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

Abstract

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.