Atomic scale friction velocity

Figure 5 Typical velocity relationship of kinetic friction for a sliding contact in which friction is from adsorbed layers confined between two incommensurate walls. The kinetic friction F is normalized by the static friction Fs. At extremely small velocities v, the confined layer is close to thermal equilibrium and, consequently, F is linear in v, as to be expected from linear response theory. In an intermediate velocity regime, the velocity dependence of F is logarithmic. Instabilities or pops of the atoms can be thermally activated. At large velocities, the surface moves too quickly for thermal effects to play a role. Time-temperature superposition could be applied. All data were scaled to one reference temperature. Reprinted with permission from Ref. 25. 

Simulations of incommensurate surfaces showed a similar dependence on Vi, with first-order instabilities occurring if Vi < Vj, where Vj is some positive, critical value that depends on the degree of mismatch between the lattice constants of the top and bottom surfaces. This process leads to nonvanishing Fk as l o goes to zero. In the case where Vi < V, the atoms are dragged with the wall that exerts the maximum lateral force. It, in turn, leads to friction that scales linearly with the sliding velocity. As a result, the friction force will go to zero with vq. 

An atomic force microscope is used to stuviscoelastic state at the temperature of experiment. It is shown that, during the preliminary phase of friction and before the transition to the sliding regime, the contact area remains nearly constant. This allows for a determination of the relaxation and of the complex modulus of the material. A good agreement is found between moduli measured by this method and macroscopically determined ones. The position of the transition is seen to scale with the characteristic size of the contact area but it does not depend on the displacement velocity. Finally, a transient stick-slip regime is observed before the sliding steady state is reached. 

It is usually desired to perform molecular dynamics simulations at constant temperature. In the simulations considered here, constant temperature is accomplished in one of two ways. In the first, stochastic forces and associated frictional forces are introduced which act individually on each atom of the system. This approach is hereafter referred to as stochastic dynamics (SD) simulation. The mean-square magnitude of the stochastic forces, which are purely random and Gaussian, is proportional to the temperature of the system, as described in Ref. 24. A canonical ensemble is simulated if the friction coefficient 7 for the frictional forces is chosen such that 1 /7 is much smaller than the total simulation time. The resulting damping forces do influence dynamic quantities, however, and this is the primary drawback of the SD method. The SD method was used in Refs 24, 25 and 31. The second method for constant temperature simulations involves either direct scaling of atomic velocities, as in Refs 29 and 30, or the inclusion of an additional temperature degree of freedom to the system by the Nose method,as appUed in Refs 31 and 32. Such simulations are hereafter referred to as molecular dynamics (MD) simulations. Of the MD methods considered, only the Nose method yields a true canonical ensemble. 

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