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Prediction of Nanoscale Friction for Two-Dimensional Materials Using a Machine Learning Approach

Abstract

Several two-dimensional (2D) materials such as graphene, molybdenum disulfide, or boron nitride are emerging as alternatives for lubrication additives to control friction and wear at the interface. On the other hand, the initiative to accelerate materials discovery through data-driven computational methods has identified numerous novel topologies and families of 2D materials that can potentially be designed as low-friction additives. Hence, generating a structure–property (friction) correlations for 2D material-based additives that present a large variation in atomic composition is the next big challenge. Herein, we present a machine learning (ML) method using the Bayesian modeling and transfer learning approach to predict the maximum energy barrier (MEB) of the potential surface energy (correlated to intrinsic friction) of ten different 2D materials that were previously unexplored for their tribological properties. The descriptors (or properties) required to train the ML model with high accuracy are identified by taking into account the established physical models for dissipation in 2D materials. As a result, a difference of less than 8% in MEB values as predicted via the ML model presented here and the PES profiles generated using molecular dynamics simulations, for a select few 2D materials, was obtained. The model also enabled the identification of material properties that present the highest sensitivity to the corrugated potential, hence enabling the development of design routes for the synthesis of 2D materials with optimal tribological properties.

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References

  1. Persson, B.N.: Sliding Friction: Physical Principles and Applications. Springer Science, New York (2013)

    Google Scholar 

  2. Cho, M.H., Ju, J., Kim, S.J., Jang, H.: Tribological properties of solid lubricants (graphite, Sb2S3, MoS2) for automotive brake friction materials. Wear 260, 855–860 (2006)

    CAS  Google Scholar 

  3. Savan, A., Pflüger, E., Voumard, P., Schröer, A., Simmonds, M.: Modern solid lubrication: recent developments and applications of MoS2. Lubr. Sci. 12, 185–203 (2000)

    CAS  Google Scholar 

  4. Berman, D., Erdemir, A., Sumant, A.V.: Approaches for achieving superlubricity in two-dimensional materials. ACS Nano 12, 2122–2137 (2018)

    CAS  Google Scholar 

  5. Kim, K.-S., Lee, H.-J., Lee, C., Lee, S.-K., Jang, H., Ahn, J.-H., Kim, J.-H., Lee, H.-J.: Chemical vapor deposition-grown graphene: the thinnest solid lubricant. ACS Nano 5, 5107–5114 (2011)

    CAS  Google Scholar 

  6. Rapoport, L., Bilik, Y., Feldman, Y., Homyonfer, M., Cohen, S., Tenne, R.: Hollow nanoparticles of WS 2 as potential solid-state lubricants. Nature 387, 791 (1997)

    CAS  Google Scholar 

  7. Xiao, H., Liu, S.: 2D nanomaterials as lubricant additive: a review. Mater. Des. 135, 319–332 (2017)

    CAS  Google Scholar 

  8. Berman, D., Erdemir, A., Sumant, A.V.: Graphene: a new emerging lubricant. Mater. Today 17, 31–42 (2014)

    CAS  Google Scholar 

  9. Song, H.-J., Li, N.: Frictional behavior of oxide graphene nanosheets as water-base lubricant additive. Appl. Phys. A 105, 827–832 (2011)

    CAS  Google Scholar 

  10. Zu, S.-Z., Han, B.-H.: Aqueous dispersion of graphene sheets stabilized by pluronic copolymers: formation of supramolecular hydrogel. J. Phys. Chem. C 113, 13651–13657 (2009)

    CAS  Google Scholar 

  11. Hilton, M.R., Bauer, R., Didziulis, S.V., Dugger, M.T., Keem, J.M., Scholhamer, J.: Structural and tribological studies of MoS2 solid lubricant films having tailored metal-multilayer nanostructures. Surf. Coat. Technol. 53, 13–23 (1992)

    CAS  Google Scholar 

  12. Lee, C., Wei, X., Kysar, J.W., Hone, J.: Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321, 385–388 (2008)

    CAS  Google Scholar 

  13. Liu, K., Yan, Q., Chen, M., Fan, W., Sun, Y., Suh, J., Fu, D., Lee, S., Zhou, J., Tongay, S.: Elastic properties of chemical-vapor-deposited monolayer MoS2, WS2, and their bilayer heterostructures. Nano Lett. 14, 5097–5103 (2014)

