Dynamic Heterogeneity in Ring-Linear Polymer Blends

Abstract

We present results from a direct statistical analysis of long molecular dynamics (MD) trajectories for the orientational relaxation of individual ring molecules in blends with equivalent linear chains. Our analysis reveals a very broad distribution of ring relaxation times whose width increases with increasing ring/linear molecular length and increasing concentration of the blend in linear chains. Dynamic heterogeneity is also observed in the pure ring melts but to a lesser extent. The enhanced degree of dynamic heterogeneity in the blends arises from the substantial increase in the intrinsic timescales of a large subpopulation of ring molecules due to their involvement in strong threading events with a certain population of the linear chains present in the blend. Our analysis suggests that the relaxation dynamics of the rings are controlled by the different states of their threading by linear chains. Unthreaded or singly-threaded rings exhibit terminal relaxation very similar to that in their own melt, but multiply-threaded rings relax much slower due to the long lifetimes of the corresponding topological interactions. By further analyzing the MD data for ring molecule terminal relaxation in terms of the sum of simple exponential functions we have been able to quantify the characteristic relaxation times of the corresponding mechanisms contributing to ring relaxation both in their pure melts and in the blends, and their relative importance. The extra contribution due to ring-linear threadings in the blends becomes immediately apparent through such an analysis.

Dynamics and Rheology of Ring-Linear Blend Semidilute Solutions in Extensional Flow: Single Molecule Experiments

“…In particular, the fraction of double-mode relaxation trajectories shows a maximum for ring-linear blends with 17% R-83% L composition and decreases upon further increases in ring fraction. A similar trend of heterogeneous relaxation of ring polymers was recently observed in ringlinear blend melts using MD simulations [69], where the distribution width of different relaxation modes for rings decreased with increasing ring composition in the blend. However, it is important to note that the heterogeneous relaxation behavior for rings observed here is qualitatively different than the relaxation of linear polymers in ultra-dilute solutions (10 −5 c * ) [42], linear polymers in semidilute solutions of purely linear chains [48,51], and ring polymers in ultra-dilute solutions (10 [52, 53], all of which exhibit a simple single-mode exponential decay for polymer relaxation in the terminal regime.…”

Linear Catenanes in Channel Confinement

“…We further examined the characteristic reorientation time of the rings, τ TACF . Following ref , we consider the generalization to circular chains of the time-lagged terminal autocorrelation function (TACF) of linear chains: C TACF false( τ false) = ⟨ d̂ i , i + m / 2 false( t + τ false) · d̂ i , i + m / 2 false( t false) ⟩ t , i where d̂ i , i + m / 2 is the normalized distance vector (diameter) of beads i and i + m /2; ⟨ ⟩ i , t indicates averaging over time and bead index i . C TACF thus measures the time-lagged orientational correlation of all diameters of the ring of interest.…”

Molecular Dynamics Simulations of Ring Shapes on a Ring Fraction in Ring–Linear Polymer Blends

“…Topological effects (threading) between a ring and a linear chain cause slow dynamics in ring–linear blends. Even for pure linear chains, slow dynamics occur owing to another topological effect (entanglement) that prevents chains from crossing each other. , Recently, the threading behavior of ring–linear polymer blends − and the ring polymer melts − has been extensively examined. From the experiments and simulations of ring–linear polymer melts under uniaxial elongational flow, it was found that the ring dynamics was strongly affected by the presence of even a few linear chains through threading.…”

“…In particular, λ 1 /λ 3 and λ 2 /λ 3 ratios increased with the decreasing f ring . Mavrantzas et al studied the polymer melts of poly­(ethylene oxide) rings threaded with linear chains , and the dynamic heterogeneity of ring–linear blends . They found that the dynamics in ring–linear polymer blends is highly heterogeneous due to extensive threading where the linear chains dramatically obstructed the mobility of the rings.…”