Influence of stiffness gradient on friction between graphene layers

Dong Yun; Duan Zao-Qi; Tao Yi; Gueye Birahima; Zhang Yan; Chen Yun-Fei

doi:10.7498/aps.68.20181905

Abstract

According to the molecular dynamics simulations and the mechanism of energy dissipation of nanofriction, we construct a model system with a flake sliding in commensurate configuration on a monolayer suspended graphene anchored on a bed of springs. The system is to analyze the contributions of different regions (T1-T7) of the graphene flake to friction force, with the substrate characterized by different stiffness gradients and midpoint stiffness.
The results indicate that the soft region of contact (T1) always contributes to the driving force, whereas the hard region (T7) leads to the biggest friction force on all column atoms of the flake. Moreover, as the support stiffness increases, when the stiffness gradient and the midpoint stiffness are equal to 1.34 nN/nm² and 12 nN/nm, respectively, the contribution ratio of T7 to the total friction increases from 33% to 47%, which is approximately 4-15 times greater than those of each column atoms in T3-T6. The results also indicate that the energy barrier decreases with the increase of support stiffness along the stiffness gradient direction of the substrate, which induces the resistance forces on the relative motion to decrease. Meanwhile, the amplitude of the thermal atomic fluctuation is higher in the softer region while lower in the harder one. This difference in amplitude leads to the considerable potential gradient that ultimately causes the driving force. Finally, for a given point at the end of the flake (T1 or T7), the intensity of the van der Waals potential field is mainly determined by the nearest substrate atoms at that point. Part of these nearest atoms lie inside the contact region while the others do not. Consequently, the thermal vibration of the atoms inside the contact region is different from that of the atoms outside the confinement. The different thermal vibrations induce the greater edge barriers. In addition, T1 lies in the soft edge region and T7 in the hard one. As a result, the normal deformations of these two regions are always different, and therefore they also generate the driving force.
At these points, the results reported here suggest that the friction force in each contact region is caused by the coupling of the energy barrier and the elastic deformation between the graphene surfaces. The former contribution, i.e.the energy barrier, includes the interfacial potential barrier in commensurate state which is against the sliding of the surfaces with respect to each other, and the potential gradient caused by the different vibration magnitudes of the substrate atoms against the different spring stiffness in the direction of stiffness gradient. The latter contribution, i.e. the elastic deformation, is the unbalanced edge energy barrier resulting from the asymmetrical deformation and the different degrees of freedom between the edge atoms of the slider and atoms inside and outside the contact area of the substrate. Results of this paper are expected to be able to provide theoretical guidance in considering the influence of stiffness gradient on friction between commensurate surfaces and in designing the nanodevices.

Keywords:

Authors and contacts

1. School of Mechanical Engineering, Jiangsu Key Laboratory for Design and Manufacture of Micro-Nano Biomedical Instruments, Southeast University, Nanjing 211189, China;
2. School of Mechanical and Electronical Engineering, Lanzhou University of Technology, Lanzhou 730050, China

