Flow-induced orientation and stretching of entangled polymers

A single-mode constitutive equation is proposed which accounts, in a very simple way, for the most important feature of the molecular theory for entangled polymers based on the 'tube' concept, i.e. that the orientation of the tubes and the stretching of the chain within them relax over different time-scales. The much faster relaxation of stretch is essentially a Rouse process, whereas orientational relaxation takes place by a combination of several factors, including reptation, tube-length fluctuations and constraint release, both thermal and convective. The model presented here accounts for all of these mechanisms, albeit in a simplified way, with the exception of fluctuations, which cannot be dealt with in a single-mode theory. Extension to a multi-mode version should, however, be easy.