Molecular Models for Entangled Polymer Rheology

Molecular models for capturing the behavior of various entangled polymer systems were developed based on the physical framework of the tube model by Doi and Edwards and stochastic slip-link simulations built on similar ingredients. Using such models, we confronted three problems involving entangled polymers in this work. First, we investigated the eﬀects of entanglements on the elastic behavior of polymer networks using slip-link simulations. In particular, we simulated randomly-crosslinked networks using the Primitive Chain Network model of Masubuchi and co-workers. We observed that the obtained stress-strain behavior for these networks from simulations compared reasonably with the replica theory of Edwards and Vilgis, which is consistent with experiments. This contrasts with previous ﬁndings in end-linked networks where applica- tion of the model was less successful. We explored possible mechanisms to eliminate the discrepancies on predictions for the latter. However, none of these mechanisms seem physically reasonable in the context of the present model. We also confronted the issue of thermodynamic inconsistency of the model by considering an alternative sliding equation based on the chemical potential. This new sliding equation gave a slightly diﬀerent stress-strain response for randomly-crosslinked networks but the diﬀerence was minimal in contrast with the huge discrepancy observed in end-linked systems. Second, we modeled data on parallel superposition ﬂows of monodisperse and nearly monodisperse solutions from the experiments of Wang and co-workers using a simple tube-based constitutive equation with convective constraint release (CCR). By doing a linear expansion on this equation, we obtained analytic expressions for superposition spectra as a function of shear rate and the CCR parameter β. We then compared predictions based on these expressions with the experimental data. Model agreement was quite satisfactory and was independent of the choice of β. Predictions on the shifting of the crossover frequency of these spectra as a function of the shear rate were also consistent with the empirical trend reported by Wang and co-workers which they rationalized using the concept of CCR. However, as our predictions did not vary with the inclusion or non-inclusion of CCR in the model, we claim that the observed shifting by Wang and co-workers is due simply to orientation and ﬂow and not CCR. Finally, we modiﬁed simple tube-based constitutive equations to account for ﬂow-induced monomer friction reduction (MFR). We then used these constitutive equations to model data on the elongational rheology of monodisperse polystyrene melts and solutions from ﬁlament stretching rheometry. MFR has been proposed previously as a mechanism which could explain the qualitatively diﬀerent behavior of melts and solutions revealed by recent experiments. These systems are expected to behave similarly from the perspective of classical tube models with chain stretch. We show that inclusion of MFR in combination with CCR and chain stretch in simple tube models allows for a semi-quantitative ﬁtting of the available data sets on both polystyrene melts and solutions. We also applied the modiﬁed equations in the analysis of shear ﬂows and stress relaxation after cessation of ﬂow of PS melts to further understand the MFR mechanism. We ﬁnd that the MFR eﬀect is triggered only when the stretching of the system is suﬃcient to align the Kuhn segments. Further tests of this model by applying it to bidisperse polystyrene melts would give further credence to this approach.