Damping Tube model predictions

Turning to the behavior of typical melts, it is found that the damping function is not nearly as sensitive to molecular structure as are the linear viscoelastic properties, e.g. the storage and loss moduli. The rubberlike liquid, as well as the tube model, predict that the ratio of the first normal stress difference to the shear stress in step shear should be equal to the strain at all strains, and this is in fact observed. The other quantity measured in simple shear experiments is the second normal stress difference, but this is difficult to measure and few data are available. Of the shear histories other than step strain than have been used to study nonlinear viscoelasticity, start-up of steady simple shear has been the most used. If the shear rate is sufficiently large, some degree of chain stretch can be generated in the early stages. 

Since the arm of the star-branched chain has a free end and can contract as similar to the linear chain, the fixed tube model predicts that h y) is the same for the linear and star-branched chains. This prediction is consistent with the experimental observation (Figure 14). Furthermore, the rigorous DE damping function, numerically calculated from eqns [62a] and [62b] and shown with the dashed curve in Figure 14 (which is indistinguishable from an empirical equation fr(y) = l/(l + 0.27y ) for ySlO), is close to the h(y) data. These results have been considered to lend support to the concept of tube. 

It is of interest to note that Wagner s Eq. 10.10 predicts shear thinning, even though it does not seem to contain any feature that would represent the effect of convective constraint release. We will see later in this chapter that any form of the damping function h y) that decreases monotonically to a small value around a strain of unity will provide a rough estimate of the viscosity function. Thus, the form precise of the damping function has only a weak effect on shear thinning, and this is consistent with predictions of tube models that incorporate convective constraint release. 

Step strain experiments have been carried out using lubricated squeeze flow to determine the damping function for biaxial extension h e ). The Doi-Edwards tube model (without lA assumption) prediction of this function is as follows [24] ... 

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