    CAS  Google Scholar 

  14. Balandin, A.A., Ghosh, S., Bao, W., Calizo, I., Teweldebrhan, D., Miao, F., Lau, C.N.: Superior thermal conductivity of single-layer graphene. Nano Lett. 8, 902–907 (2008)

    CAS  Google Scholar 

  15. Lee, C., Li, Q., Kalb, W., Liu, X.-Z., Berger, H., Carpick, R.W., Hone, J.: Frictional characteristics of atomically thin sheets. Science 328, 76–80 (2010)

    CAS  Google Scholar 

  16. Spear, J.C., Ewers, B.W., Batteas, J.D.: 2D-nanomaterials for controlling friction and wear at interfaces. Nano Today 10, 301–314 (2015)

    CAS  Google Scholar 

  17. Liu, L., Zhou, M., Jin, L., Li, L., Mo, Y., Su, G., Li, X., Zhu, H., Tian, Y.: Recent advances in friction and lubrication of graphene and other 2D materials: Mechanisms and applications. Friction 7, 199–216 (2019)

    Google Scholar 

  18. 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 86, 245434 (2012)

    Google Scholar 

  19. Liang, T., Sawyer, W.G., Perry, S.S., Sinnott, S.B., Phillpot, S.R.: First-principles determination of static potential energy surfaces for atomic friction in Mo S 2 and Mo O 3. Phys. Rev. B 77, 104105 (2008)

    Google Scholar 

  20. Wang, L.-F., Ma, T.-B., Hu, Y.-Z., Wang, H., Shao, T.-M.: Ab initio study of the friction mechanism of fluorographene and graphane. J. Phys. Chem. C 117, 12520–12525 (2013)

    CAS  Google Scholar 

  21. Shi, R., Gao, L., Lu, H., Li, Q., Ma, T.-B., Guo, H., Du, S., Feng, X.-Q., Zhang, S., Liu, Y.: Moiré superlattice-level stick-slip instability originated from geometrically corrugated graphene on a strongly interacting substrate. 2D Mater. 4, 025079 (2017)

    Google Scholar 

  22. Wang, L.-F., Ma, T.-B., Hu, Y.-Z., Zheng, Q., Wang, H., Luo, J.: Superlubricity of two-dimensional fluorographene/MoS2 heterostructure: a first-principles study. Nanotechnology 25, 385701 (2014)

    Google Scholar 

  23. Levita, G., Molinari, E., Polcar, T., Righi, M.C.: First-principles comparative study on the interlayer adhesion and shear strength of transition-metal dichalcogenides and graphene. Phys. Rev. B 92, 085434 (2015)

    Google Scholar 

  24. Dong, Y.: Effects of substrate roughness and electron–phonon coupling on thickness-dependent friction of graphene. J. Phys. D 47, 055305 (2014)

    Google Scholar 

  25. Ding, Z., Pei, Q.-X., Jiang, J.-W., Huang, W., Zhang, Y.-W.: Interfacial thermal conductance in graphene/MoS2 heterostructures. Carbon 96, 888–896 (2016)

    CAS  Google Scholar 

  26. Müser, M.H., Wenning, L., Robbins, M.O.: Simple microscopic theory of Amontons's laws for static friction. Phys. Rev. Lett. 86, 1295 (2001)

    Google Scholar 

  27. Müser, M.H.: Nature of mechanical instabilities and their effect on kinetic friction. Phys. Rev. Lett. 89, 224301 (2002)

    Google Scholar 

  28. Guo, Y., Qiu, J., Guo, W.: Reduction of interfacial friction in commensurate graphene/h-BN heterostructures by surface functionalization. Nanoscale 8, 575–580 (2016)

    CAS  Google Scholar 

  29. Vazirisereshk, M.R., Ye, H., Ye, Z., Otero-de-la-Roza, A., Zhao, M.-Q., Gao, Z., Johnson, A.C., Johnson, E.R., Carpick, R.W., Martini, A.: Origin of nanoscale friction contrast between supported graphene, MoS2, and a graphene/MoS2 heterostructure. Nano Lett. 19, 5496–5505 (2019)

