Elastic effects in polymer melts

Converging flow occurs in a wedge or tapering tube (restrained converging flow) and in the drawing of a molten filament (unrestrained converging flow). Polymer melts often behave very differently from Newtonian fluids under these circumstances. 

31 (A) Efflux of an elastic fluid into a narrow tube from a large reservoir. (B) Die swell at efflux of an 

In general, when a thermoplastic melt flowing in a channel encounters an abrupt decrease in channel diameter, the material conforms to a natural angle of convergence for streamline flow. Cogswell (1972) derived the following expressions  

In appendix II of this chapter the most important rheological equations for converging flow are summarised. 

In principle, extrudate swell or die swell is dependent on the terminal relaxation time and on the time of residence in a capillary. The shorter the time of residence in the capillary or the longer the relaxation time the higher the die swell. This leads to (see, e.g. Te Nijenhuis, General References, 2007, Chap. 9.4) 

When polymer melts are deformed, polymer molecules not only slide past each other, but they also tend to uncoil—or at least they are deformed from their random coiled-up configuration. On release of the deforming stresses these molecules tend to revert to random coiled-up forms. Since molecular entanglements cause the molecules to act in a co-operative manner some recovery of shape corresponding to the re-coiling occurs. In phenomenological terms we say that the melt shows elasticity. 

Such elastic effects are of great importance in polymer processing. They are dominant in determining die swell and calender swell via the phenomenon often 

If we consider the total deformation (T totai) occurring during flow to be almost entirely composed of a viscous flow (Dyisc) and a high elastic deformation due to chain uncoiling then we may write 

Viscous deformations, at a fixed deforming stress, increase rapidly with temperature whereas elastic deformations change much more slowly. For this reason the high elastic deformation component tends to be more important at lower processing temperatures than at high processing temperatures. 

Whilst the origin of such turbulence (melt fracture) remains a subject of debate it does appear to be associated with the periodic relief of built-up elastic stresses by slippage effects at or near polymer-metal interfaces. 

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Elastic effects in polymer melts, 578 Elastic moduli of some materials, 732 Elastic parameters, 383,386,391 Elastic shear deformation, 500, 531 Elastic shear quantities, 556 Electret, 329,331... 

The elastic effects in polymer melts are associated with the molecular coil deformation shown in Fig. 3.9. The effects include die swell, a diameter increase when the melt exits from a die and flow instabilities such as melt fracture (causing a rough surface). One measure of the elastic effects is the tensile stress difference — a-yy that occurs in shear flow in the xy axes. There can be a tensile stress in the direction of flow, or a compressive stress (Tyy on the channel walls, or a combination of the two. Figure 5.7 shows that, as the shear rate increases, the value of m... 

Schreiber.H. P., Rudin, A., Bagley.E.B. Separation of elastic and viscous effects in polymer melt extrusion. J. Appl. Polymer Sci. 9,887-892 (1965). 

In general, the reasonable agreement between the predicted and measured values of the elastic modulus suggests that the effect of swelling on the elastic properties can be approximated as a sum of two distinct contributions one due to the chemical crosslinks and the other due to the entanglements. The latter in polymer melts is independent of chain lengths and represent an entanglement contribution... 

Accurate description of flow of the polymer melt through the die requires knowledge of the viscoelastic behavior of the polymer melt. The polymer melt can no longer be considered a purely viscous fluid because elastic effects in the die region can be significant. Unfortunately, there are no simple constitutive equations that adequately describe the flow behavior of polymer melt over a wide range of flow conditions. Thus, a simple die flow analysis is generally very approximate, while more accurate die flow analyses tend to be quite complicated. 

All of these melt studies were based on consideration of the melt as a liquid, but the early work on application properties where from the solid mechanics point of view. Elastic effects were also very important in the melt state. Consideration of the viscoelastic characteristics of polymers in both the liquid and solid states led to the investigation of the elastic, or solid like, behavior of polymer melts. Studies of the recoverable strain in polymer melts indicated that if the molecular weight was high enough the melt exhibited almost a one-hundred percent recovery. Obviously true understanding of melt processing required consideration of both the viscous and elastic behavior. 

The thermal expansion effect can be estimated in a simplified way. Suppose that the initial average volume of voids in the composite is V , the temperature is Tq, and the corresponding pressure is p . Suppose that the air inside the void can be assumed as the ideal gas. During the reheating process, the temperature of the air increases from Tq to Tand correspondingly the voids expand from V to Vg. Let the external pressure remain in the whole process. Then, ignoring the constraints of the elasticity of the polymer melt and surface tension, the equilibrium of the void expansion yields... 

Once in a while, polymer systems will falsely appear to be thixotropic or rheopectic. Careful checking (including before and after molecular weight determinations) invariably shows that the phenomenon is not reversible and is due to degradation or crosslinking of the polymer when in the viscometer for long periods of time, particularly at elevated temperatures. Other transient time-dependent effects in polymers are due to elasticity, and will be considered later, but for chemically stable polymer melts or solutions, the steady-state viscous properties are time independent. We treat only such systems from here on. 

Melt Viscosity. The study of the viscosity of polymer melts (43—55) is important for the manufacturer who must supply suitable materials and for the fabrication engineer who must select polymers and fabrication methods. Thus melt viscosity as a function of temperature, pressure, rate of flow, and polymer molecular weight and stmcture is of considerable practical importance. Polymer melts exhibit elastic as well as viscous properties. This is evident in the swell of the polymer melt upon emergence from an extmsion die, a behavior that results from the recovery of stored elastic energy plus normal stress effects. 

Viscoelastic Measurement. A number of methods measure the various quantities that describe viscoelastic behavior. Some requite expensive commercial rheometers, others depend on custom-made research instmments, and a few requite only simple devices. Even quaHtative observations can be useful in the case of polymer melts, paints, and resins, where elasticity may indicate an inferior batch or unusable formulation. Eor example, the extmsion sweU of a material from a syringe can be observed with a microscope. The Weissenberg effect is seen in the separation of a cone and plate during viscosity measurements or the climbing of a resin up the stirrer shaft during polymerization or mixing. 

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