Challenging Tube and Slip-Link Models: Predicting the Linear Rheology of Blends of Well-Characterized Star and Linear 1,4-Polybutadienes

We compare predictions of two of the most advanced versions of the tube model, namely the "Hierarchical model" by Wang et al. [ J. Rheol. 2010, 54, 223 ] and the BoB (branch-on-branch) model by Das et al. [ J. Rheol. 2006, 50, 207 ], against linear viscoelastic G′ and G″ data of binary blends of nearly monodisperse 1,4-polybutadiene 4-arm star polymer of arm molar mass 24 000 g/mol with a monodisperse linear 1,4-polybutadiene of molar mass 58 000 g/mol. The star was carefully synthesized and characterized by temperature gradient interaction chromatography and by linear rheology over a wide frequency region through time-temperature superposition. We found large failures of both the Hierarchical and BoB models to predict the terminal relaxation behavior of the star/linear blends, despite their success in predicting the rheology of the pure star and pure linear polymers. This failure occurred regardless of the choices made concerning constraint release, such as assuming arm retraction in "fat" or "skinny" tubes. Allowing for "disentanglement relaxation" to cut off the constraint release Rouse process at long times does lead to improved predictions for our blends, but leads to much worse predictions for other star/linear blends described in the literature, especially those of Shivokhin et al. [ Macromolecules 2014, 47, 2451 ]. In addition, our blends and those of Shivokhin et al. were also tested against a coarse-grained slip-link model, the "clustered fixed slip-link model (CFSM)" of Schieber and co-workers [ J. Rheol. 2014, 58, 723 ], in which several Kuhn steps are clustered together for computational efficiency. The CFSM with only two molecular-weight- and chain-architecture-independent parameters was able to give very good agreement with all experimental data for both of these sets of blends. In light of its success, the CFSM slip-link model may be used to address the constraint release issue more rigorously and potentially help develop improved tube models.