    CAS  Google Scholar 

  30. Filleter, T., McChesney, J.L., Bostwick, A., Rotenberg, E., Emtsev, K.V., Seyller, T., Horn, K., Bennewitz, R.: Friction and dissipation in epitaxial graphene films. Phys. Rev. Lett. 102, 086102 (2009)

    CAS  Google Scholar 

  31. Sheehan, P.E., Lieber, C.M.: Nanotribology and nanofabrication of MoO3 structures by atomic force microscopy. Science 272, 1158–1161 (1996)

    CAS  Google Scholar 

  32. Popov, V.L., Gray, J.: Prandtl-Tomlinson model: History and applications in friction, plasticity, and nanotechnologies. ZAMM 92, 683–708 (2012)

    Google Scholar 

  33. Schwarz, U.D., Hölscher, H.: Exploring and explaining friction with the Prandtl-Tomlinson model. ACS Nano 10, 38–41 (2016)

    CAS  Google Scholar 

  34. Mounet, N., Gibertini, M., Schwaller, P., Campi, D., Merkys, A., Marrazzo, A., Sohier, T., Castelli, I.E., Cepellotti, A., Pizzi, G.: Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nat. Nanotechnol. 13, 246 (2018)

    CAS  Google Scholar 

  35. Zhou, J., Shen, L., Costa, M.D., Persson, K.A., Ong, S.P., Huck, P., Lu, Y., Ma, X., Chen, Y., Tang, H., Feng, Y.P.: 2DMatPedia, an open computational database of two-dimensional materials from top-down and bottom-up approaches. Sci Data 6, 86 (2019)

    Google Scholar 

  36. Gavrishchaka, V., Senyukova, O., Koepke, M.: Synergy of physics-based reasoning and machine learning in biomedical applications: towards unlimited deep learning with limited data. Adv. Phys. 4, 1582361 (2019)

    Google Scholar 

  37. Ye, Z., Otero-De-La-Roza, A., Johnson, E.R., Martini, A.: Oscillatory motion in layered materials: graphene, boron nitride, and molybdenum disulfide. Nanotechnology 26, 165701 (2015)

    Google Scholar 

  38. Hermann, K.: Periodic overlayers and moiré patterns: theoretical studies of geometric properties. J. Phys. 24, 314210 (2012)

    Google Scholar 

  39. Popov, A.M., Lebedeva, I.V., Knizhnik, A.A., Lozovik, Y.E., Potapkin, B.V.: Molecular dynamics simulation of the self-retracting motion of a graphene flake. Phys. Rev. B 84, 245437 (2011)

    Google Scholar 

  40. Smolyanitsky, A.: Effects of thermal rippling on the frictional properties of free-standing graphene. RSC Adv. 5, 29179–29184 (2015)

    CAS  Google Scholar 

  41. Sahoo, S., Gaur, A.P., Ahmadi, M., Guinel, M.J.-F., Katiyar, R.S.: Temperature-dependent Raman studies and thermal conductivity of few-layer MoS2. J. Phys. Chem. C 117, 9042–9047 (2013)

    CAS  Google Scholar 

  42. Mate, C.M.: Tribology on the small scale: a bottom up approach to friction, lubrication, and wear. Oxford University Press, Oxford (2008)

    Google Scholar 

  43. Levita, G., Cavaleiro, A., Molinari, E., Polcar, T., Righi, M.C.: Sliding properties of MoS2 layers: load and interlayer orientation effects. J. Phys. Chem. C 118, 13809–13816 (2014)

    CAS  Google Scholar 

  44. Ko, J.-H., Kwon, S., Byun, I.-S., Choi, J.S., Park, B.H., Kim, Y.-H., Park, J.Y.: Nanotribological properties of fluorinated, hydrogenated, and oxidized graphenes. Tribol. Lett. 50, 137–144 (2013)

