Frenkel-Kontorova模型中基底势振动的影响

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

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.