Tube Model Under Tension

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 longstanding 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.

Molecular Dynamics Investigation of the Relaxation Mechanism of Entangled Polymers after a Large Step Deformation

“…Our additional analysis of the mean-square internal separation in both the parallel and perpendicular directions indicates the absence of nonmonotonic features at all length scales. Considering the unmistakable, monotonic trend revealed by the current simulation, we reason that it is unlikely for NEMD simulations on a larger, more entangled system to produce qualitatively different results . Lastly, it is worth noting that a previous NEMD simulation study of unentangled polymer melts also reported a monotonic change of the radius of gyration tensor during the stress relaxation after a large step deformation …”

“…Considering the unmistakable, monotonic trend revealed by the current simulation, we reason that it is unlikely for NEMD simulations on a larger, more entangled system to produce qualitatively different results. 25 Lastly, it is worth noting that a previous NEMD simulation study of unentangled polymer melts also reported a monotonic change of the radius of gyration tensor during the stress relaxation after a large step deformation. 50 In summary, we have performed large-scale nonequilibrium molecular dynamics simulations on well-entangled polymers to critically test the chain retraction hypothesis of the nonlinear tube theory.…”

“…23 This finding immediately raises questions of the validity of the central hypothesis of the nonlinear tube theory. Considering the gravity of the issue, as well as the presence of contradictory SANS results in the literature, 22,25 we naturally wonder what "computer experiments" have to say. It turns out that implementing the spherical harmonic expansion analysis of the single-chain structure factor S(Q) is quite straightforward in MD simulations.…”

“…Despite this recent development in small-angle neutron scattering experiments, it is still necessary to examine the chain retraction hypothesis of the tube model by using a different technique to corroborate the findings. When experimentalists disagree, ,, computational simulations can offer tremendous insights that potentially help resolve the issues. Looking back, it is a bit astonishing that computer simulations have not been employed to critically and directly examine the chain retraction hypothesis, in a manner originally envisioned by Doi and Edwards in their 1978 paper .…”