    CAS  Google Scholar 

  45. Kwon, S., Lee, K.E., Lee, H., Koh, S.J., Ko, J.-H., Kim, Y.-H., Kim, S.O., Park, J.Y.: The effect of thickness and chemical reduction of graphene oxide on nanoscale friction. J. Phys. Chem. B 122, 543–547 (2017)

    Google Scholar 

  46. Li, Q., Liu, X.-Z., Kim, S.-P., Shenoy, V.B., Sheehan, P.E., Robinson, J.T., Carpick, R.W.: Fluorination of graphene enhances friction due to increased corrugation. Nano Lett. 14, 5212–5217 (2014)

    CAS  Google Scholar 

  47. Cammarata, A., Polcar, T.: Overcoming nanoscale friction barriers in transition metal dichalcogenides. Phys. Rev. B 96, 085406 (2017)

    Google Scholar 

  48. Dong, Y., Wu, X., Martini, A.: Atomic roughness enhanced friction on hydrogenated graphene. Nanotechnology 24, 375701 (2013)

    Google Scholar 

  49. Wang, L.-F., Ma, T.-B., Hu, Y.-Z., Wang, H.: Atomic-scale friction in graphene oxide: an interfacial interaction perspective from first-principles calculations. Phys. Rev. B 86, 125436 (2012)

    Google Scholar 

  50. Kwon, S., Ko, J.-H., Jeon, K.-J., Kim, Y.-H., Park, J.Y.: Enhanced nanoscale friction on fluorinated graphene. Nano Lett. 12, 6043–6048 (2012)

    CAS  Google Scholar 

  51. Wendler, F., Knorr, A., Malic, E.: Ultrafast carrier dynamics in Landau-quantized graphene. Nanophotonics 4, 224–249 (2015)

    CAS  Google Scholar 

  52. Kaul, A.B.: Two-dimensional layered materials: Structure, properties, and prospects for device applications. J. Mater. Res. 29, 348–361 (2014)

    CAS  Google Scholar 

  53. Peng, B., Zhang, H., Shao, H., Xu, Y., Zhang, X., Zhu, H.: Thermal conductivity of monolayer MoS 2, MoSe 2, and WS 2: interplay of mass effect, interatomic bonding and anharmonicity. RSC Adv. 6, 5767–5773 (2016)

    CAS  Google Scholar 

  54. Fang, L., Liu, D.-M., Guo, Y., Liao, Z.-M., Luo, J.-B., Wen, S.-Z.: Thickness dependent friction on few-layer MoS2, WS2, and WSe2. Nanotechnology 28, 245703 (2017)

    Google Scholar 

  55. Ataca, C., Sahin, H., Ciraci, S.: Stable, single-layer MX2 transition-metal oxides and dichalcogenides in a honeycomb-like structure. J. Phys. Chem. C 116, 8983–8999 (2012)

    CAS  Google Scholar 

  56. Liepins, G.E., Uppuluri, V.: Data Quality Control: Theory and Pragmatics. CRC Press, Boca Raton (1990)

    Google Scholar 

  57. Scholkopf, B., Smola, A.J.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT press, Cambridge (2001)

    Google Scholar 

  58. Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., Rubin, D.B.: Bayesian Data Analysis. Chapman and Hall/CRC, Boca Raton (2013)

    Google Scholar 

  59. Raina, R., Ng, A.Y., Koller, D.: Constructing informative priors using transfer learning. In: Proceedings of the 23rd international conference on Machine learning, pp. 713–720. ACM, Place ACM (2006)

  60. Stuart, S.J., Tutein, A.B., Harrison, J.A.: A reactive potential for hydrocarbons with intermolecular interactions. J. Chem. Phys. 112, 6472–6486 (2000)

    CAS  Google Scholar 

  61. Rappé, A.K., Casewit, C.J., Colwell, K., Goddard III, W.A., Skiff, W.M.: UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. J. Am. Chem. Soc. 114, 10024–10035 (1992)

    Google Scholar 

  62. Stillinger, F.H., Weber, T.A.: Computer simulation of local order in condensed phases of silicon. Phys. Rev. B 31, 5262 (1985)

