Molecular Dynamics Simulations: Thermal Fluctuations and Kinetic Friction

Recent development in nanotribology suggests that solid friction in nanoscale and atomic levels can be more complicated than Coulomb macroscopic laws. In particular, Ben-David and Fineberg showed how local normal load could affect the friction coefficient [1]. Therefore, the friction coefficient can be dependent on the contact area and the normal load. Indeed, the deviation from the Amontons’ law has been reported in this research. In another study, for the case of thin films, friction is more like dissipation in liquids in the absence of a net normal load [2]. Consequently, more investigations on friction coefficient at the nano and atomic scales are of great importance.

In this paper, molecular dynamic simulations are utilized to study friction at the nanoscale. The system has two parts. Some graphene layers are utilized as a surface, and a a normal load in the z-direction 𝐹z, and a horizontal force, 𝐹x, in the x-direction. The horizontal 𝑧𝑥 surface fluctuations in a nearly constant temperature. In the theory, we consider a Langevin dissipation, 𝐹 = 𝛾𝑣 + 𝜁(𝑡), where 𝜁(𝑡) is a random spherical metal particle moves on the surface. In our case study, the spherical metal particle consists of roughly 32000 aluminum atoms in an FCC lattice. Besides, two forces are exerted on the particle; force provides movement for the particle on the surface. Moreover, a Langevin thermostat adds 𝑓𝑟 force with zero mean, < 𝜁(𝑡) >=0, according to the fluctuation-dissipation theorem. The particle starts to accelerate and finally reaches a steady-state with a nearly constant velocity <v(t)>≅ 𝑣. At this point, the friction force < 𝐹𝑓𝑟 > is equal to the horizontal force. That is 𝐹𝑥 = < 𝐹𝑓𝑟 >. For this, one can investigate the linear proportionality of friction force on the velocity of the particle after reaching a steady state 𝑣. Namely, 𝐹𝑥=𝛾𝑣 where 𝛾 stands for the friction coefficient. Thereupon, simulated points will be velocities for different horizontal forces in a constant normal load. As the first result, the friction coefficient will be evaluated by a linear fitting method for the simulated points. As the second result, we have done simulations for different temperatures to investigate the thermal dependency of the friction coefficient. The friction coefficient decreases with increasing temperature.

AAT and NVB gratefully acknowledge the Russian Foundation for Basic Research (RFBR), Grant No. 18-29-19198. The research was carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University [3] and Skoltech supercomputer Zhores [4].

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