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基于一维Frenkel-Kontorova模型, 研究了振动的基底势对系统纳米摩擦现象的影响. 分别在相邻原子间的距离与周期势场的周期比为不公度(incommensurate)、可公度(commensurate)两种情形下, 探讨了基底势振动的振幅和频率对滞回现象(hysteresis)、最大静摩擦力以及超滑现象的作用机理. 两种情形下, 固定频率, 随着振幅的增大, 滞回区域的面积以及最大静摩擦力都将减小, 对于不同的频率, 减小的趋势不同. 系统甚至产生了超滑现象. 但当频率过大时, 振幅的改变不会影响滞回区域的面积以及最大静摩擦力的大小, 此时与基底不加振动时的情形一致; 当振幅固定, 随着频率的增大, 滞回区域的面积将增大, 对于不同振幅, 增大的趋势不同. 特别地, 对于某些固定的振幅, 最大静摩擦力随着振动频率的增大先逐步减小直至出现超滑现象, 再进一步增大频率, 最大静摩擦力又转而逐步增大. 这一现象类似于共振, 表明存在最佳的振动频率促进系统内所有原子的共同运动, 使得整个系统的最大静摩擦力几乎消失. 另外, 两种情形的区别是, 对于某些固定的频率(如ω= 0.5)和不同的小振幅, 不可公度情形往往具有相同的平均终止速度, 而可公度情形则不同, 表明相同前提下后者具有更复杂的动力学行为.
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关键词:
- Frenkel-Kontorova模型 /
- 滞回 /
- 最大静摩擦力 /
- 超润滑
[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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