References

[1]	Krim J 1996 Sci. Am. 275 74
[2]	Ren S L, Yang S R, Zhao Y P 2003 Langmuir 19 2763
[3]	Ren S L, Yang S R, Wang J Q, Liu W M, Zhao Y P 2004 Chem. Mater. 16 428
[4]	Hu Y Z, Ma T B, Wang H 2013 Friction 1 24
[5]	Liu S W, Wang H P, Xu Q, Ma T B, Yu G, Zhang C, Geng D, Yu Z, Zhang S, Wang W 2017 Nat. Commun. 8 14029
[6]	Lee C, Li Q, Kalb W, Liu X Z, Berger H, Carpick R W, Hone J 2010 Science 328 76
[7]	Geim A K 2009 Science 324 1530
[8]	de Wijn A S, Fusco C, Fasolino A 2010 Phys. Rev. E 81 046105
[9]	Xu Z, Li X, Yakobson B I, Ding F 2013 Nanoscale 5 6736
[10]	Schedin F, Geim A, Morozov S, Hill E, Blake P, Katsnelson M, Novoselov K 2007 Nat. Mater. 6 652
[11]	Stoller M D, Park S, Zhu Y, An J, Ruoff R S 2008 Nano Lett. 8 3498
[12]	Lin Y M, Dimitrakopoulos C, Jenkins K A, Farmer D B, Chiu H Y, Grill A, Avouris P 2010 Science 327 662
[13]	Yang J, Liu Z, Grey F, Xu Z, Li X, Liu Y, Urbakh M, Cheng Y, Zheng Q 2013 Phys. Rev. Lett. 110 255504
[14]	Berman D, Erdemir A, Sumant A V 2014 Mater. Today 17 31
[15]	Koren E, Lörtscher E, Rawlings C, Knoll A W, Duerig U 2015 Science 348 679
[16]	Liu Z, Yang J, Grey F, Liu J Z, Liu Y, Wang Y, Yang Y, Cheng Y, Zheng Q 2012 Phys. Rev. Lett. 108 205503
[17]	Bailey S, Amanatidis I, Lambert C 2008 Phys. Rev. Lett. 100 256802
[18]	Guo Z, Chang T, Guo X, Gao H 2012 J. Mech. Phys. Solids 60 1676
[19]	Somada H, Hirahara K, Akita S, Nakayama Y 2008 Nano Lett. 9 62
[20]	Shiomi J, Maruyama S 2009 Nanotechnology 20 055708
[21]	Rurali R, Hernandez E 2010 Chem. Phys. Lett. 497 62
[22]	Chang T, Zhang H, Guo Z, Guo X, Gao H 2015 Phys. Rev. Lett. 114 015504
[23]	Filippov A E, Dienwiebel M, Frenken J W, Klafter J, Urbakh M 2008 Phys. Rev. Lett. 100 046102
[24]	Lebedeva I V, Knizhnik A A, Popov A M, Ershova O V, Lozovik Y E, Potapkin B V 2011 J. Chem. Phys. 134 104505
[25]	Pálinkás A, Süle P, Szendr M, Molnár G, Hwang C, Biró L P, Osváth Z 2016 Carbon 107 792
[26]	Woods C, Britnell L, Eckmann A, Ma R, Lu J, Guo H, Lin X, Yu G, Cao Y, Gorbachev R 2014 Nat. Phys. 10 451
[27]	Lindsay L, Broido D A 2010 Phys. Rev. B 81 205441
[28]	Lebedeva I V, Knizhnik A A, Popov A M, Ershova O V, Lozovik Y E, Potapkin B V 2010 Phys. Rev. B 82 155460
[29]	Plimpton S 1995 J. Comput. Phys. 7 1
[30]	Zhang H, Guo Z, Gao H, Chang T 2015 Carbon 94 60
[31]	Smolyanitsky A, Killgore J P, Tewary V K 2012 Phys. Rev. B 85 035412
[32]	Lee H, Lee N, Seo Y, Eom J, Lee S 2009 Nanotechnology 20 325701
[33]	Filleter T, McChesney J L, Bostwick A, Rotenberg E, Emtsev K, Seyller T, Horn K, Bennewitz R 2009 Phys. Rev. Lett. 102 086102
[34]	Xu L, Ma T B, Hu Y Z, Wang H 2011 Nanotechnology 22 285708
[35]	Wang Z J, Ma T B, Hu Y Z, Xu L, Wang H 2015 Friction 3 170
[36]	Li S, Li Q, Carpick R W, Gumbsch P, Liu X Z, Ding X, Sun J, Li J 2016 Nature 539 541
[37]	Guo Z, Chang T, Guo X, Gao H 2011 Phys. Rev. Lett. 107 105502
[38]	Ma F, Zheng H, Sun Y, Yang D, Xu K, Chu P K 2012 Appl. Phys. Lett. 101 111904
[39]	Chen J, Walther J H, Koumoutsakos P 2014 Nano Lett. 14 819
[40]	Zhang Y Y, Pei Q X, Jiang J W, Wei N, Zhang Y W 2016 Nanoscale 8 483
[41]	Barreiro A, Rurali R, Hernández E R, Moser J, Pichler T, Forro L, Bachtold A 2008 Science 320 775
[42]	Zhao J, Huang J Q, Wei F, Zhu J 2010 Nano Lett. 10 4309
[43]	Cao Q, Han S J, Tulevski G S, Zhu Y, Lu D D, Haensch W 2013 Nat. Nanotechnol. 8 180
[44]	Gnecco E, Bennewitz R, Gyalog T, Loppacher C, Bammerlin M, Meyer E, Güntherodt H J 2000 Phys. Rev. Lett. 84 1172
[45]	Liu Y, Grey F, Zheng Q 2014 Sci. Rep. 4 4875
[46]	Berman D, Deshmukh S A, Sankaranarayanan S K, Erdemir A, Sumant A V 2015 Science 348 1118
[47]	Seiler S, Halbig C E, Grote F, Rietsch P, Börrnert F, Kaiser U, Meyer B, Eigler S 2018 Nat. Commun. 9 836
[48]	Ye Z, Tang C, Dong Y, Martini A 2012 J. Appl. Phys. 112 116102
[49]	Li Q, Lee C, Carpick R W, Hone J 2010 Phys. Status Solidi B 247 2909

