Constitutive equations for weakly entangled linear polymers

To interpret the viscoelastic behaviour of entangled linear polymers in terms of dynamics of a single macromolecule, we have been developing the approach, which allows one to study systematically deviations from the Rouse dynamics, when adding non-Markovian and anisotropic noise. It was shown earlier, that the introduction of specific form of non-Markovian dynamics leads to emerging of an intermediate length, which has the meaning of a tube radius and/or the length of a macromolecule between adjacent entanglements. The additional introduction of local anisotropy of mobility of particles allows one to get the results of the conventional reptation-tube model for both mobility and relaxation times of macromolecular coil and, beyond it, to estimate a transition point between weakly (the length of macromolecules M<10MeM<10Me, no reptation) and strongly (the length of macromolecules M>10MeM>10Me, reptation) entangled polymer systems. The adequate mesoscopic equation allows us to develop theory of different relaxation phenomena, in particular, a theory of viscoelasticity and to formulate constitutive equations for linear polymers, which, due to the difference of mechanisms of relaxation, appear to be different for the two types of entangled systems.