    CAS  Google Scholar 

  63. Susarla, S., Manimunda, P., Morais Jaques, Y., Hachtel, J.A., Idrobo, J.C., Syed Amnulla, S.A., Galvão, D.S., Tiwary, C.S., Ajayan, P.M.: Deformation mechanisms of vertically stacked WS2/MoS2 heterostructures; the role of interfaces. ACS Nano 12, 4036–4044 (2018)

    CAS  Google Scholar 

  64. Plimpton, S.: Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995)

    CAS  Google Scholar 

  65. 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. 105, 046801 (2010)

    Google Scholar 

  66. Fessler, G., Eren, B., Gysin, U., Glatzel, T., Meyer, E.: Friction force microscopy studies on SiO2 supported pristine and hydrogenated graphene. Appl. Phys. Lett. 104, 041910 (2014)

    Google Scholar 

  67. Johari, P., Shenoy, V.B.: Tunable dielectric properties of transition metal dichalcogenides. ACS Nano 5, 5903–5908 (2011)

    CAS  Google Scholar 

  68. Akinwande, D., Brennan, C.J., Bunch, J.S., Egberts, P., Felts, J.R., Gao, H., Huang, R., Kim, J.-S., Li, T., Li, Y.: A review on mechanics and mechanical properties of 2D materials—graphene and beyond. Extreme Mech. Lett. 13, 42–77 (2017)

    Google Scholar 

  69. Peimyoo, N., Shang, J., Yang, W., Wang, Y., Cong, C., Yu, T.: Thermal conductivity determination of suspended mono-and bilayer WS 2 by Raman spectroscopy. Nano Res. 8, 1210–1221 (2015)

    CAS  Google Scholar 

  70. Ma, Y.-Z., Valkunas, L., Bachilo, S.M., Fleming, G.R.: Exciton binding energy in semiconducting single-walled carbon nanotubes. J. Phys. Chem. B 109, 15671–15674 (2005)

    CAS  Google Scholar 

  71. Olsen, T., Latini, S., Rasmussen, F., Thygesen, K.S.: Simple screened hydrogen model of excitons in two-dimensional materials. Phys. Rev. Lett. 116, 056401 (2016)

    Google Scholar 

  72. Wu, J., Wang, B., Wei, Y., Yang, R., Dresselhaus, M.: Mechanics and mechanically tunable band gap in single-layer hexagonal boron-nitride. Mater. Res. Lett. 1, 200–206 (2013)

    CAS  Google Scholar 

  73. Aksoy, R., Selvi, E., Ma, Y.: X-ray diffraction study of molybdenum diselenide to 359 GPa. J. Phys. Chem. Solids 69, 2138–2140 (2008)

    CAS  Google Scholar 

  74. Yin, M., Cohen, M.L.: Structural theory of graphite and graphitic silicon. Phys. Rev. B 29, 6996 (1984)

    CAS  Google Scholar 

  75. Fasolino, A., Los, J., Katsnelson, M.I.: Intrinsic ripples in graphene. Nat. Mater. 6, 858 (2007)

    CAS  Google Scholar 

  76. Niyogi, S., Bekyarova, E., Itkis, M.E., McWilliams, J.L., Hamon, M.A., Haddon, R.C.: Solution properties of graphite and graphene. J. Am. Chem. Soc. 128, 7720–7721 (2006)

    CAS  Google Scholar 

  77. Topsakal, M., Ciraci, S.: Elastic and plastic deformation of graphene, silicene, and boron nitride honeycomb nanoribbons under uniaxial tension: A first-principles density-functional theory study. Phys. Rev. B 81, 024107 (2010)

    Google Scholar 

  78. Shinde, P.P., Kumar, V.: Direct band gap opening in graphene by BN doping: ab initio calculations. Phys. Rev. B 84, 125401 (2011)

    Google Scholar 

  79. Bernardi, M., Palummo, M., Grossman, J.C.: Extraordinary sunlight absorption and one nanometer thick photovoltaics using two-dimensional monolayer materials. Nano Lett. 13, 3664–3670 (2013)

