Dynamics of stars and linear chains dissolved in a polymer melt

Abstract

We derive the mobility and the relaxation time of stars (with g arms of 2 monomers each) or long linear 2-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 2, N, and Ne, the number of monomers between entanglements. These regimes correspond to different relaxation mechanisms: (1) arm retraction; (2) 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, (N, = N,6/3) separates two behaviors: for N > N,, we recover two regimes, reptation and Stokes-Einstein, as predicted long ago by Daoud and de Gennes; For N < N,, 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. OO~~-~~~~I~~~~~~