful discussions. This work was supported by National Key R&D Program of China (No. 2017YFB0702303), the National Natural Science Foundation of China (Nos. 51775535 and 11772169), and Key Program of the Chinese Academy of Sciences (No. QYZDY-SSW-JSC009).

(1) Vanossi, A.; Manini, N.; Urbakh, M.; Zapperi, S.; Tosatti, E. Colloquium: Modeling friction: From nanoscale to mesoscale. Rev. Mod. Phys. 2013, 85, 529−552. (2) Urbakh, M.; Klafter, J.; Gourdon, D.; Israelachvili, J. The nonlinear nature of friction. Nature 2004, 430, 525−528. (3) Gao, J.; Luedtke, W. D.; Gourdon, D.; Ruths, M.; Israelachvili, J. N.; Landman, U. Frictional forces and Amontons’ law: from the molecular to the macroscopic scale. J. Phys. Chem. B 2004, 108, 3410− 3425. (4) Deng, Z.; Smolyanitsky, A.; Li, Q.; Feng, X.-Q.; Cannara, R. J. Adhesion-dependent negative friction coefficient on chemically modified graphite at the nanoscale. Nat. Mater. 2012, 11, 1032−1037. (5) Liu, Z. The diversity of friction behavior between bi-layer graphenes. Nanotechnology 2014, 25, 075703−075709. (6) Thormann, E. Negative Friction Coefficients. Nat. Mater. 2013, 12, 468−468. (7) Luan, B.; Robbins, M. O. The Breakdown of Continuum Models for Mechanical Contacts. Nature 2005, 435, 929−932. (8) Mo, Y.; Turner, K. T.; Szlufarska, I. Friction laws at the nanoscale. Nature 2009, 457, 1116−1119. (9) Sun, X.-Y.; Qi, Y. Z.; Ouyang, W.; Feng, X.-Q.; Li, Q. Energy Corrugation in atomic-scale Friction on Graphite Revisited by Molecular Dynamics Simulations. Acta Mech. Sin. 2016, 32, 604−610. (10) Gao, L.; Ma, Y.; Liu, Y.; Song, A.; Ma, T.; Hu, Y.; Su, Y.; Qiao, L. Anomalous Frictional Behaviors of Ir and Au Tips Sliding on Graphene/Ni (111) Substrate: Density Functional Theory Calculations. J. Phys. Chem. C 2017, 121, 21397−21404. (11) Righi, M. C.; Ferrario, M. Pressure Induced Friction Collapse of Rare Gas Boundary Layers Sliding over Metal Surfaces. Phys. Rev. Lett. 2007, 99, 176101−176104. (12) Sun, J.; Zhang, Y.; Lu, Z.; Xue, Q.; Wang, L. Attraction Induced Frictionless Sliding of Rare Gas Monolayer on Metallic Surfaces: An Efficient Strategy for Superlubricity. Phys. Chem. Chem. Phys. 2017, 19, 11026−11031. (13) Cieplak, M.; Smith, E. D.; Robbins, M. O. Molecular Origins of Friction: The Force on Adsorbed Layers. Science 1994, 265, 1209− 1212. (14) Krim, J. Friction and Energy Dissipation Mechanisms in Adsorbed Molecules and Molecularly Thin Films. Adv. Phys. 2012, 61, 155−323. (15) Park, J. Y.; Salmeron, M. Fundamental Aspects of Energy Dissipation in Friction. Chem. Rev. 2014, 114, 677−711. (16) Cahangirov, S.; Ciraci, S.; Ö zçelik, V. O. Superlubricity Through Graphene Multilayers Between Ni(111) Surfaces. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 205428−205435. (17) Pierno, M.; Bruschi, L.; Fois, G.; Mistura, G.; Boragno, C.; de Mongeot, F. B.; Valbusa, U. Nanofriction of Neon Films on Superconducting Lead. Phys. Rev. Lett. 2010, 105, 016102−016105. (18) Park, J.; Ogletree, D. F.; Thiel, P. A.; Salmeron, M. Electronic Control of Friction in Silicon pn Junctions. Science 2006, 313, 186− 186. (19) Highland, M.; Krim, J. Superconductivity Dependent Friction of Water, Nitrogen, and Superheated He Films Adsorbed on Pb(111). Phys. Rev. Lett. 2006, 96, 226107−226110. (20) Kadau, D.; Hucht, A.; Wolf, D. E. Magnetic Friction in Ising Spin Systems. Phys. Rev. Lett. 2008, 101, 137205−137208. (21) Filleter, T.; McChesney, J. L.; Bostwick, A.; Rotenberg, E.; Emtsev, K. V.; Seyller, Th.; Horn, K.; Bennewitz, R.; et al. Friction and

