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The excellent tribological characteristics of two-dimensional (2D) materials have received great attention, however, how to effectively predict their frictions is still lacking. Here, we propose to obtain the sliding potential energy surface by density functional theory calculations, instead of simplified potential energy function. Thus it is able to solve the frictional behaviors of 2D materials with irregular complex potential energy surfaces. Firstly, we reveal the mechanism of dual-scale stick-slip behavior between a tip and a graphene/Ru(0001) heterostructure. With a dual-wavelength potential energy surface, we observe a similar frictional behavior to those captured in atomic force microscopy experiments, in which a significant long-range stick-slip sawtooth modulation emerges with a period coinciding with the Moir superlattice structure. Secondly, we discuss the interlayer frictions of 2D materials, including graphene/graphene, fluorinated graphene/fluorinated graphene, MoS2/MoS2, graphene/MoS2 and fluorinated graphene/MoS2. With sliding potential energy surface obtained by density functional theory calculations, the interlayer friction is estimated according to the Prandtl-Tomlinson model calculation method. Compared with the friction between homostructures, the friction between heterostructures is lowered by orders of magnitude, which could be attributed to its ultralow sliding potential barrier. The stick-slip instability could be observed in homostructure, while heterostructure exihibits smooth friction loops. The 2D sliding path between the layers is recorded in the sliding process, showing its dependence on both the potential energy barrier and the spring constant. The sliding path shift increases with the increase of potential energy barrier and the decrease of spring constant in the y direction. This method is also applicable to tribological systems with dominated interfacial van der Waals interaction.
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Keywords:
- atomic scale friction /
- Prandtl-Tomlinson model /
- two-dimensional materials /
- interlayer sliding
[1] Tomlinson G A 1929 Phil. Mag. 7 905
[2] Zhao Y P 2012 Surface and Interface Mechanics (Beijing:Science Press) p301 (in Chinese)[赵亚溥 2012 表面与界面物理力学(北京:科学出版社) 第301页]
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[4] Wang Z, Ma T, Hu Y, Xu L, Wang H 2015 Friction 3 170
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[6] Zheng X, Gao L, Yao Q, Li Q, Zhang M, Xie X, Qiao S, Wang G, Ma T, Di Z, Luo J, Wang X 2016 Nat. Commun. 7 13204
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[8] Liu S, Wang H, Xu Q, Ma T, Yu G, Zhang C, Geng D, Yu Z, Zhang S, Wang W, Hu Y, Wang H, Luo J 2017 Nat. Commun. 8 14029
[9] Wang L F, Ma T B, Hu Y Z, Zheng Q, Wang H, Luo J 2014 Nanotechnology 25 385701
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[12] Kresse G, Furthmller J 1996 Comput. Mater. Sci. 6 15
[13] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[14] Blchl P E 1994 Phys. Rev. B 50 17953
[15] Kresse G, Joubert D https://doi.org/10.1103/PhysRevB.59.1758 1999 Phys. Rev. B 59 1758
[16] Geim A K, Grigorieva I V 2013 Nature 499 419
[17] Zhu X, Yuan Q, Zhao Y P 2014 Nanoscale 6 5432
[18] Pan Y, Zhang H, Shi D, Sun J, Du S, Liu F, Gao H J 2009 Adv. Mater. 21 2777
[19] Pan Y, Shi D, Gao H J 2007 Chin. Phys. 16 3151
[20] Shi R, Gao L, Lu H, Li Q, Ma T, Guo H, Du S, Feng X, Zhang S, Liu Y, Cheng P, Hu Y, Gao H, Luo J 2017 2D Mater. 4 025079
[21] Gao L, Liu Y, Ma T, Shi R, Hu Y, Luo J 2016 Appl. Phys. Lett. 108 261601
[22] Filleter T, Bennewitz R 2010 Phys. Rev. B 81 155412
[23] Hirano M, Shinjo K 1990 Phys. Rev. B 41 11837
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[1] Tomlinson G A 1929 Phil. Mag. 7 905
[2] Zhao Y P 2012 Surface and Interface Mechanics (Beijing:Science Press) p301 (in Chinese)[赵亚溥 2012 表面与界面物理力学(北京:科学出版社) 第301页]
[3] Dong Y, Vadakkepatt A, Martini A 2011 Tribol. Lett. 44 367
[4] Wang Z, Ma T, Hu Y, Xu L, Wang H 2015 Friction 3 170
[5] Li Q, Dong Y, Martini A, Carpick R W 2011 Tribol. Lett. 43 369
[6] Zheng X, Gao L, Yao Q, Li Q, Zhang M, Xie X, Qiao S, Wang G, Ma T, Di Z, Luo J, Wang X 2016 Nat. Commun. 7 13204
[7] Maier S, Gnecco E, Baratoff A, Bennewitz R, Meyer E 2008 Phys. Rev. B 78 045432
[8] Liu S, Wang H, Xu Q, Ma T, Yu G, Zhang C, Geng D, Yu Z, Zhang S, Wang W, Hu Y, Wang H, Luo J 2017 Nat. Commun. 8 14029
[9] Wang L F, Ma T B, Hu Y Z, Zheng Q, Wang H, Luo J 2014 Nanotechnology 25 385701
[10] Grimme S 2006 J. Comput. Chem. 27 1787
[11] Kresse G, Hafner J 1994 Phys. Rev. B 49 14251
[12] Kresse G, Furthmller J 1996 Comput. Mater. Sci. 6 15
[13] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[14] Blchl P E 1994 Phys. Rev. B 50 17953
[15] Kresse G, Joubert D https://doi.org/10.1103/PhysRevB.59.1758 1999 Phys. Rev. B 59 1758
[16] Geim A K, Grigorieva I V 2013 Nature 499 419
[17] Zhu X, Yuan Q, Zhao Y P 2014 Nanoscale 6 5432
[18] Pan Y, Zhang H, Shi D, Sun J, Du S, Liu F, Gao H J 2009 Adv. Mater. 21 2777
[19] Pan Y, Shi D, Gao H J 2007 Chin. Phys. 16 3151
[20] Shi R, Gao L, Lu H, Li Q, Ma T, Guo H, Du S, Feng X, Zhang S, Liu Y, Cheng P, Hu Y, Gao H, Luo J 2017 2D Mater. 4 025079
[21] Gao L, Liu Y, Ma T, Shi R, Hu Y, Luo J 2016 Appl. Phys. Lett. 108 261601
[22] Filleter T, Bennewitz R 2010 Phys. Rev. B 81 155412
[23] Hirano M, Shinjo K 1990 Phys. Rev. B 41 11837
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