Stress Relaxation of Star-Shaped Molecules in a Polymer Melt

Abstract

We present a theoretical study of stress relaxation of star-shaped polymers starting from a Rouse model for a polymer in a tube. Instead of focusing on the potential in which the chain moves, we mathematically study the Rouse equation with a time-dependent boundary condition. This boundary condition arises as a consequence of tube dilution, which is implemented in the model through a tube diameter that increases with time, depending on position along the tube. We derive a Fokker−Planck equation for the probability distribution of the position of the chain end and find an analytical expression for the mean first passage time. Our approach helps identifying the origin of the potentials, which are commonly used in existing models for stress relaxation in star polymers. Moreover, it clearly displays the underlying approximations and allows easy generalization to the case of a tethered chain in a flow.