Nonlinear viscoelasticity flexible polymers

Accordingly, given the necessity from equilibrium coil dimensions that bt> 1, the shear rate and frequency departures predicted by FENE dumbbells are displaced from each other. Moreover, the displacement increases with chain length. This is a clearly inconsistent with experimental behavior at all levels of concentration, including infinite dilution. Thus, finite extensibility must fail as a general model for the onset of nonlinear viscoelastic behavior in flexible polymer systems. It could, of course, become important in some situations, such as in elongational and shear flows at very high rates of deformation. 

As remarked earlier, the nonlinear viscoelastic behavior of entangled wormy micellar solutions is similar to that of entangled flexible polymer molecules. Cates and coworkers (Cates 1990 Spenley et al. 1993, 1996) derived a full constitutive equation for entangled wormy micellar solutions, based on suitably modified reptation ideas. The stress tensor obtained from this theory is (Spenley et al. 1993)... 

More evidence comes from the study of viscoelasticity, which has been done extensively in the past and established the characteristic aspects common to all flexible polymers. The reptation model has succeeded in explaining many of these features and also predicting some of the behaviour in nonlinear viscoelasticity. In this chapter we shall describe the reptation theory for viscoelasticity in detail, and discuss the validity of the reptation model in solutions and melts. 

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