Constitutive equation for polymer networks with phonon fluctuations

Rasmus Hansen, Anne Ladegaard Skov, and Ole Hassager
Phys. Rev. E 77, 011802 – Published 14 January 2008

Abstract

Recent research by Xing et al. [Phys. Rev. Lett. 98, 075502 (2007)] has provided an expression for the Helmholtz free energy related to phonon fluctuations in polymer networks. We extend this result by constructing the corresponding nonlinear constitutive equation, usable for entirely general, volume conserving deformation fields. Constitutive equations for the sliplink model and the tube model are derived and the three models are examined by comparison with each other and with data from Xu and Mark [Rubber Chem. Technol. 63, 276 (1990)] and Wang and Mark [J. Polym. Sci., Part B: Polym. Phys. 30, 801 (1992)]. Elastic moduli are derived for the three models and compared with the moduli determined from the chemical stoichiometry. We conclude that the sliplink model and the phonon fluctuation model are relatively consistent with each other and with the data. The tube model seems consistent neither with the other models nor with the data.

  • Figure
  • Figure
  • Figure
  • Received 13 September 2007

DOI:https://doi.org/10.1103/PhysRevE.77.011802

©2008 American Physical Society

Authors & Affiliations

Rasmus Hansen1, Anne Ladegaard Skov2, and Ole Hassager3

  • 1Center for Fluid Dynamics at DTU, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
  • 2The Danish Polymer Center, Department of Chemical Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
  • 3Center for Fluid Dynamics at DTU & The Danish Polymer Center, Department of Chemical Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 77, Iss. 1 — January 2008

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×