Dynamics and rheology of entangled linear polymers

In order to describe the dynamics of the linear polymer in monodisperse melts, we present the so-called reaction–diffusion type equation that contains contributions from reptation and contour-length fluctuation based on the tube model. The relaxation function calculated from this equation is in good agreement with the experimental results of the dielectric relaxation function and also gives the stress relaxation function in binary blends by use of semi-empirical scheme called double reptation. We add advection term to this equation in order to predict the nonlinear rheological properties of steady shear. The calculated shear stress and the first normal stress difference at steady state agree well with the measurements.