Constitutive equation for polymer networks with phonon fluctuations

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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 and the tube model are applied. 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] on end-linked polydimethylsiloxane networks. 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 also with the data. The tube model seems consistent neither with the other models nor with the data. © 2008 American Institute of Physics.
Original languageEnglish
Title of host publicationCP1027, The XVth International Congress on Rheology, The Society of Rheology 80th Annual Meeting
EditorsA. Co, L. G. Leal, R. H. Colby, A. J. Giacomin
Volume1027
Publication date2008
Pages1369-1371
DOIs
Publication statusPublished - 2008
SeriesAip Conference Proceedings
ISSN0094-243X

Keywords

  • Constitutive equation
  • Elastomer
  • Phonon fluctuations
  • Polymer network
  • Rheology
  • Sliplink
  • Tube model

Cite this

Hansen, R., Hassager, O., & Skov, A. L. (2008). Constitutive equation for polymer networks with phonon fluctuations. In A. Co, L. G. Leal, R. H. Colby, & A. J. Giacomin (Eds.), CP1027, The XVth International Congress on Rheology, The Society of Rheology 80th Annual Meeting (Vol. 1027, pp. 1369-1371). Aip Conference Proceedings https://doi.org/10.1063/1.2964577