Viscoelastic Behavior in the Terminal Zone

Other features of the viscoelastic behavior in the terminal zone are represented by the constants rjo and Rearrangement of equations 7 and 9, together in the equation 51 of Chapter 9 with omission of r)s as appropriate for undiluted polymer, gives for these quantities... 

The dependence of the non-Newtonian viscosity jj on shear rate at relatively low shear rates is a property which can be classed with viscoelastic behavior in the terminal zone, since it reflects long-range conHgurational motions which are influenced by entanglements to the maximum degree. As pointed out in Chapter 10, the characteristic time r, which specifies the onset of non-Newtonian, behavior with increasing shear rate is closely related to the terminal viscoelastic relaxation time. (In this discussion of shear viscosity, the subscript 21 will be omitted from stress [Pg.380]

Isothermal measurements of the dynamic mechanical behavior as a function of frequency were carried out on the five materials listed in Table I. Numerous isotherms were obtained in order to describe the behavior in the rubbery plateau and in the terminal zone of the viscoelastic response curves. An example of such data is shown in Figure 6 where the storage shear modulus for copolymer 2148 (1/2) is plotted against frequency at 10 different temperatures. 

The influence of particulate fillers mixed with a polymer on the linear viscoelastic properties in the transition zone have been discussed briefly in Section C4 of Chapter 12. We now discuss briefly their effects in the plateau and terminal zones and at equilibrium, including nonlinear behavior. 

Some practical aspects of viscoelastic behavior in dilute solutions (Chapter 9, Section G) and in the terminal zone (Chapter 10, Section C5) have already been mentioned others are inherent in Chapters 16 and 17. We now call attention to some additional applications. 

The practical significance of the terminal relaxation time r in several qualitative aspects of behavior has already been mentioned in connection with equation 7 for polymers of low molecular weight. The same considerations apply to polymers of high molecular weight, where t (or Ta, in the framework of the tube model) and the other two viscoelastic constants ijo and Jg which characterize the terminal zone are even more important in the processing and use of polymeric materials. Rough estimates of these quantities can sometimes be made from the equations in Section C3 above for practical purposes. 

Small-amplitude oscillatory shear is the technique most often used to determine the linear viscoelastic characteristics of a molten polymer. Figure 5.5 shows the storage modulus for the samples whose relaxation moduli are shown in Fig. 5.2. Note that logarithmic scales have been used for both axes. The same features are present as in a plot of G(f), but the terminal zone is now found at the left end of the curve, while the short-time response corresponds to high-frequency behavior. And here again it is the behavior in the plateau and terminal zones that is sensitive to molecular structure and is thus of primary interest in this book. 

---