Cited By

[1]	Krim J 1996 Sci. Am. 275 74
[2]	Ren S L, Yang S R, Zhao Y P 2003 Langmuir 19 2763
[3]	Ren S L, Yang S R, Wang J Q, Liu W M, Zhao Y P 2004 Chem. Mater. 16 428
[4]	Hu Y Z, Ma T B, Wang H 2013 Friction 1 24
[5]	Liu S W, Wang H P, Xu Q, Ma T B, Yu G, Zhang C, Geng D, Yu Z, Zhang S, Wang W 2017 Nat. Commun. 8 14029
[6]	Lee C, Li Q, Kalb W, Liu X Z, Berger H, Carpick R W, Hone J 2010 Science 328 76
[7]	Geim A K 2009 Science 324 1530
[8]	de Wijn A S, Fusco C, Fasolino A 2010 Phys. Rev. E 81 046105
[9]	Xu Z, Li X, Yakobson B I, Ding F 2013 Nanoscale 5 6736
[10]	Schedin F, Geim A, Morozov S, Hill E, Blake P, Katsnelson M, Novoselov K 2007 Nat. Mater. 6 652
[11]	Stoller M D, Park S, Zhu Y, An J, Ruoff R S 2008 Nano Lett. 8 3498
[12]	Lin Y M, Dimitrakopoulos C, Jenkins K A, Farmer D B, Chiu H Y, Grill A, Avouris P 2010 Science 327 662
[13]	Yang J, Liu Z, Grey F, Xu Z, Li X, Liu Y, Urbakh M, Cheng Y, Zheng Q 2013 Phys. Rev. Lett. 110 255504
[14]	Berman D, Erdemir A, Sumant A V 2014 Mater. Today 17 31
[15]	Koren E, Lörtscher E, Rawlings C, Knoll A W, Duerig U 2015 Science 348 679
[16]	Liu Z, Yang J, Grey F, Liu J Z, Liu Y, Wang Y, Yang Y, Cheng Y, Zheng Q 2012 Phys. Rev. Lett. 108 205503
[17]	Bailey S, Amanatidis I, Lambert C 2008 Phys. Rev. Lett. 100 256802
[18]	Guo Z, Chang T, Guo X, Gao H 2012 J. Mech. Phys. Solids 60 1676
[19]	Somada H, Hirahara K, Akita S, Nakayama Y 2008 Nano Lett. 9 62
[20]	Shiomi J, Maruyama S 2009 Nanotechnology 20 055708
[21]	Rurali R, Hernandez E 2010 Chem. Phys. Lett. 497 62
[22]	Chang T, Zhang H, Guo Z, Guo X, Gao H 2015 Phys. Rev. Lett. 114 015504
[23]	Filippov A E, Dienwiebel M, Frenken J W, Klafter J, Urbakh M 2008 Phys. Rev. Lett. 100 046102
[24]	Lebedeva I V, Knizhnik A A, Popov A M, Ershova O V, Lozovik Y E, Potapkin B V 2011 J. Chem. Phys. 134 104505
[25]	Pálinkás A, Süle P, Szendr M, Molnár G, Hwang C, Biró L P, Osváth Z 2016 Carbon 107 792