    CAS  Google Scholar 

  80. Wu, X., Varshney, V., Lee, J., Pang, Y., Roy, A.K., Luo, T.: How to characterize thermal transport capability of 2D materials fairly?–Sheet thermal conductance and the choice of thickness. Chem. Phys. Lett. 669, 233–237 (2017)

    CAS  Google Scholar 

  81. Peng, B., Zhang, H., Shao, H., Xu, Y., Ni, G., Zhang, R., Zhu, H.: Phonon transport properties of two-dimensional group-IV materials from ab initio calculations. Phys. Rev. B 94, 245420 (2016)

    Google Scholar 

  82. Song, L., Ci, L., Lu, H., Sorokin, P.B., Jin, C., Ni, J., Kvashnin, A.G., Kvashnin, D.G., Lou, J., Yakobson, B.I.: Large scale growth and characterization of atomic hexagonal boron nitride layers. Nano Lett. 10, 3209–3215 (2010)

    CAS  Google Scholar 

  83. Kern, G., Kresse, G., Hafner, J.: Ab initio calculation of the lattice dynamics and phase diagram of boron nitride. Phys. Rev. B 59, 8551 (1999)

    CAS  Google Scholar 

  84. Lebedev, A.V., Lebedeva, I.V., Knizhnik, A.A., Popov, A.M.: Interlayer interaction and related properties of bilayer hexagonal boron nitride: ab initio study. RSC Adv. 6, 6423–6435 (2016)

    CAS  Google Scholar 

  85. Wirtz, L., Marini, A., Rubio, A.: Excitons in boron nitride nanotubes: dimensionality effects. Phys. Rev. Lett. 96, 126104 (2006)

    Google Scholar 

  86. Şahin, H., Ataca, C., Ciraci, S.: Electronic and magnetic properties of graphane nanoribbons. Phys. Rev. B 81, 205417 (2010)

    Google Scholar 

  87. He, C., Zhang, C., Sun, L., Jiao, N., Zhang, K., Zhong, J.: Structure, stability and electronic properties of tricycle type graphane. Phys. Status Solidi (RRL) 6, 427–429 (2012)

    CAS  Google Scholar 

  88. Topsakal, M., Cahangirov, S., Ciraci, S.: The response of mechanical and electronic properties of graphane to the elastic strain. Appl. Phys. Lett. 96, 091912 (2010)

    Google Scholar 

  89. Leenaerts, O., Peelaers, H., Hernández-Nieves, A., Partoens, B., Peeters, F.: First-principles investigation of graphene fluoride and graphane. Phys. Rev. B 82, 195436 (2010)

    Google Scholar 

  90. Li, Y., Zhou, Z., Shen, P., Chen, Z.: Structural and electronic properties of graphane nanoribbons. J. Phys. Chem. C 113, 15043–15045 (2009)

    CAS  Google Scholar 

  91. Koski, K.J., Cui, Y.: The new skinny in two-dimensional nanomaterials. ACS Nano 7, 3739–3743 (2013)

    CAS  Google Scholar 

  92. Nair, R.R., Ren, W., Jalil, R., Riaz, I., Kravets, V.G., Britnell, L., Blake, P., Schedin, F., Mayorov, A.S., Yuan, S.: Fluorographene: a two-dimensional counterpart of Teflon. Small 6, 2877–2884 (2010)

    CAS  Google Scholar 

  93. Cheng, S.-H., Zou, K., Okino, F., Gutierrez, H.R., Gupta, A., Shen, N., Eklund, P., Sofo, J., Zhu, J.: Reversible fluorination of graphene: evidence of a two-dimensional wide bandgap semiconductor. Phys. Rev. B 81, 205435 (2010)

    Google Scholar 

  94. Tang, S., Zhang, S.: Structural and electronic properties of hybrid fluorographene–graphene nanoribbons: Insight from first-principles calculations. J. Phys. Chem. C 115, 16644–16651 (2011)

    CAS  Google Scholar 

  95. Karlický, F., Otyepka, M.: Band gaps and optical spectra from single-and double-layer fluorographene to graphite fluoride: many-body effects and excitonic states. Ann. Phys. 526, 408–414 (2014)

