Experimental Assessment of Constraint Release Physics in Entangled Polymers and Its Implication for Rheological Modeling

Abstract

Innovations in the predictive theory, particularly tube models such as the Hierarchical 3.0 model (Wang et al. J. Rheol., 54(2): 223-260, 2010), Branch-on-Branch (BoB) model (Das et al. J. Rheol., 50(2), 207-234, 2006), and the Time-Marching Algorithm (van Ruymbeke et al. J. Non-Newtonian Fluid Mech., 128, 7-22, 2005), have contributed greatly towards the improvement of industrial-scale polymer processing. However, recent studies conducted by Desai et. al. (Macromolecules, 49(13): 4964-4977, 2016) and Park et al. (Macromolecules, 37, 597-604, 2004) concerning the accuracy of Hierarchical and BoB model predictions have uncovered shortcomings in the tube theory. These shortcomings include 1) confusion in the choice of model parameters, particularly the dilution exponent; 2) the failure of Dynamic Tube Dilation (DTD) physics, especially in predicting the rheology of branched polymers; and 3) uncertainty of Constraint Release-Rouse (CR-Rouse) physics, which is important in predicting the rheology of polydisperse linear polymers, binary linear blends, and star-linear blends. In the two studies presented here, we attempt to address all three of the above shortcomings and provide a foundation for rebuilding tube theory. First, we determine experimentally the dilution exponent for entangled polymers from the scaling of terminal crossover frequency with entanglement density from the linear rheology of three 1,4-polybutadiene star polymers that are blended with low-molecular-weight, unentangled linear 1,4-polybutadiene at various star volume fractions. Assuming that the rheology of monodisperse stars depends solely on the plateau modulus, the number of entanglements per chain, and the tube-segment frictional Rouse time, we show that only a dilution exponent of unity, and not the alternative of 4/3 superposes the dependence of the terminal crossover frequency of the blends on entanglement density with those of pure stars obtained from literature. This is the first determination of the dilution exponent for star polymers that does not rely on any particular tube model implementation. We also show that the Hierarchical model, using the “Das” parameter set, which assumes a dilution exponent value of unity, reasonably predicts the rheological data of the melts and blends. Second, we generate the most comprehensive dataset of star-linear blends (over 50 blends in total) to investigate further the failings of DTD and uncertainty of CR-Rouse physics. This work is coherent with the study of Desai et al. (Macromolecules, 49(13): 4964-4977, 2016) that showed the failure of the Hierarchical and BoB models to predict the linear rheological star-linear blend data when the pure linear polymer has a shorter relaxation time, but within 3-4 orders of magnitude, of the star polymer.. However, when the linear polymer has a longer relaxation time than the star, this new work, surprisingly, finds that both experimental data and model predictions are non-monotonic in the dependence of terminal relaxation time on star volume fraction.. We suspect that multiple regimes of constraint-release dynamics exist in star-linear polymer blends, only some of which are captured by current tube models. In addition to illuminating polymer relaxation physics, this vast dataset of star-linear blends serves as a rigorous benchmark for all existing predictive models, as well as for models that may be developed in the future.