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In this paper, the effect of the oscillation of the substrate potential in a one-dimensional Frenkel-Kontorova model is considered. The relationship between the oscillating amplitude, frequency of the substrate and the nanofriction phenomena such as hysteresis, maximum static friction force, super-lubricity are investigated. Similar results are obtained for the two cases in which the ratios of the atomic distance to the period of potential field of the substrate potential field are incommensurate and commensurate respectively. The results show that on one hand, with the appropriate frequency, the area of the hysteresis will decrease while the amplitude increases, and the tendency of the decrease depends on the frequency. In particular, suitable frequency and amplitude give rise to super-lubricity. However, when the frequency is too high, the result is the same as those in the case without oscillation. On the other hand, fixing the amplitude, the area of the hysteresis will increase with the increase of frequency in spite of tendencies being different. At the same time, on a whole, the maximum static friction force has an increasing tendency. Interestingly and importantly, for a certain amplitude, as the frequency increases, the maximum static friction force first decreases to zero (corresponding to super-lubricity), and then increases. That is, there is an optimum oscillating frequency which makes the system have the minimum static friction force. Furthermore, the difference between the above two circumstances lies in that for commensurate interfaces, there are the same start-up velocities for a certain frequency and various small amplitudes, which is different from the incommensurate mating contacts. Hence, it shows that the latter has a more complex dynamic behavior under the same hypothesis.
[1] Luo J B, Li J J 2010 Lubr. Eng. 35 1 (in Chinese) [雒建斌, 李津津 2010 润滑与密封 35 1]
[2] Rozman M G, Urbakh M, Klafter J 1996 Phys. Rev. Lett. 77 683
[3] Braun O M, Kivshar Y S 2004 The Frenkel-Kontorova Model: Concepts, Methods, and Applications (Berlin: Springer) pp1-5
[4] Braun O M, Kivshar Y S 1998 Phys. Reports 306 1
[5] Yang Y, Duan W S, Yang L, Chen J M, Lin M M 2011 Euro. Phys. Lett. 93 16001
[6] Braun O M, Dauxois T, Paliy M V, Peyrard M 1997 Phys. Rev. E 55 3598
[7] Braun O M, Vanossi A, Tosatti E 2005 Phys. Rev. Lett. 95 026102
[8] Vanossi A, Röder J, Bishop A R, Bortolani V 2000 Phys. Rev. E 63 017203
[9] Li X L, Liu F, Lin M M, Chen J M, Duan W S 2010 Acta Phys. Sin. 59 2589 (in Chinese) [李晓礼, 刘锋, 林麦麦, 陈建敏, 段文山 2010 59 2589]
[10] Yang Y, Wang C L, Duan W S, Shi Y R, Chen J M 2012 Acta Phys. Sin. 61 130501 (in Chinese) [杨阳, 王苍龙, 段文山, 石玉仁, 陈建敏 2012 61 130501]
[11] Xu A G, Wang G R, Chen S G, Yang Z R 1999 Prog. Phys. 19 109 (in Chinese) [许爱国, 王光瑞, 陈式刚, 杨展如 1999 物理学进展 19 109]
[12] Vanossi A, Manini N, Divitini G, Santoro G E, Tosatti E 2006 Phys. Rev. Lett. 97 056101
[13] Tekić J, He D, Hu B 2009 Phys. Rev. E 79 036604
[14] Mali P, Tekić J, Ivić Z, Pantić M 2012 Phys. Rev. E 86 046209
[15] Guerra R, Vanossi A, Ferrario M 2007 Surf. Sci. 601 3676
[16] Jia R J, Wang C L, Yang Y, Gou X Q, Chen J M, Duan W S 2013 Acta Phys. Sin. 62 068104 (in Chinese) [贾汝娟, 王苍龙, 杨阳, 苟学强, 陈建敏, 段文山 2013 62 068104]
[17] Mali P, Tekić J, Pantić M 2014 Commun. Nolinear Sci. Numer. Simulat. 19 3469
[18] Soloviev I I, Klenov N V, Pankratov A L, Il'ichev E, Kuzmin L S 2013 Phys. Rev. E 87 060901
[19] Bhattacharya M, Dutta A, Barat P 2013 Phys. Rev. B 87 214107
[20] Lin M M, Duan W S, Chen J M 2010 Chin. Phys. B 19 026201
[21] Braun O M, Bishop A R, Röder J 1997 Phys. Rev. Lett. 79 3692
[22] Braun O M, Dauxois T, Paliy M V, Peyrard M 1997 Phys. Rev. Lett. 78 1295
