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  • Featured in Physics
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Fingerprinting Molecular Relaxation in Deformed Polymers

Zhe Wang1,*, Christopher N. Lam2, Wei-Ren Chen1, Weiyu Wang2, Jianning Liu3, Yun Liu4,5, Lionel Porcar6, Christopher B. Stanley1, Zhichen Zhao3 et al.

Kunlun Hong2 and Yangyang Wang2,†

  • 1Biology and Soft Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
  • 2Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
  • 3Department of Polymer Science, University of Akron, Akron, Ohio 44325, USA
  • 4Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
  • 5Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716, USA
  • 6Institut Laue-Langevin, B.P. 156, F-38042 Grenoble CEDEX 9, France

  • *zwang.thu@gmail.com
  • †wangy@ornl.gov
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Phys. Rev. X 7, 031003 – Published 10 July, 2017

DOI: https://doi.org/10.1103/PhysRevX.7.031003

Abstract

The flow and deformation of macromolecules is ubiquitous in nature and industry, and an understanding of this phenomenon at both macroscopic and microscopic length scales is of fundamental and practical importance. Here, we present the formulation of a general mathematical framework, which could be used to extract, from scattering experiments, the molecular relaxation of deformed polymers. By combining and modestly extending several key conceptual ingredients in the literature, we show how the anisotropic single-chain structure factor can be decomposed by spherical harmonics and experimentally reconstructed from its cross sections on the scattering planes. The resulting wave-number-dependent expansion coefficients constitute a characteristic fingerprint of the macromolecular deformation, permitting detailed examinations of polymer dynamics at the microscopic level. We apply this approach to survey a long-standing problem in polymer physics regarding the molecular relaxation in entangled polymers after a large step deformation. The classical tube theory of Doi and Edwards predicts a fast chain retraction process immediately after the deformation, followed by a slow orientation relaxation through the reptation mechanism. This chain retraction hypothesis, which is the keystone of the tube theory for macromolecular flow and deformation, is critically examined by analyzing the fine features of the two-dimensional anisotropic spectra from small-angle neutron scattering by entangled polystyrenes. We show that the unique scattering patterns associated with the chain retraction mechanism are not experimentally observed. This result calls for a fundamental revision of the current theoretical picture for nonlinear rheological behavior of entangled polymeric liquids.

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Tube Model Under Tension

Published 10 July, 2017

Results from a new method of analyzing neutron-scattering data from polymer samples under deformation may challenge the prevailing “tube model” of polymer motion.

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Popular Summary

Every year, several hundred billion pounds of polymers are consumed to make commercial rubber and plastic products. Many of these processes involve entangled polymers, chainlike molecules sufficiently long such that the motion of a chain is constrained by those of its neighboring molecules, which leads to perplexing nonlinear flow behavior. Our current understanding of the transport and dynamics of entangled polymers is built upon a theoretical framework known as the “tube model,” which describes polymer movement as being restricted along a virtual tube. Despite its impressive success, a key molecular relaxation mechanism of the tube model—chain retraction—has not been validated by experiment. We developed mathematical tools to resolve ambiguities in data analysis and used these tools to show that there is no experimental support for chain retraction.

Small-angle neutron scattering, in which a beam of neutrons is aimed at a sample, has long been recognized as a powerful tool for revealing the structural properties of flowing polymers. But investigations have been plagued by ambiguities that stem from technical difficulties and limitations in the data analysis. We developed a new approach based on spherical harmonic expansion, allowing one to obtain the wave-number-dependent expansion coefficients that constitute a characteristic fingerprint of a macromolecular deformation. We then analyzed neutron scattering data of entangled linear polymers after a large step deformation and found no evidence for the distinct fingerprint features associated with chain retraction.

This result provides crucial experimental evidence against the central hypothesis of the tube theory for nonlinear flow behavior of entangled polymers. Moreover, the spherical harmonic expansion approach employed in this work opens a new venue for improving our understanding of macromolecular flow and deformation via small-angle-scattering techniques.

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Phys. Rev. X 7, 031003– Published 10 July, 2017
  • Received 23 March 2017
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