Quantifying molecular deformation in polymer melts by a generalized Zimm plot approach

Christopher N. Lam, Lilin He, Changwoo Do, Wei Ren Chen, Weiyu Wang, Kunlun Hong, Yangyang Wang, V. T. Forsyth

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The Zimm plot has been widely used to characterize the molecular dimensions of polymers from small-angle scattering experiments, where the reciprocal intensity is analyzed as a function of the square of the magnitude of the scattering wavevector Q. This work explores the benefits of analyzing the reciprocal scattering intensity from deformed polymers, extending the original Zimm plot to anisotropic materials. In the small-angle limit, a tensorial extension of the Guinier law is found for the gyration tensor and the reciprocal single-chain structure factor. In the high-Q limit, application of the spherical harmonic expansion technique to the reciprocal structure factor permits direct model-independent analysis of spatially dependent molecular deformation of polymers. Additionally, the contributions from high-order spherical harmonics become insignificant in the reciprocal-intensity representation. The proposed generalized Zimm plot approach is demonstrated computationally with the affine deformation model and the Rouse model, and experimentally with small-angle neutron scattering measurements of deformed polystyrene melts.

Original languageEnglish
Pages (from-to)1168-1179
Number of pages12
JournalJournal of Applied Crystallography
Volume56
DOIs
StatePublished - Jul 25 2023

Keywords

  • Zimm plots
  • polymer deformation
  • polymer melts
  • reciprocal intensity
  • small-angle neutron scattering
  • spherical harmonics

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