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Normal stresses at the gelation transition.

Kurt Broderix1, Peter Müller, Annette Zippelius

  • 1Institut für Theoretische Physik, Georg-August-Universität, D-37073 Göttingen, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 15, 2002
PubMed
Summary

This study models polymeric liquids near gelation, predicting the first normal-stress coefficient diverges with a critical exponent. Results align with percolation theory, offering insights into polymer dynamics.

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Area of Science:

  • Polymer Physics
  • Rheology
  • Soft Matter Science

Background:

  • Polymeric liquids exhibit complex rheological behavior, particularly near the gelation transition.
  • Understanding normal-stress coefficients is crucial for characterizing viscoelasticity in polymer solutions.

Purpose of the Study:

  • To theoretically predict the critical behavior of normal-stress coefficients (Psi(1) and Psi(2)) in polymeric liquids approaching gelation.
  • To investigate the influence of chemical cross-links on these coefficients.

Main Methods:

  • Utilized a generalized Rouse-type model incorporating chemical cross-links.
  • Applied a scaling ansatz to determine the critical exponent for Psi(1).
  • Employed replica calculations and percolation theory (mean-field and 3D) for cross-link distribution.

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Main Results:

  • The second normal-stress coefficient (Psi(2)) was found to be zero.
  • The first normal-stress coefficient (Psi(1)) diverges with a critical exponent l=k+z.
  • For mean-field percolation, l=3, consistent with exact calculations.
  • For 3D percolation, l was approximately 4.9.

Conclusions:

  • The study provides a theoretical framework for understanding normal-stress behavior near gelation.
  • Results highlight the dependence of critical exponents on the nature of cross-link distribution.
  • Offers insights into time-dependent normal-stress responses in cross-linked polymers.