Constitutive equation for polymer networks with phonon fluctuations

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.