Fingerprinting Molecular Relaxation in Deformed Polymers

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.

From Wall Slip to Bulk Shear Banding in Entangled Polymer Solutions

“…Computer simulations have started to shed light on the molecular origin of strain localization contrary to those from the tube model. Moreover, a recent small‐angle neutron scattering (SANS) study found no evidence to support the basic and central assumption of barrier‐free Rouse retraction that was used to construct the tube theory. In other words, no chain retraction was observed in the SANS measurements, implying that the basis of the tube theory lacks experimental support.…”

Optical Tweezers Microrheology Maps the Dynamics of Strain-Induced Local Inhomogeneities in Entangled Polymers

“…However, the flow field produced in these experiments is much more complex than analogous bulk rheology measurements and can lead to transient local inhomogeneities [13,[20][21][22][23], which complicate accurate evaluation of rheological properties. The potential for inhomogeneities can become prohibitively large in nonlinear regimes where the physics is the most intriguing and least understood [1,5,18,21,[24][25][26]. These issues further pose a major obstacle to implementing a microrheological analog of large-amplitudeoscillatory-shear (LAOS) measurements that have been proven extremely effective in elucidating the nonlinear response of polymer systems [27][28][29][30][31][32].…”

Characterization of microscopic deformation through two-point spatial correlation functions

“…Since Wi gives a measure of strain, this formula in principle allows one to determine the microscopic deformation by analyzing the anisotropic component of ( ), from either scattering experiments (via Fourier transform) or computer simulation [1][2][3][4][5][6][7][8][9][10][11][12][13][18][19][20][21][22][23].…”

“…However, recent experimental and computational studies have demonstrated that the microscopic strain in complex fluids undergoing shear flow is generally not only non-affine, but 3 also dependent on the molecular position [14][15][16][17][18][19][20][21][22][23]. In other words, Eq.…”