搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Frenkel-Kontorova模型中基底势振动的影响

雷佑铭 李毅伟 赵云平

引用本文:
Citation:

Frenkel-Kontorova模型中基底势振动的影响

雷佑铭, 李毅伟, 赵云平

Effect of the oscillation of substrate potential in driven Frenkel-Kontorova chains

Lei You-Ming, Li Yi-Wei, Zhao Yun-Ping
PDF
导出引用
  • 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.
    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.
    • 基金项目: 国家自然科学基金(批准号:11102156)和西北工业大学基础研究基金资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11102156) and the Northwestern Polytechnical University Foundation for Fundamental Research, China
    [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

  • [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

  • [1] 苏瑞霞, 黄霞, 郑志刚. 耦合Frenkel-Kontorova双链的格波解及其色散关系. 物理学报, 2022, 71(15): 154401. doi: 10.7498/aps.71.20212362
    [2] 李毅伟, 雷佑铭, 杨勇歌. 随机激励下Frenkel-Kontorova模型的纳米摩擦现象. 物理学报, 2021, 70(9): 090501. doi: 10.7498/aps.70.20201254
    [3] 王美欧, 肖倩, 金霞, 曹燕燕, 徐亚东. 基于亚波长金属超构光栅的中红外大角度高效率回射器. 物理学报, 2020, 69(1): 014211. doi: 10.7498/aps.69.20191144
    [4] 严柏平, 张成明, 李立毅, 吕福在, 邓双. Tb0.3Dy0.7Fe2合金磁畴偏转的滞回特性研究. 物理学报, 2016, 65(6): 067501. doi: 10.7498/aps.65.067501
    [5] 史云胜, 刘秉琦, 杨兴, 董华来. 微米级超润滑石墨接触面的表征与分析. 物理学报, 2016, 65(23): 234601. doi: 10.7498/aps.65.234601
    [6] 经昊达, 张向军, 田煜, 孟永钢. 计入固液界面作用的润滑热力学模型与分析. 物理学报, 2015, 64(16): 168101. doi: 10.7498/aps.64.168101
    [7] 蒋国平, 郝洪, 曾春航, 郝逸飞, 吴如军, 刘纪超. 冲击作用下的摩擦力效应实验研究. 物理学报, 2013, 62(11): 116203. doi: 10.7498/aps.62.116203
    [8] 贾汝娟, 王苍龙, 杨阳, 苟学强, 陈建敏, 段文山. 二维Frenkel-Kontorova模型中六角对称结构的摩擦现象. 物理学报, 2013, 62(6): 068104. doi: 10.7498/aps.62.068104
    [9] 杨阳, 王苍龙, 段文山, 石玉仁, 陈建敏. 基底势函数的无序性对静摩擦力的影响. 物理学报, 2012, 61(13): 130501. doi: 10.7498/aps.61.130501
    [10] 韩秀琴, 姜虹, 石玉仁, 刘妍秀, 孙建华, 陈建敏, 段文山. 一维 Frenkel-Kontorova(FK)模型原子链的相变研究. 物理学报, 2011, 60(11): 116801. doi: 10.7498/aps.60.116801
    [11] 张茂平, 钟伟荣, 艾保全. 非对称双链分子结构的热整流效应. 物理学报, 2011, 60(6): 060511. doi: 10.7498/aps.60.060511
    [12] 王军, 李京颍, 郑志刚. 热整流效应的消失与翻转现象. 物理学报, 2010, 59(1): 476-481. doi: 10.7498/aps.59.476
    [13] 李晓礼, 刘锋, 林麦麦, 陈建敏, 段文山. Frenkel-Kontorova模型中垫底势对最大静摩擦力的影响. 物理学报, 2010, 59(4): 2589-2594. doi: 10.7498/aps.59.2589
    [14] 陈学锋, 李华梅, 李东杰, 曹 菲, 董显林. 脉冲电容器用细电滞回线铁电陶瓷材料的研究. 物理学报, 2008, 57(11): 7298-7304. doi: 10.7498/aps.57.7298
    [15] 丁凌云, 龚中良, 黄 平. 基于耦合振子模型的摩擦力计算研究. 物理学报, 2008, 57(10): 6500-6506. doi: 10.7498/aps.57.6500
    [16] 孔维姝, 胡 林, 杜学能, 张兴刚, 王伟明, 吴 宇. 用探测棒研究颗粒堆中的最大静摩擦力. 物理学报, 2007, 56(4): 2318-2322. doi: 10.7498/aps.56.2318
    [17] 李宝山, 朱志刚, 李国荣, 殷庆瑞, 丁爱丽. 铌锰锆钛酸铅铁电陶瓷电滞回线的温度和频率响应. 物理学报, 2005, 54(2): 939-943. doi: 10.7498/aps.54.939
    [18] 王龙海, 于 军, 王耘波, 彭 刚, 刘 锋, 高峻雄. 基于静态电滞回线的铁电电容模型. 物理学报, 2005, 54(2): 949-954. doi: 10.7498/aps.54.949
    [19] 胡 林, 杨 平, 徐 亭, 江 阳, 须海江, 龙 为, 杨昌顺, 张 弢, 陆坤权. 颗粒物质中圆棒受到的静摩擦力. 物理学报, 2003, 52(4): 879-882. doi: 10.7498/aps.52.879
    [20] 钱林茂, 雒建斌, 温诗铸, 萧旭东. 二氧化硅及其硅烷自组装膜微观摩擦力与粘着力的研究(Ⅰ)摩擦力的实验与分析. 物理学报, 2000, 49(11): 2240-2246. doi: 10.7498/aps.49.2240
计量
  • 文章访问数:  4857
  • PDF下载量:  550
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-05-20
  • 修回日期:  2014-06-26
  • 刊出日期:  2014-11-05

/

返回文章
返回