[26]	Woods C, Britnell L, Eckmann A, Ma R, Lu J, Guo H, Lin X, Yu G, Cao Y, Gorbachev R 2014 Nat. Phys. 10 451
[27]	Lindsay L, Broido D A 2010 Phys. Rev. B 81 205441
[28]	Lebedeva I V, Knizhnik A A, Popov A M, Ershova O V, Lozovik Y E, Potapkin B V 2010 Phys. Rev. B 82 155460
[29]	Plimpton S 1995 J. Comput. Phys. 7 1
[30]	Zhang H, Guo Z, Gao H, Chang T 2015 Carbon 94 60
[31]	Smolyanitsky A, Killgore J P, Tewary V K 2012 Phys. Rev. B 85 035412
[32]	Lee H, Lee N, Seo Y, Eom J, Lee S 2009 Nanotechnology 20 325701
[33]	Filleter T, McChesney J L, Bostwick A, Rotenberg E, Emtsev K, Seyller T, Horn K, Bennewitz R 2009 Phys. Rev. Lett. 102 086102
[34]	Xu L, Ma T B, Hu Y Z, Wang H 2011 Nanotechnology 22 285708
[35]	Wang Z J, Ma T B, Hu Y Z, Xu L, Wang H 2015 Friction 3 170
[36]	Li S, Li Q, Carpick R W, Gumbsch P, Liu X Z, Ding X, Sun J, Li J 2016 Nature 539 541
[37]	Guo Z, Chang T, Guo X, Gao H 2011 Phys. Rev. Lett. 107 105502
[38]	Ma F, Zheng H, Sun Y, Yang D, Xu K, Chu P K 2012 Appl. Phys. Lett. 101 111904
[39]	Chen J, Walther J H, Koumoutsakos P 2014 Nano Lett. 14 819
[40]	Zhang Y Y, Pei Q X, Jiang J W, Wei N, Zhang Y W 2016 Nanoscale 8 483
[41]	Barreiro A, Rurali R, Hernández E R, Moser J, Pichler T, Forro L, Bachtold A 2008 Science 320 775
[42]	Zhao J, Huang J Q, Wei F, Zhu J 2010 Nano Lett. 10 4309
[43]	Cao Q, Han S J, Tulevski G S, Zhu Y, Lu D D, Haensch W 2013 Nat. Nanotechnol. 8 180
[44]	Gnecco E, Bennewitz R, Gyalog T, Loppacher C, Bammerlin M, Meyer E, Güntherodt H J 2000 Phys. Rev. Lett. 84 1172
[45]	Liu Y, Grey F, Zheng Q 2014 Sci. Rep. 4 4875
[46]	Berman D, Deshmukh S A, Sankaranarayanan S K, Erdemir A, Sumant A V 2015 Science 348 1118
[47]	Seiler S, Halbig C E, Grote F, Rietsch P, Börrnert F, Kaiser U, Meyer B, Eigler S 2018 Nat. Commun. 9 836
[48]	Ye Z, Tang C, Dong Y, Martini A 2012 J. Appl. Phys. 112 116102
[49]	Li Q, Lee C, Carpick R W, Hone J 2010 Phys. Status Solidi B 247 2909

