Entangled system dynamic modulus

The difference in the molecular-weight dependence of the terminal relaxation time can be attributed to the change of the mechanisms (diffusive and repta-tion, correspondingly) of conformational relaxation in these systems. Further on in this section, we shall calculate dynamic modulus and discuss characteristic quantities both for weakly and strongly entangled systems. 

We are calculating dynamic modulus and characteristic quantities for entangled systems, when the linear approximation of dynamic equation is used. 

Thus in the mesoscopic approximation or, in other words, in the mean-field approximation, the dynamic shear modulus of the melt or the concentrated solution of the polymer (strongly entangled systems) is represented by a function of a small number of parameters... 

For the weakly entangled system, the steady-state modulus depends on the molecular weight of polymer as M 1, while for strongly entangled system, the steady-state modulus does not depend on the molecular weight of polymer, which is consistent with typical experimental data for concentrated polymer systems (Graessley 1974). The expression for the modulus is exactly the same as for the plateau value of the dynamic modulus (equations (6.52) and (6.58)) Expressions (9.42) lead to the following relation for the ratio of the normal stresses differences... 

Data for a 60 mole % PHB/PET system are shown in Figure 20, We observe at all strain levels that G continues to relax to zero rather than approach a plateau as would be the case when a yield stress exists. The relaxation modulus also seems to be highly stain dependent which is in contrast to the fact that dynamic and steady shear material functions agree so well. For flexible chain polymers the strain dependence of G is associated with the rate of loss of entanglements. For LCP it is not clear as to the significance of the strain dependence of G. 

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