Dynamic Heterogeneity in Entangled Linear and Ring Polymers: Single Molecule Studies Reveal Surprises due to Molecular Architecture

We directly observe the non-equilibrium dynamics of single ring polymers suspended in semi-dilute solutions of linear chains. Our results show that ring polymers fluctuate drastically in chain extension even at steady-state, yet ring polymers exhibit markedly less molecular individualism during transient stretching compared to linear chains. We hypothesize that ring polymer extension fluctuations arise due to threading of linear polymers through open ring polymer chains in flow. The fluctuation frequency as a function of strain rate and concentration is quantified, and trends are consistent with increasing concentration. We further study the relaxation of linear polymers in entangled solutions of purely linear chains. Our results show dynamic heterogeneity in relaxation such that single polymer relaxation trajectories exhibit either a single-mode or double-mode exponential decay, which starkly contrasts relaxation behaviors from dilute and semi-dilute unentangled solutions. We interpret the power law scalings of these relaxation times as a function of concentration, and our single molecule results are discussed in the context of the classic tube model and reptation theory. Our results show that molecular behavior is markedly heterogeneous in non-dilute polymer solutions.