    Google Scholar 

  96. Ivanovskaya, V.V., Zobelli, A., Gloter, A., Brun, N., Serin, V., Colliex, C.: Ab initio study of bilateral doping within the MoS 2-NbS 2 system. Phys. Rev. B 78, 134104 (2008)

    Google Scholar 

  97. Li, W., Carrete, J., Mingo, N.: Thermal conductivity and phonon linewidths of monolayer MoS2 from first principles. Appl. Phys. Lett. 103, 253103 (2013)

    Google Scholar 

  98. Kumar, A., Ahluwalia, P.: Electronic structure of transition metal dichalcogenides monolayers 1H-MX 2 (M= Mo, W; X= S, Se, Te) from ab-initio theory: new direct band gap semiconductors. Eur. Phys. J. B 85, 186 (2012)

    Google Scholar 

  99. Ding, Y., Wang, Y., Ni, J., Shi, L., Shi, S., Tang, W.: First principles study of structural, vibrational and electronic properties of graphene-like MX2 (M= Mo, Nb, W, Ta; X= S, Se, Te) monolayers. Phys. B 406, 2254–2260 (2011)

    CAS  Google Scholar 

  100. Karunadasa, H.I., Montalvo, E., Sun, Y., Majda, M., Long, J.R., Chang, C.J.: A molecular MoS2 edge site mimic for catalytic hydrogen generation. Science 335, 698–702 (2012)

    CAS  Google Scholar 

  101. Buck, V.: Lattice parameters of sputtered MoS2 films. Thin Solid Films 198, 157–167 (1991)

    CAS  Google Scholar 

  102. Cordero, B., Gómez, V., Platero-Prats, A.E., Revés, M., Echeverría, J., Cremades, E., Barragán, F., Alvarez, S.: Covalent radii revisited. Dalton Trans. 21, 2832–2838 (2008)

    Google Scholar 

  103. Amin, B., Singh, N., Schwingenschlögl, U.: Heterostructures of transition metal dichalcogenides. Phys. Rev. B 92, 075439 (2015)

    Google Scholar 

  104. Ramasubramaniam, A.: Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides. Phys. Rev. B 86, 115409 (2012)

    Google Scholar 

  105. Kumar, A., Ahluwalia, P.: Effect of quantum confinement on electronic and dielectric properties of niobium dichalcogenides NbX2 (X= S, Se, Te). J. Alloys Compd. 550, 283–291 (2013)

    CAS  Google Scholar 

  106. Dawson, W., Bullett, D.: Electronic structure and crystallography of MoTe2 and WTe2. J. Phys. C 20, 6159 (1987)

    CAS  Google Scholar 

  107. Shafique, A., Shin, Y.-H.: Strain engineering of phonon thermal transport properties in monolayer 2H-MoTe 2. Phys. Chem. Chem. Phys. 19, 32072–32078 (2017)

    CAS  Google Scholar 

  108. Kalikhman, V., Umanskiĭ, Y.S.: Transition-metal chalcogenides with layer structures and features of the filling of their Brillouin zones. Soviet Physics Uspekhi 15, 728 (1973)

    Google Scholar 

  109. Ma, Y., Kuc, A., Jing, Y., Philipsen, P., Heine, T.: Two-dimensional haeckelite NbS2: a diamagnetic high-mobility semiconductor with Nb4+ Ions. Angew. Chem. Int. Ed. 56, 10214–10218 (2017)

    CAS  Google Scholar 

  110. Xu, Y., Liu, X., Guo, W.: Tensile strain induced switching of magnetic states in NbSe 2 and NbS 2 single layers. Nanoscale 6, 12929–12933 (2014)

    CAS  Google Scholar 

  111. Bucko, T., Hafner, J.R., Lebegue, S., Angyán, J.G.: Improved description of the structure of molecular and layered crystals: ab initio DFT calculations with van der Waals corrections. J. Phys. Chem. A 114, 11814–11824 (2010)

    CAS  Google Scholar 

  112. Shi, H., Pan, H., Zhang, Y.-W., Yakobson, B.I.: Quasiparticle band structures and optical properties of strained monolayer MoS 2 and WS 2. Phys. Rev. B 87, 155304 (2013)

