# Determining tube theory parameters by slip-spring model simulations of entangled star polymers in fixed networks

(2019) Determining tube theory parameters by slip-spring model simulations of entangled star polymers in fixed networks. Polymers, 11 (3). 496. ISSN 2073-4360

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To link to this item DOI: 10.3390/polym11030496

## Abstract/Summary

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 $\mu(t)$, or equivalently arm end-to-end vector relaxation function $\phi(t)$, through the mean FP time spectrum $\tau(s)$ of the tube segments after careful consideration of the inner-most entanglements.

Item Type: Article Yes Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics 82710 MDPI