Intermediate Time Sub-Diffusion and Stress Relaxation in Ring Polymer Melts

The slow dynamics of dense non-concatenated rings melts remains a frontier problem in polymer science including implications for cellular biophysics. Here we report large-scale simulations of model ring melts that analyze the monomer and center-of-mass (CM) mean square displacements (MSD) and stress relaxation function on intermediate time and length scales. The degree of dynamical slowing down is characterized by the maximally sub-diffusive fractional time scaling exponents. The data span an exceptionally wide range of ring degrees of polymerization and stiffnesses and is not successfully organized based on the classic measure linear chain entanglement, N/Ne. Rather, we find the crossover degree of polymerization, ND, based on ring macromolecular caging that successfully allows master curves to be constructed for the long-time CM self-diffusion constant also collapses these temporal dynamic scaling exponents. Different properties display different exponents, and exhibit one or two regimes of linear variation with the logarithm of ND/N. A distinct crossover of the CM-MSD and stress relaxation exponents emerges at sufficiently large N or stiffness that is not found for the monomer MSD, indicating a novel form of dynamic decoupling. This crossover aligns with the predicted critical degree of polymerization for transitioning from a weak to strong caging regime indicative of activated transport. The latter may reflect the emergence of an intermolecular collective contribution to stress in analogy with dense soft colloidal matter. Suggestions are made for future theoretical work to address the rich patterns of behavior discovered.