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.8b00877. S1. Details of first-principle calculations for graphene/ graphene, Xe/Cu, Pd/graphite, and MoS2/MoS2 sliding systems. S2. Supplementary discussion for graphene/ graphene system. S3. Supplementary discussion for Xe/ Cu system. S4. Supplementary discussion for Pd/ Graphite sliding system. S5. Supplementary discussion for interlayer sliding in 2H-MoS2 under pressure. Figure S1. Calculated models of high-symmetry top (T), bridge (B), hollow (H), and saddle (S) sites for graphene/ graphene system. Figure S2. Binding energy Eb(z) as a function of interplanar distance z for graphene/graphene. Figure S3. Interplanar distance (stress) dependence of the structure stability for graphene/graphene system. Figure S4. Crossing of binding energy curves studied by various density functionals for graphene/graphene. Figure S5. Comparison of the total and electrostatic interaction for graphene/graphene. Figure S6. Sliding model for Xe/Cu sliding system. Figure S7. Sliding potential corrugation for Xe/Cu system along the minimum energy pathway in the region of compression. Figure S8. Interplanar distance dependence of the structure stability for Xe/Cu system. Figure S9. Normal pressure σN(z) and frictional shear strength τf(z) for Xe/ Cu systems. Figure S10. The atomic sliding model for Pd monolayer over graphite surface (Pd/graphite). Figure S11. Sliding potential corrugation for Pd/graphite system in the region of compressive stress. Figure S12. Calculated binding energy Eb(z) for Pd/graphite system. Figure S13. Pressure-induced modification of PES corrugations in MoS2 bilayer. (PDF)

■

Letter

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (Z.L.). *E-mail:[email protected] (Q.L.). *E-mail:[email protected] (L.W.). ORCID

Zhibin Lu: 0000-0003-3145-2934 Qunyang Li: 0000-0002-6865-3863 Shiyu Du: 0000-0001-6707-3915 Notes

