Dynamics of entangled associating polymers with large aggregates

We develop a theory for the dynamics in entangled solutions of associating polymers with many stickers per chain. The stickers strongly associate and form large aggregates that control both the equilibrium structure of the system and its dynamics. The association results in formation of micelles that separate macroscopically yielding a reversible gel phase of interconnected, closely packed micelles. We identify two mechanisms for stress relaxation: (a) polymer chain diffusion and (b) positional rearrangements of the micelles, and predict that the second process is exponentially slower than chain diffusion. Hence, a polymer chain may diffuse through many of its gyration radii during the terminal stress relaxation time. We predict an exponentially strong concentration dependence of the micellar gel viscosity typically involving one or more anomalous regimes where the viscosity is decreasing with concentration. We also show that the chain self-diffusion constant decreases exponentially with concentration in the strongly entangled regime (entangled spacers connecting the stickers).