Stick-slip transition

Stick-Slip Transitions from an Equilibrium Perspective... 

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... 

So far we have compared the static friction with the stick-slip transition. In both cases the system has to choose between the states of rest and motion, depending on which one is more favorable to the energy minimization. On the other hand, the differences between the two processes deserve a discussion, too. In stick-slip, when the moving surface slides in an average velocity V, there is a characteristic time, t =d.Ql V, that defines how long the two surfaces can... 

In static friction, the change of state from rest to motion is caused by the same mechanism as the stick-slip transition. The creation of static friction is in fact a matter of choice of system state for a more stable and favorable energy condition, and thus does not have to be interpreted in terms of plastic deformation and shear of materials at adhesive junctions. 

Fig. 1. Typical flow curve of commercial LPE. There are five characteristic flow regimes (i) Newtonian (ii) shear thinning (iii) sharkskin (iv) flow discontinuity or stick-slip transition in controlled stress, and oscillating flow in controlled rate (v) slip flow. There are three leading types of extrudate distortion (a) sharkskin like, (b) alternating bamboo like in the shaded region, and (c) spiral like on the slip branch. Industrial extrusion of polyethylenes is most concerned with flow instabilities occurring in regimes (iii) to (v) where the three kinds of extrudate distortion must be dealt with. The unit shows the approximate levels of stress where the sharkskin and flow discontinuity occur respectively. There is appreciable molecular weight and temperature dependence of the critical stress for the discontinuity. Other highly entangled melts such as 1,4 polybutadienes also exhibit most of the features illustrated herein...

Fig. 6. A rough surface of die wall, where the stagnant (thin) chains allow the unbound chains (the middle thick chain without dot) to entangle and adsorb at the effective interface (dashed line). Adsorbed chains (thick chains with dots) are also present. Such an interface can also produce a stick-slip transition upon a coil-stretch transition involving the thick chains. See Ref. [27]. For clarity, we only draw three tethered chains (two adsorbed and one entangled) besides the stagnant chains in one valley. The chains not drawn here, of course, fill up all the space away from the rough wall...

The only observation of a stick-slip transition in a simple shear geometry is the unique experimental study of Laun [39]. This controlled stress experiment not only observed a stick-slip transition but also explicitly recorded the time scale (a few milliseconds) on which the boundary condition (BC) evolved from... 

Many polymers exhibit neither a measurable stick-slip transition nor flow oscillation. For example, commercial polystyrene (PS), polypropylene (PP), and low density polyethylene (LDPE) usually do not undergo a flow discontinuity transition nor oscillating flow. This does not mean that their extrudate would remain smooth. The often observed spiral-like extrudate distortion of PS, LDPE and PP, among other polymer melts, normally arises from a secondary (vortex) flow in the barrel due to a sharp die entry and is unrelated to interfacial slip. Section 11 discusses this type of extrudate distortion in some detail. Here we focus on the question of why polymers such as PS often do not exhibit interfacial flow instabilities and flow discontinuity. The answer is contained in the celebrated formula Eqs. (3) or (5). For a polymer to show an observable wall slip on a length scale of 1 mm requires a viscosity ratio q/q equal to 105 or larger. In other words, there should be a sufficient level of bulk chain entanglement at the critical stress for an interfacial breakdown (i.e., disentanglement transition between adsorbed and unbound chains). The above-mentioned commercial polymers do not meet this criterion. 

It was thought in the past that the only mechanism for wall slip would be polymer desorption, i.e., an adhesive breakdown [25, 53]. However, lack of a strong temperature dependence would be inconsistent with an activation process of chain desorption. Since the onset of the flow discontinuity (i.e., stick-slip) transition was found to occur at about the same stress over a range of experimental temperatures, it was concluded from the outset [9] that the phenomena could not possibly have an interfacial origin. Thus, the idea of regarding the flow discontinuity as interfacial did not receive sufficient and convincing theoretical and experimental support in the past, not only because the transition was often accompanied by severe extrudate distortion and hysteresis, but also because the molecular mechanism for such an interfacial transition involving wall slip was elusive. 

Fig. 12. Temperature dependence of a stick-slip transition of an HDPE (MH20 of Mw= 316,600) from BP Chemicals in the controlled pressure mode using a capillary die of L/D= 15 and D=1.0mm, reproduced from [29]. The identical amplitude observed at different temperatures is an impressive feature of the interfacial transition...

