Atomic Stick-Slip

The tip is assumed to be coupled to a support via a spring with spring constant K. The support moves at a velocity vq. Its coordinate changes according to xo = vot. The total energy of the system can then be written as 

Initially, the tip will reside within the local minimum given by the condition 

For the beginning of one stick-slip cycle, we can use the approximation sin z w z for small z. This leads to 

The initial velocity of the tip Vtip will therefore be given by 

If the support position xo has changed sufficiently far, the tip could be forced to a position, where d E/dx changes it sign. This will be exactly at the point x where 

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Zhang, T., Wang, H., and Hu, Y. Z., Atomic Stick-Slip Friction Between Commensurate Self-Assembled Monolayers," Tribology Letters, Vol. 14, No. 2,2003, pp. 69-76. 

The validity of Coulomb s law has been verified also on the nanoscale Zworner et al. [484] showed that, for different carbon compound surfaces, friction does not depend on sliding velocity in the range between 0.1 /xm/s and up to 24 /xm/s. At low speeds, a weak (logarithmic) dependence of friction on speed was observed by Gnecco et al. [485] on a NaCl(lOO) surface and by Bennewitz et al. [486] on a Cu (111) surface. This can be modeled when taking into account thermal activation of the irreversible jumps in atomic stick-slip [487],... 

The most drastic constraints are required when the goal is to achieve contrast at the atomic scale, either with the contact mode, atomic stick-slip (44-46), or using the resonant non contact mode (23-26). The necessary requirement is that the driving interaction between the tip and sample must vary at the angstrdm scale. Such a constraint implies that the surface must be properly prepared. It seems that uniquely ultra high vacuum (UHV) and low temperature conditions can meet this requirement. As noted in reference (24) a tip preparation may also be needed. The tip was sputtered in situ with Argon ions to remove the oxide layer from the tip. Cleaning the tip was found to be of importance to achieve stable atomic resolution. 

A fundamental question not yet resolved regarding stick-slip motion is the exact mechanism for the occurrence of stick-slip with a periodicity of the surface lattice. For interpretation of the stick-slip motion by the Prandtl-Tomlinson model, the tip is commonly treated as a single, pointlike entity without any additional internal degree of freedom. However, the contact area between AFM tip and crystal surface will typically contain some 10 unit cells. Atomic stick-slip was observed even for amorphous silicon and silicon nitride tips [1003] and for crystalline tips, atoms of tip and surface lattice will usually not be in registry, making the observation of stick-slip with a periodicity of the surface lattice surprising. 

The dependence of friction on sliding velocity is more complicated. Apparent stick-slip motions between SAM covered mica surfaces were observed at the low velocity region, which would disappear when the sliding velocity excesses a certain threshold [35]. In AFM experiments when the tip scanned over the monolayers at low speeds, friction force was reported to increase with the logarithm of the velocity, which is similar to that observed when the tip scans on smooth substrates. This is interpreted in terms of thermal activation that results in depinning of interfacial atoms in case that the potential barrier becomes small [36]. 

It can be seen from Fig. 15(a) that the atom moves in a stick-slip way. In forward motion, for example, it is a stick phase from A to B during which the atom stays in a metastable state with little change in position as the support travels forward. Meanwhile, the lateral force gradually climbs up in the same period, leading to an accumulation of elastic energy, as illustrated in Fig. 15(fo). When reaching the point B where a saddle-node bifurcation appears, the metastable... 

It has been recognized that the behavior of atomic friction, such as stick-slip, creep, and velocity dependence, can be understood in terms of the energy structure of multistable states and noise activated motion. Noises like thermal activities may cause the atom to jump even before AUq becomes zero, but the time when the atom is activated depends on sliding velocity in such a way that for a given energy barrier, AI/q the probability of activation increases with decreasing velocity. It has been demonstrated [14] that the mechanism of noise activation leads to "the velocity... 

In summary, sliding can be regarded as a process during which interfacial atoms would experience a series of stick-slip motions, similar to the jump in and out in the adhesion case, and it is the energy loss in this approach/separation cycle that determines the level of friction. 

From the point of view of system d5mamics, the transition from rest to sliding observed in static friction originates from the same mechanism as the stick-slip transition in kinetic friction, which is schematically shown in Fig. 31. The surfaces at rest are in stable equilibrium where interfacial atoms sit in energy minima. As lateral force on one of the surfaces increases (loading), the system experiences a similar process as to what happens in the stick phase that the surface... 

Friction and Atomic Level Stick-Slip Motion. 

Transition from Stick-Slip to Continuous Sliding in Atomic Friction Entering a New Regime of Ultralow Friction. 

Differences in the frictional properties of most plastics can be explained in terms of the ratio of shear strenghth to hardness. Shooter and Tabor observed that the coefficients of friction for polytetrafluoroethylene are 2—3 times lower than anticipated by this calculation. It is believed that this discrepancy is caused by the inherently low cohesive forces between adjacent polymer chains and is responsible for the absence of stick-slip. The large fluorine atoms effectively screen the large carbon-fluorine dipole, reducing molecular cohesion so that the shear force at the interface is low. The shear strength of the bulk material is higher because of interlocking molecular chains. 

Macroscopic stick-slip motion described above applies to the center of mass movement of the bodies. However, even in situations where the movement of the overall mass is smooth and steady, there may occur local, microscopic stick-slip. This involves the movement of single atoms, molecular groups, or asperities. In fact, such stick-slip events form the basis of microscopic models of friction and are the explanation why the friction force is largely independent of speed (see Section 11.1.9). 

Figure 7 Examples of nanotribology on dry carbon surfaces for atomic force microscopy (AFM) (a) schematic description of the out-of-plane graphene deformation with the sliding AFM (Lee et al., 2010), (b) nanotube without tip (left) and tip-nanotube interaction under 2.5 nN normal force (right) (Lucas et al., 2009), (c) stick-slip rolling model with a step rotation of a C60 molecule (Miura et al., 2003), and (d) ballistic sliding of gold nanocluster on graphite (Schirmeisen, 2010).

In the SFA experiments there is no way to determine whether shear occurs primarily within the film or is localized at the interface. The assumption, made by experimentalists, of a no-slip flow boundary condition is invalid when shear localizes at the interface. It has also not been possible to examine structural changes in shearing films directly. MD simulations offer a way to study these properties. Simulations allow one to study viscosity profiles of fluids across the slab [21], local effective viscosity inside the solid-fluid interface and in the middle part of the film [28], and actual viscosity of confined fluids [29]. Manias et al. [28] found that nearly all the shear thinning takes place inside the adsorbed layer, whereas the response of the whole film is the weighted average of the viscosity in the middle and inside the interface. Furthermore, MD simulations also allow one to examine the structures of thin films during a shear process, resulting in an atomic-scale explanation [12] of the stick-slip phenomena observed in SFA experiments of boundary lubrication [7]. 

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