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Polymers 2019, 11(3), 496; https://doi.org/10.3390/polym11030496

Determining Tube Theory Parameters by Slip-Spring Model Simulations of Entangled Star Polymers in Fixed Networks

School of Mathematical, Physical and Computational Sciences, University of Reading, Reading RG6 6AX, UK
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Received: 20 February 2019 / Revised: 8 March 2019 / Accepted: 11 March 2019 / Published: 14 March 2019
(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)
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Abstract

Dynamical properties of branched polymer melts are determined by the polymer molecular weights and architectures containing junction points. Relaxation of entangled symmetric star polymers proceeds via arm-retraction and constraint release (CR). In this work, we investigate arm-retraction dynamics in the framework of a single-chain slip-spring model without CR effect where entanglements are treated as binary contacts, conveniently modeled as virtual “slip-links”, each involving two neighboring strands. The model systems are analogous to isolated star polymers confined in a permanent network or a melt of very long linear polymers. We find that the distributions of the effective primitive path lengths are Gaussian, from which the entanglement molecular weight N e , a key tube theory parameter, can be extracted. The procured N e value is in good agreement with that obtained from mapping the middle monomer mean-square displacements of entangled linear chains in slip-spring model to the tube model prediction. Furthermore, the mean first-passage (FP) times of destruction of original tube segments by the retracting arm end are collected in simulations and examined quantitatively using a theory recently developed in our group for describing FP problems of one-dimensional Rouse chains with improbable extensions. The asymptotic values of N e as obtained from the static (primitive path length) and dynamical (FP time) analysis are consistent with each other. Additionally, we manage to determine the tube survival function of star arms μ ( t ) , or equivalently arm end-to-end vector relaxation function ϕ ( t ) , through the mean FP time spectrum τ ( s ) of the tube segments after careful consideration of the inner-most entanglements, which shows reasonably good agreement with experimental data on dielectric relaxation. View Full-Text
Keywords: entangled polymers; slip-spring model; slip-link; tube theory; arm retraction dynamics; first passage time; primitive path; relaxation correlation function entangled polymers; slip-spring model; slip-link; tube theory; arm retraction dynamics; first passage time; primitive path; relaxation correlation function
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Cao, J.; Wang, Z.; Likhtman, A.E. Determining Tube Theory Parameters by Slip-Spring Model Simulations of Entangled Star Polymers in Fixed Networks. Polymers 2019, 11, 496.

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