The authors declare no competing financial interest. 2558

DOI: 10.1021/acs.jpclett.8b00877 J. Phys. Chem. Lett. 2018, 9, 2554−2559

Letter

The Journal of Physical Chemistry Letters Dissipation in Epitaxial Graphene Films. Phys. Rev. Lett. 2009, 102, 086102−086105. (22) Zhong, W.; Tománek, D. First-principles Theory of Atomicscale Friction. Phys. Rev. Lett. 1990, 64, 3054−3057. (23) Marom, N.; Bernstein, J.; Garel, J.; Tkatchenko, A.; Joselevich, E.; Kronik, L.; Hod, O. Stacking and Registry Effects in Layered Materials: The Case of Hexagonal Boron Nitride. Phys. Rev. Lett. 2010, 105, 046801−046804. (24) Charlier, J. C.; Gonze, X.; Michenaud, J. P. Graphite Interplanar Bonding: Electronic Delocalization and van der Waals Interaction. Europhys. Lett. 1994, 28, 403−408. (25) Reguzzoni, M.; Fasolino, A.; Molinari, E.; Righi, M. C. Potential Energy Surface for Graphene on Graphene: Ab initio Derivation, Analytical Description, and Microscopic Interpretation. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 245434−245440. (26) Shi, Y. J.; Du, Y. L.; Chen, G.; Chen, G. L. First Principle Study on Phase Stability and Electronic Structure of YCu. Phys. Lett. A 2007, 368, 495−498. (27) Grüneis, A.; Vyalikh, D. V. Tunable Hybridization Between Electronic States of Graphene and a Metal Surface. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 193401−193404. (28) Zhou, S. Y.; Gweon, G.-H.; Fedorov, A. V.; First, P. N.; de Heer, W. A.; Lee, D.-H.; Guinea, F.; Castro Neto, A. H.; Lanzara, A. Substrate-induced bandgap opening in epitaxial graphene. Nat. Mater. 2007, 6, 770−775. (29) Chi, Z. H.; Zhao, X.-M.; Zhang, H.; Goncharov, A. F.; Lobanov, S. S.; Kagayama, T.; Sakata, M.; Chen, X.-J.; et al. Pressure-induced Metallization of Molybdenum Disulfide. Phys. Rev. Lett. 2014, 113, 036802−036806. (30) Rondinelli, J. M.; Coh, S. Large Isosymmetric Reorientation of Oxygen Octahedra Rotation Axes in Epitaxially Strained Perovskites. Phys. Rev. Lett. 2011, 106, 235502−235505. (31) Zhang, Y. N.; Bortolani, V.; Mistura, G. Determination of Corrugation and Friction of Cu(111) Toward Adsorption and Motion of Ne and Xe. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 165414−165418. (32) Righi, M. C.; Ferrario, M. Potential Energy Surface for Rare Gases Adsorbed on Cu(111): Parameterization of the Gas/metal Interaction potential. J. Phys.: Condens. Matter 2007, 19, 305008− 305017. (33) Mate, C. M.; McClelland, G. M.; Erlandsson, R.; Chiang, S. Atomic-Scale Friction of a Tungsten Tip on a Graphite Surface. Phys. Rev. Lett. 1987, 59, 1942−1945. (34) Long, F.; Yasaei, P.; Yao, W.; Salehi-Khojin, A.; ShahbazianYassar, R. Anisotropic Friction of Wrinkled Graphene Grown by Chemical Vapor Deposition. ACS Appl. Mater. Interfaces 2017, 9, 20922−20927. (35) Reguzzoni, M.; Fasolino, A.; Molinari, E.; Righi, M. C. Friction by Shear Deformations in Multilayer Graphene. J. Phys. Chem. C 2012, 116, 21104−21108. (36) Coffey, T.; Krim, J. Impact of Substrate Corrugation on the Sliding Friction Levels of Adsorbed Films. Phys. Rev. Lett. 2005, 95, 07610−07613. (37) Hapala, P.; Kichin, G.; Wagner, C.; Tautz, F. S.; Temirov, R.; Jelínek, P. Mechanism of high-resolution STM/AFM imaging with functionalized tips. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90, 085421−085429. (38) Hromadová, L.; Martoňaḱ , R.; Tosatti, E. Structure Change, Layer Sliding, and Metallization in High-pressure MoS2. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 144105−144110. (39) Nayak, A. P.; Bhattacharyya, S.; Zhu, J.; Liu, J.; Wu, X.; Pandey, T.; Jin, C.; Singh, A. K.; Akinwande, D.; Lin, J.-F.; et al. PressureInduced Semiconducting to Metallic Transition in Multilayered Molybdenum Disulphide. Nat. Commun. 2014, 5, 3731−3739. (40) Ke, F.; Liu, C.; Gao, Y.; Zhang, J.; Tan, D.; et al. Interlayer-glidedriven isosymmetric phase transition in compressed In2Se3. Appl. Phys. Lett. 2014, 104, 212102−212105.

(41) Lu, X.-Z.; Rondinelli, J. M. Epitaxial-strain-induced Polar-tononpolar Transitions in Layered Oxides. Nat. Mater. 2016, 15, 951− 956. (42) Jang, H. W.; Felker, D. A.; Bark, C. W.; Wang, Y.; Niranjan, M. K.; et al. Metallic and Insulating Oxide Interfaces Controlled by Electronic Correlations. Science 2011, 331, 886−889. (43) Hirano, M.; Shinjo, K. Atomistic Locking and Friction. Phys. Rev. B: Condens. Matter Mater. Phys. 1990, 41, 11837−11851. (44) Socoliuc, A.; Bennewitz, R.; Gnecco, E.; Meyer, E. Transition from Stick-slip to Continuous Sliding in Atomic Friction: Entering a New Regime of Ultralow Friction. Phys. Rev. Lett. 2004, 92, 134301− 134304. (45) Medyanik, S. N.; Liu, W. K.; Sung, I. H.; Carpick, R. W. Predictions and Observations of Multiple Slip Modes in Atomic-scale Friction. Phys. Rev. Lett. 2006, 97, 136106−136109.

2559

DOI: 10.1021/acs.jpclett.8b00877 J. Phys. Chem. Lett. 2018, 9, 2554−2559