[1]	Wang Xiao-Feng, Tao Gang, Xu Ning, Wang Peng, Li Zhao, Wen Peng. Molecular dynamics analysis of shock wave-induced nanobubble collapse in water. Acta Physica Sinica, 2021, 70(13): 134702. doi: 10.7498/aps.70.20210058
[2]	Yang Quan, Ma Li, Geng Song-Chao, Lin Yi-Ni, Chen Tao, Sun Li-Ning. Molecular dynamics simulation of contact behaviors between multiwall carbon nanotube and metal surface. Acta Physica Sinica, 2021, 70(10): 106101. doi: 10.7498/aps.70.20202194
[3]	Li Jie-Jie, Lu Bin-Bin, Xian Yue-Hui, Hu Guo-Ming, Xia Re. Characterization of nanoporous silver mechanical properties by molecular dynamics simulation. Acta Physica Sinica, 2018, 67(5): 056101. doi: 10.7498/aps.67.20172193
[4]	Yuan Lin, Jing Peng, Liu Yan-Hua, Xu Zhen-Hai, Shan De-Bin, Guo Bin. Molecular dynamics simulation of polycrystal silver nanowires under tensile deformation. Acta Physica Sinica, 2014, 63(1): 016201. doi: 10.7498/aps.63.016201
[5]	Ma Bin, Rao Qiu-Hua, He Yue-Hui, Wang Shi-Liang. Molecular dynamics simulation of tensile deformation mechanism of the single crystal tungsten nanowire. Acta Physica Sinica, 2013, 62(17): 176103. doi: 10.7498/aps.62.176103
[6]	Ma Wen, Lu Yan-Wen. Molecular dynamics investigation of shock front in nanocrystalline copper. Acta Physica Sinica, 2013, 62(3): 036201. doi: 10.7498/aps.62.036201
[7]	Zhang Zhao-Hui, Li Hai-Peng, Han Kui. Relations between the structure, symmetry and the energy mechanism of the polar-organic molecule ultra-films during the tribology. Acta Physica Sinica, 2013, 62(15): 158701. doi: 10.7498/aps.62.158701
[8]	Lan Hui-Qing, Xu Cang. Molecular dynamics simulation on friction process of silicon-doped diamond-like carbon films. Acta Physica Sinica, 2012, 61(13): 133101. doi: 10.7498/aps.61.133101
[9]	Zhang Zhao-Hui, Han Kui, Cao Juan, Wang Fan, Yang Li-Juan. The influence of the structure of the organic ultra-film on friction. Acta Physica Sinica, 2012, 61(2): 028701. doi: 10.7498/aps.61.028701
[10]	Wang Zhi-Gang, Wu Liang, Zhang Yang, Wen Yu-Hua. Phase transition and coalescence behavior of fcc Fe nanoparticles: a molecular dynamics study. Acta Physica Sinica, 2011, 60(9): 096105. doi: 10.7498/aps.60.096105
[11]	Yang Ping, Wu Yong-Sheng, Xu Hai-Feng, Xu Xian-Xin, Zhang Li-Qiang, Li Pei. Molecular dynamics simulation of thermal conductivity for the TiO2/ZnO nano-film interface. Acta Physica Sinica, 2011, 60(6): 066601. doi: 10.7498/aps.60.066601
[12]	Gu Fang, Zhang Jia-Hong, Yang Li-Juan, Gu Bin. Molecular dynamics simulation of resonance properties of strain graphene nanoribbons. Acta Physica Sinica, 2011, 60(5): 056103. doi: 10.7498/aps.60.056103
[13]	Ma Wen, Zhu Wen-Jun, Zhang Ya-Lin, Chen Kai-Guo, Deng Xiao-Liang, Jing Fu-Qian. Construction of metallic nanocrystalline samples by molecular dynamics simulation. Acta Physica Sinica, 2010, 59(7): 4781-4787. doi: 10.7498/aps.59.4781
[14]	Wang Wei, Zhang Kai-Wang, Meng Li-Jun, Li Zhong-Qiu, Zuo Xue-Yun, Zhong Jian-Xin. Molecular dynamics simulation of the evaporation of the surface wall of multi-wall carbon nanotubes at high temperature. Acta Physica Sinica, 2010, 59(4): 2672-2678. doi: 10.7498/aps.59.2672
[15]	Chen Kai-Guo, Zhu Wen-Jun, Ma Wen, Deng Xiao-Liang, He Hong-Liang, Jing Fu-Qian. Propagation of shockwave in nanocrystalline copper: Molecular dynamics simulation. Acta Physica Sinica, 2010, 59(2): 1225-1232. doi: 10.7498/aps.59.1225
[16]	Zhang Zhao-Hui, Han Kui, Li Hai-Peng, Tang Gang, Wu Yu-Xi, Wang Hong-Tao, Bai Lei. Study of friction between hydrocarboxylic acid Langmuir-Blodgett films and its mechanism using molecular dynamics simulation. Acta Physica Sinica, 2008, 57(5): 3160-3165. doi: 10.7498/aps.57.3160
[17]	Zhou Guo-Rong, Gao Qiu-Ming. Freezing of Ni nanowires investigated by molecular dynamics simulation. Acta Physica Sinica, 2007, 56(3): 1499-1505. doi: 10.7498/aps.56.1499
[18]	Yang Quan-Wen, Zhu Ru-Zeng. Freezing of Cu nanoclusters studied by molecular dynamics simulation. Acta Physica Sinica, 2005, 54(9): 4245-4250. doi: 10.7498/aps.54.4245
[19]	Liang Hai-Ge, Wang Xiu-Xi, Wu Heng-An, Wang Yu and. . Acta Physica Sinica, 2002, 51(10): 2308-2314. doi: 10.7498/aps.51.2308
[20]	Wu Heng-An, Ni Xiang-Gui, Wang Yu, Wang Xiu-Xi. . Acta Physica Sinica, 2002, 51(7): 1412-1415. doi: 10.7498/aps.51.1412

Catalog

Vol. 68, Issue 1 - 2019-01-05

Metrics

Abstract views: 6530
PDF Downloads: 94
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板