Analysis of Slow Modes in Ring Polymers: Threading of Rings Controls Long-Time Relaxation

Atomistic configurations of pure, precisely monodisperse ring poly(ethylene oxide) (PEO) melts accumulated in the course of very long molecular dynamics (MD) simulations at T = 413 K and P = 1 atm have been subjected to a detailed geometric analysis involving three steps (reduction to ensembles of coarse-grained paths, triangulation of the resulting three-dimensional polygons, and analysis of interpenetrations using vector calculus) in order to locate ring-ring threading events and quantify their strength and survival times. A variety of threading situations have been identified corresponding to single and multiple penetrations. The percentage of inter-ring threadings that correspond to full penetrations has also been quantified. By repeating the analysis for several PEO melts, the dependence of the degree of inter-ring threading on molecular weight (MW) has been obtained. Simulations with MWs up to 10 times the reported entanglement molecular weight (M_e) of linear PEO have revealed several multiple threading events in all systems, with their relative number increasing with increasing MW. Our analysis indicates the existence of strong ring-ring topological interactions, which can last up to several times the corresponding average orientational ring polymer relaxation time. We show that these ring-ring interactions, together with the additional ring-linear threadings due to the remaining linear impurities, can explain the appearance of slow relaxation modes observed experimentally in entangled rings.