[23] Vanossi A, Santoro G, Bortolani V 2004 J. Phys.: Condens. Matter 16 2895
[24] Manini N, Vanossi A, Santoro G E, Tosatti E 2007 Phys. Rev. E 76 046603
[25] Woulanché R L, Vanossi A, Manini N 2013 Phys. Rev. E 88 012810
[26] Yang Y, Wang C L, Duan W S, Chen J M 2011 Chin. Phys. Lett. 28 030503
[27] Vanossi A, Manini N, Caruso F, Santoro G E, Tosatti E 2007 Phys. Rev. Lett. 99 206101
[28] Vanossi A, Röder J, Bishop A R, Bortolani V 2003 Phys. Rev. E 67 016605
[29] Vanossi A, Bishop A R, Bortolani V 2004 Nanotechnology 15 790
[30] Lei Y M, Guan F L 2012 Int. J. Mod. Phys. C 23 1250071
[31] Yung K L, Lei Y M, Xu Y 2010 Chin. Phys. B 19 010503
[32] Vanossi A, Benassi A, Varini N, Tosatti E 2013 Phys. Rev. B 87 045412
[33] Capozza R, Vanossi A, Vezzani A, Zapperi S 2009 Phys. Rev. Lett. 103 085502
[34] Guerra R, Vanossi A, Urbakh M 2008 Phys. Rev. E 78 036110
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[1] Luo J B, Li J J 2010 Lubr. Eng. 35 1 (in Chinese) [雒建斌, 李津津 2010 润滑与密封 35 1]
[2] Rozman M G, Urbakh M, Klafter J 1996 Phys. Rev. Lett. 77 683
[3] Braun O M, Kivshar Y S 2004 The Frenkel-Kontorova Model: Concepts, Methods, and Applications (Berlin: Springer) pp1-5
[4] Braun O M, Kivshar Y S 1998 Phys. Reports 306 1
[5] Yang Y, Duan W S, Yang L, Chen J M, Lin M M 2011 Euro. Phys. Lett. 93 16001
[6] Braun O M, Dauxois T, Paliy M V, Peyrard M 1997 Phys. Rev. E 55 3598
[7] Braun O M, Vanossi A, Tosatti E 2005 Phys. Rev. Lett. 95 026102
[8] Vanossi A, Röder J, Bishop A R, Bortolani V 2000 Phys. Rev. E 63 017203
[9] Li X L, Liu F, Lin M M, Chen J M, Duan W S 2010 Acta Phys. Sin. 59 2589 (in Chinese) [李晓礼, 刘锋, 林麦麦, 陈建敏, 段文山 2010 59 2589]
[10] Yang Y, Wang C L, Duan W S, Shi Y R, Chen J M 2012 Acta Phys. Sin. 61 130501 (in Chinese) [杨阳, 王苍龙, 段文山, 石玉仁, 陈建敏 2012 61 130501]
[11] Xu A G, Wang G R, Chen S G, Yang Z R 1999 Prog. Phys. 19 109 (in Chinese) [许爱国, 王光瑞, 陈式刚, 杨展如 1999 物理学进展 19 109]
[12] Vanossi A, Manini N, Divitini G, Santoro G E, Tosatti E 2006 Phys. Rev. Lett. 97 056101
[13] Tekić J, He D, Hu B 2009 Phys. Rev. E 79 036604
[14] Mali P, Tekić J, Ivić Z, Pantić M 2012 Phys. Rev. E 86 046209
[15] Guerra R, Vanossi A, Ferrario M 2007 Surf. Sci. 601 3676
[16] Jia R J, Wang C L, Yang Y, Gou X Q, Chen J M, Duan W S 2013 Acta Phys. Sin. 62 068104 (in Chinese) [贾汝娟, 王苍龙, 杨阳, 苟学强, 陈建敏, 段文山 2013 62 068104]
[17] Mali P, Tekić J, Pantić M 2014 Commun. Nolinear Sci. Numer. Simulat. 19 3469
[18] Soloviev I I, Klenov N V, Pankratov A L, Il'ichev E, Kuzmin L S 2013 Phys. Rev. E 87 060901
[19] Bhattacharya M, Dutta A, Barat P 2013 Phys. Rev. B 87 214107
[20] Lin M M, Duan W S, Chen J M 2010 Chin. Phys. B 19 026201
[21] Braun O M, Bishop A R, Röder J 1997 Phys. Rev. Lett. 79 3692
[22] Braun O M, Dauxois T, Paliy M V, Peyrard M 1997 Phys. Rev. Lett. 78 1295
[23] Vanossi A, Santoro G, Bortolani V 2004 J. Phys.: Condens. Matter 16 2895
[24] Manini N, Vanossi A, Santoro G E, Tosatti E 2007 Phys. Rev. E 76 046603
[25] Woulanché R L, Vanossi A, Manini N 2013 Phys. Rev. E 88 012810
[26] Yang Y, Wang C L, Duan W S, Chen J M 2011 Chin. Phys. Lett. 28 030503
[27] Vanossi A, Manini N, Caruso F, Santoro G E, Tosatti E 2007 Phys. Rev. Lett. 99 206101
[28] Vanossi A, Röder J, Bishop A R, Bortolani V 2003 Phys. Rev. E 67 016605
[29] Vanossi A, Bishop A R, Bortolani V 2004 Nanotechnology 15 790
[30] Lei Y M, Guan F L 2012 Int. J. Mod. Phys. C 23 1250071
[31] Yung K L, Lei Y M, Xu Y 2010 Chin. Phys. B 19 010503
[32] Vanossi A, Benassi A, Varini N, Tosatti E 2013 Phys. Rev. B 87 045412
[33] Capozza R, Vanossi A, Vezzani A, Zapperi S 2009 Phys. Rev. Lett. 103 085502
[34] Guerra R, Vanossi A, Urbakh M 2008 Phys. Rev. E 78 036110
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