Application of the Slip-Link Model to Bidisperse Systems

Although the LVE predictions of monodisperse systems by the discrete slip-link model (DSM) are at least as good as those made by tube models, there are significant differences in contributions to relaxation from polymer chain dynamics and environment dynamics (Khaliullin et al. Macromolecules 2009, 42, 7504−7517). This observation suggests that tube models and DSM might yield different predictions for the observable relaxation modulus of bidisperse blends. Here we compare DSM to experimental data as well as the Park and Larson tube model (Park et al. Macromolecules 2004, 37, 597−604) and the des Cloizeaux tube model with modified double reptation (van Ruymbeke et al. Macromolecules 2002, 35, 2689−2699). Our self-consistent implementation of constraint dynamics avoids factorization assumptions, or tube dilation processes, so no new parameter, such as the Struglinski-Graessley parameter, is necessary. All three models compare very well with experiments. We then use the DSM to analyze the molecular probe rheology experiments of Liu et al. (Liu et al. Macromolecules 2006, 39, 7415−7424). By examining the dynamic modulus of blends of very long and short entangled chains, those authors concluded that constraint release plays a significant role in molecular weight scaling of the longest relaxation time. Here we show that their conclusion is incorrect because their analysis neglects constraint dynamics of the long chains. Moreover, we show that a correct analysis can be used to distinguish between tube and slip-link models. Namely, probe rheology can be used to estimate a sum of relaxation from sliding dynamics and constraint dynamics. Because the dynamic modulus of monodisperse systems measures a product of these two processes, the combination of the two experiments can be used to distinguish between sliding and constraint dynamics. Only DSM can describe both experiments.