Dynamics of Stars and Linear Chains Dissolved in a Polymer Melt

We derive the mobility and the relaxation time of stars (with g arms of Z monomers each) or long linear Z-mers embedded in a homopolymer melt of linear chains of N monomers, using a dissipation approach recently proposed by de Gennes.20 For stars, we expect three main regimes depending on Z, N, and Ne, the number of monomers between entanglements. These regimes correspond to different relaxation mechanisms: (1) arm retraction; (2) " Rouse-like " or " Stokes-like " constraint release, in which the stars relax by reptation of surrounding iV-mers; (3) Stokes-Einstein regime, in which the stars, ideal or swollen, move like compact spheres in a viscous solvent. For linear chains, a critical value Nc (Nc = 1V " 6/3) separates two behaviors: forN\textgreater Nc, we recover two regimes, reptation and Stokes-Einstein, as predicted long ago by Daoud and de Gennes; For N \textless Nc, an extra Rouse-like constraint release regime shows up between the two mentioned above. This may explain experimental results showing that tube renewal processes are important for stars and also for linear chains.