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.
Highlights
Orientational relaxation in polymers is typically quantified by examining the rate of decay of the time autocorrelation function (TACF) of a unit vector directed along the longest polymer distance and computing the time needed for this function to drop to zero
As we have shown in a recent publication [14], ring relaxation in the blends is dramatically affected by the intensity of regular or transient threading events that ring molecules undergo with the linear chains present in the melt, and how fast these are created or released [13]
A detailed analysis of molecular dynamics (MD) data for the orientational dynamics of ring molecules in blends with equivalent linear chains has revealed strong heterogeneities in their orientational relaxation, which become more pronounced as their molecular length or the concentration of the blend in linear chains increases
Summary
Orientational relaxation in polymers is typically quantified by examining the rate of decay of the time autocorrelation function (TACF) of a unit vector directed along the longest polymer distance and computing the time needed for this function to drop to zero. Using SMFM techniques, Zhou et al [8] have examined the relaxation dynamics and transient stretching behavior of DNA rings in semidilute unentangled linear DNA solutions They found that rings undergoing extensional flow exhibit a broad distribution of conformations, even for times long after the stretching process has stopped. From a simulation point of view, the individual behavior of rings in matrices of linear chains at the molecular level under equilibrium conditions has been addressed through Monte Carlo simulations by Yang et al [9] These authors found that short rings exhibit structural and dynamic heterogeneity due to different threading states of certain subpopulations of the ring molecules, suggesting that ring diffusion involves a combination of elements from three different mechanisms: (a) constraint release [10]; (b) restricted reptation [11]; and (c) diffusion following the contour of the linear chains [12].
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