    Google Scholar 

  113. Ataca, C., Topsakal, M., Akturk, E., Ciraci, S.: A comparative study of lattice dynamics of three-and two-dimensional MoS2. J. Phys. Chem. C 115, 16354–16361 (2011)

    CAS  Google Scholar 

  114. Ramakrishna Matte, H., Gomathi, A., Manna, A.K., Late, D.J., Datta, R., Pati, S.K., Rao, C.: MoS2 and WS2 analogues of graphene. Angew. Chem. Int. Ed. 49, 4059–4062 (2010)

    Google Scholar 

  115. Amin, B., Kaloni, T.P., Schwingenschlögl, U.: Strain engineering of WS 2, WSe 2, and WTe 2. RSC Adv. 4, 34561–34565 (2014)

    CAS  Google Scholar 

  116. Zhu, B., Chen, X., Cui, X.: Exciton binding energy of monolayer WS 2. Sci. Rep. 5, 9218 (2015)

    Google Scholar 

  117. Gu, X., Yang, R.: Phonon transport in single-layer transition metal dichalcogenides: a first-principles study. Appl. Phys. Lett. 105, 131903 (2014)

    Google Scholar 

  118. Akinwande, D., Petrone, N., Hone, J.: Two-dimensional flexible nanoelectronics. Nat. Commun. 5, 5678 (2014)

    CAS  Google Scholar 

  119. Jana, M.K., Singh, A., Late, D.J., Rajamathi, C.R., Biswas, K., Felser, C., Waghmare, U.V., Rao, C.: A combined experimental and theoretical study of the structural, electronic and vibrational properties of bulk and few-layer Td-WTe2. J. Phys. 27, 285401 (2015)

    Google Scholar 

  120. Inoue, M., Negishi, H.: Interlayer spacing of 3D transition-metal intercalates of 1T-cadmium iodide-type titanium disulfide (TiS2). J. Phys. Chem. 90, 235–238 (1986)

    CAS  Google Scholar 

  121. Reshak, A.H., Auluck, S.: Electronic and optical properties of the 1 T phases of TiS 2, TiSe 2, and TiTe 2. Phys. Rev. B 68, 245113 (2003)

    Google Scholar 

  122. Fang, C., De Groot, R., Haas, C.: Bulk and surface electronic structure of 1 T− TiS 2 and 1 T− TiSe 2. Phys. Rev. B 56, 4455 (1997)

    CAS  Google Scholar 

  123. Wan, C., Gu, X., Dang, F., Itoh, T., Wang, Y., Sasaki, H., Kondo, M., Koga, K., Yabuki, K., Snyder, G.J.: Flexible n-type thermoelectric materials by organic intercalation of layered transition metal dichalcogenide TiS 2. Nat. Mater. 14, 622 (2015)

    CAS  Google Scholar 

  124. Goli, P., Khan, J., Wickramaratne, D., Lake, R.K., Balandin, A.A.: Charge density waves in exfoliated films of van der Waals materials: evolution of Raman spectrum in TiSe2. Nano Lett. 12, 5941–5945 (2012)

    CAS  Google Scholar 

  125. Sugawara, K., Nakata, Y., Shimizu, R., Han, P., Hitosugi, T., Sato, T., Takahashi, T.: Unconventional charge-density-wave transition in monolayer 1 T-TiSe2. ACS Nano 10, 1341–1345 (2015)

    Google Scholar 

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Correspondence to Kristofer G. Reyes or Prathima C. Nalam.

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Appendix

Appendix

See Tables 2 and 3.

Table 2 Definitions of the descriptors selected based on the physical models developed to estimate dissipation in 2D materials
Table 3 Quantified values for the properties impacting PES for fifteen 2D materials, as obtained from the literature

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Sattari Baboukani, B., Ye, Z., G. Reyes, K. et al. Prediction of Nanoscale Friction for Two-Dimensional Materials Using a Machine Learning Approach. Tribol Lett 68, 57 (2020). https://doi.org/10.1007/s11249-020-01294-w

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Keywords

  • Van der waals
  • Potential energy surface
  • Friction
  • 2D materials
  • Transfer learning
  • Bayesian model
  • Maximum energy barrier