A UNIFIED THEORY OF THE DYNAMICS OF LINEAR-CHAIN MACROMOLECULES - FROM UNENTANGLED TO ENTANGLED POLYMER FLUIDS

We present an analytically tractable model of the dynamics of a flexible linear polymer. The polymer is presented by a freely jointed chain that undergoes two types of motion. The first motion is a slithering along its contour that mimics reptation. The second type of motion is a generalization of the Stockmayer "kink-jump" algorithm that includes the effects of a medium that relaxes with a finite time scale. A fixed fraction of the beads are immobilized by obstacles that relax with a rate whose magnitude may be smaller than, larger than, or comparable to the rate at which a bead executes jumps in the absence of obstacles. The calculation of observables such as the autocorrelation function of the end-to-end vector, viscoelastic moduli, and the diffusion coefficient is related to the solution of a set of random walk problems with dynamical disorder. Analytical results based on the dynamical effective medium approximation are presented. Our results recover the behavior of an isolated (Rouse) chain and of a reptating chain in an entangled melt as limiting cases, and describe the crossover regime between these limits.