  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
wavenumber-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, was critically
examined by analyzing the fine features of the two-dimensional anisotropic
spectra from small-angle neutron scattering by entangled polystyrenes. It is
shown that the unique scattering patterns associated with the chain retraction
mechanism were not experimentally observed. This result calls for a fundamental
revision of the current theoretical picture for nonlinear rheological behavior
of entangled polymeric liquids.
