Modeling nonlinear rheology of unentangled polymer melts based on a single integral constitutive equation

The experimental data of Matsumiya et al. [Macromolecules 51, 9710–9729 (2018)] for start-up and the steady-state elongational flow of monodisperse unentangled polystyrene PS27k and poly(p-tert-butylstyrene) PtBS53k melts are analyzed based on the relaxation spectrum of the Rouse model and a single integral constitutive equation. As shown by Lodge and Wu [Rheol. Acta 10, 539–553 (1971)], the stress tensor of the Rouse model is equivalent to the rubberlike-liquid constitutive equation, and the relaxation modes of Rouse chains can be represented by an ensemble of virtual viscoelastic “strands” with relaxation times and creation rates. Instead of the affine deformation hypothesis, we assume that due to the flow, strands are oriented and stretched. The use of a history integral avoids preaveraging of orientation and stretch. Stretch is limited by a finite conformational stretch parameter. We find good agreement between model predictions and experimental data for start-up and the steady-state elongational flow of melts PS27k and PtBS53k and qualitative agreement with stress-relaxation after the stop of elongation. Extension-thickening and extension-thinning observed are caused by finite chain stretch in combination with strand orientation. The model predicts a scaling exponent for high Weissenberg number elongational flows of $ηE∝Wi−1/2$ in agreement with experimental evidence. The same scaling exponent was observed and predicted earlier for high Weissenberg number shear flows [R. Colby et al., Rheol. Acta, 46, 569–575 (2007)], and we show that the steady-shear data of unentangled polystyrene melts are in nearly quantitative agreement with model prediction assuming only the orientation of strands in the shear flow with no stretch.