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 N-e, 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 N-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 N-c (N-c = N-e(5/3))separates two behaviors: for N > N-c, we recover two regimes, reptation and Stobes-Einstein, as predicted long ago by Daoud and de Gennes; For N < N-c, 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.