Stick-slip motions

Klein and co-workers have documented the remarkable lubricating attributes of polymer brushes tethered to surfaces by one end only [56], Studying zwitterionic polystyrene-X attached to mica by the zwitterion end group in a surface forces apparatus, they found /i < 0.001 for loads of 100 and speeds of 15-450 nm/sec. They attributed the low friction to strong repulsions existing between such polymer layers. At higher compression, stick-slip motion was observed. In a related study, they compared the friction between polymer brushes in toluene (ji < 0.005) to that of mica in pure toluene /t = 0.7 [57]. 

Yoshizawa FI, McGuiggan P and Israelaohvili J N 1993 Identification of a second dynamic state during stick-slip motion Science 259 1305-8... 

Figure C2.9.2 Shear force versus time during (a) sliding and (b) stick-slip motion. The motion of the surface beneath the sliding block of figure C2.9.1 is at constant velocity.

M. G. Rozman, M. Urbakh, J. Klafter. Stick-slip motion and force fluctuations in a driven two-wave potential. Phys Rev Lett 77 683-686, 1996. 

A torque feedback system has been developed to dampen the surface torque oscillations and consequently the stick-slip motion at the bit. The system consists of (see Figure 4-309)... 

Stick-slip motion is another issue that has been explored using SFA. It is found that the occurrence of stick-slip depends on the sliding velocity and the stiffness of the system, and the mechanism of the phenomenon can be interpreted in terms of periodic transition between liquid and solid states of the conhned lubricant [40],... 

The solidihed layer yields and returns to the liquid phase if the shear stress excesses the critical value, which initiates the sliding. When the stress is relaxed as a result of slip, the solid phase resumes again. The periodic transition between the solid and liquid states has been interpreted in the literature as a major cause of the stick-slip motion in lubricated sliding. Understanding the stick-slip and static friction in terms of solid-liquid transitions in thin films makes a re-... 

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]. 

Fig. 19—Shear stress and chain angle as a function of sliding distance, from simulations of alkanethiolates on Au(111) at temperature 1 K (a) results from commensurate sliding show a stick-slip motion with a period of 2.5 A, (b) in incommensurate case both shear stress and chain angle exhibit random fluctuations with a much smaller average friction [45],...

In the studies that attribute the boundary friction to confined liquid, on the other hand, the interests are mostly in understanding the role of the spatial arrangement of lubricant molecules, e.g., the molecular ordering and transitions among solid, liquid, and amorphous states. It has been proposed in the models of confined liquid, for example, that a periodic phase transition of lubricant between frozen and melting states, which can be detected in the process of sliding, is responsible for the occurrence of the stick-slip motions, but this model is unable to explain how the chemical natures of lubricant molecules would change the performance of boundary lubrication. 

The example demonstrates that the instability and consequent energy dissipation, similar to those in the Tomlinson model, do exist in a real molecule system. Keep in mind, however, that it is observed only in a commensurate system in which the lattice constants of two monolayers are in a ratio of rational value. For incommensurate sliding, the situation is totally different. Results shown in Fig. 21(b) were obtained under the same conditions as those in Fig. 21 (a), but from an incommensurate system. The lateral force and tilt angle in Fig. 21(b) fluctuate randomly and no stick-slip motion is observed. In addition, the average lateral force is found much smaller, about one-fifth of the commensurate one. 

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. 

The mechanisms of static friction and stick-slip motion, as discussed in the last section, are supposed to be a good description of dry friction. Another case, perhaps more general in engineering practices, to be addressed in this section is lubricated sliding where liquid lubricant, consisting of a few molecule layers, is confined between two solid walls. Both experimental and theoretical studies indicate, as we have discussed in Chapter 5, that there are substantial changes in rheology of the confined lubricant, and the liquid may transit practically to a solid-like state when film thickness becomes molecularly thin [32,33]. 

At the beginning of sliding, the system is accelerated because the driven force must excess the resistance from lubricating film. For this reason, the system actually jumps from A to the point B, instead of B, to gain a shear stress lower than the critical value This phenomenon, so called velocity-weakening has been regarded widely in the literatures as the cause for instability and stick-slip motion in lubricated systems. 

Friction and Atomic Level Stick-Slip Motion. 

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). 

As we have seen in Section 6.6.1 such confined liquids may behave quite differently from the bulk lubricant. Near the surfaces, the formation of layered structures can lead to an oscillatory density profile (see Fig. 6.12). When these layered structures start to overlap, the confined liquid may undergo a phase transition to a crystalline or glassy state, as observed in surface force apparatus experiments [471,497-500], This is correlated with a strong increase in viscosity. Shearing of such solidified films, may lead to stick-slip motions. When a critical shear strength is exceeded, the film liquefies. The system relaxes by relative movement of the surfaces and the lubricant solidifies again. 

Friction modifiers Compounds like fatty acids form physisorbed layers on the metal surfaces. They reduce friction under conditions of mixed lubrication and help to avoid stick-slip motion. 

The coefficient of friction, as ordinarily measured, is shown clearly by the discovery of the stick-slip motion to be an average value of a rapidly... 

It may be mentioned here that a recent study (Vasconcelos 1996) of a simple noncooperative (one-block) model of stick-slip motion (described by eqn (4.2) with / o = 0 or eqn (4.4) with k = 0) shows discontinuous velocity-dependent transition in the block displacement, for generic velocity-dependent friction forces. Naive generalisation of this observation for the coupled Burridge-Knopoff model would indicate a possible absence of criticality in the model. 

Figure 13. Force per unit area/ wall displacement x and the Debye Waller fact e " as a function of time t during stick-slip motion for U= fyi k=1.2mi, eJs=2, and a,ya=l. The walls are fee solids with (111) surfeces, and the shear direction was (100) [12].

As argued by Fisher, pinned and sliding solutions can only coexist in some range of the externally applied force if the inertial term exceeds a certain threshold value [29]. This can lead to stick-slip motion as described in Section VI.A. For sufficiently small inertial terms, Middleton [85] has shown for a wide class of models, which includes the PT model as a special case, that the transition between pinned and sliding states is nonhysteretic and that there is a unique average value of F which does depend on vq but not on the initial microstate. The instantaneous value of Fk can nevertheless fluctuate, and the maximum of Fk can be used as a lower bound for the static friction force Fg. The measured values of Fj can also fluctuate, because unlike Fk they may depend on the initial microstate of the system [85]. 

The dynamics of shding systems can be very complex and depend on many factors, including the types of metastable states in the system, the times needed to transform between states, and the mechanical properties of the device that imposes the stress. At high rates or stresses, systems usually slide smoothly. At low rates the motion often becomes intermittent, with the system alternately sticking and slipping forward [31,44]. Everyday examples of such stick slip motion include the squeak of hinges and the music of violins. 

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