Critical Condition and Molecular Characteristics of Stick-Slip Transition... 

Linear polyethylenes (PE) are one polymer that possess an important ingredient necessary for a display of interfacial stick-slip transition. In the past, the coincidence that PE is both the most widely used polymer and most prone to suffer from melt flow instabilities has challenged the PE industry. Today we still face the task of how to effectively remove instabilities that result in various types of extrudate distortions. 

Thus Eq. (9) shows that the number density v of chains entangled with the loops in Fig. 5c would indeed have an Mw 11 5 dependence. When each of these adsorbed chains experiences a critical force of Fe they become disentangled and a stick-slip transition follows as observed in Fig. 12. The molecular weight dependence of the critical stress given by the combination of Eqs. (6) and (9) explains the experimental finding [27] for linear polyethylenes. ... 

Substituting Eq. (9) into Eq. (6), we obtain the following estimate of the critical stress oc for the stick-slip transition ... 

The molecular meaning of b is best seen from the second or third equality of Eq. (3). In other words, b is explicitly related to the steady shear melt viscosity q and depends on the chain-chain interactions near the melt/wall interface as quantified by the friction coefficient p. In the limit of no polymer adsorption or in absence of interfacial chain entanglements due to the coil-stretch transition, P involves an interfacial viscosity q , which is as small as the viscosity of a monomeric liquid and independent of the molecular weight Mw p=qj/a, where a is a molecular length. Thus at the stick-slip transition, the molecular weight dependence of b arises entirely from q in Eq. (3). 

Having unraveled the specific characteristics of the stick-slip transition, it is rather straightforward to describe the physical origin of the oscillating flow ob-... 

We have presented a thorough description and discussion about the molecular origin of the second kind (b) - bamboo like extrudate distortion - in the preceding Sect. 8. The present section is devoted to a specific illustration of the molecular origin of the type (a) distortion, i.e., sharkskin, which occurs in a range of stress/rate below the oscillatory flow or stick-slip transition, as indicated in Fig. 1. The next section will provide a brief discussion of the origin of the type (c), often spiral-like distortion. The macroscopic nature of the type (c) distortion was first discussed at least over 20 years ago [75]. Note that when the type (c) spiral distortion occurs on very fine length scales on the extrudate it can be and has sometimes been mistaken as sharkskin. 

Second, we have learned from our investigation of the molecular origin of the stick-slip transition that adsorbed linear chains undergo a coil-stretch transition and produce a slip boundary condition above a critical stress gc [27-29]. The adsorbed chains at the die exit rim are expected to undergo a coil-stretch transition at nominal stresses Gpeak stress Gex exceeds Gc. At the present, we do not know much about how Gex increases with G, i.e., we do not know the explicit shape of the stress distribution depicted by the thick curve in Fig. 15. 

Acknowledgements. The author would like to acknowledge the M.S. research work of P.A. Drda and sharkskin measurements by Y.W. Inn that have been discussed here. Several more discussions were made possible due to the unpublished data on monodisperse PB melts by X. Yang. The author is grateful to H. Ishida for use of the instrumental Monsanto Capillary Rheometer to collect much of the experimental data discussed here. He thanks L. Leibler for pointing out the usefulness to evaluate the value of the critical stress for the stick-slip transition in terms of melt chain statistics. The financial support of the National Science Foundation (Grant No. CTS-9632466) and BP Chemicals is greatly appreciated. 

An important element in melt fracture is also wall slip phenomenon [5, 49]. It is related to the so-called sharkskin, or sharkskin melt fracture, which is also called surface melt fracture. It is a low amplitude surface distortion of extruded polymer. Sharkskin is generally observed in case of linear polymers with narrow MWD, below the oscillating stick-slip transition. Sometimes (but not always), there is a change... 

Fig. 7.17 Illustration of conformation change in relation with the stick-slip transition near the tube wall of the exit, with the increase of shear rates of polymer coils...

With the increase of flow velocity, polymer melt extruded in the tube will become unstable due to the stick-slip transition near the tube wall, which makes the extrudate shows wave-like, bamboo-Uke, or spiral-like distortions. All these phenomena are known as melt-broken phenomena. In these cases, the shear rate suddenly rises, as illustrated in Fig. 7.17, thus this behavior is also called capillary-jet phenomenon. The string-Uke shark-skin phenomenon upon the extrusion of polyethylene melt can be attributed to the intermittent stick-slip transition near the tube wall of the exit (Wang 1999). 

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