Evaluating predictability of various constitutive equations for MAOS behavior of entangled polymer solutions

摘要

To predict the nonlinear viscoelastic behavior of polymer melts and solutions under medium amplitude oscillatory shear (MAOS) flow, we summarized known analytical MAOS material functions and derived new analytical solutions from several continuum- or molecular-based constitutive models [Johnson-Segalman, Phan-Thien-Tanner, Leonov, Larson, Pom-Pom, coupled double-convection-reptation with chain stretch (cDCR-CS), and Rouse linear entangled polymers (Rolie-Poly)]. All constitutive models discussed in this study were classified as time-strain separable or inseparable models. Whereas linear viscoelastic behavior of all constitutive models under small amplitude oscillatory shear flow was identical, the frequency-dependent signatures of four MAOS moduli (first-harmonic elastic and viscous MAOS moduli and third-harmonic elastic and viscous MAOS moduli) were model-specific, though all analytical solutions exhibited negative first-harmonic elastic MAOS moduli. In particular, tube-based constitutive models displayed a sign change in first-harmonic viscous MAOS modulus when chain retraction of the models after deformation was not instantaneous. In addition, two models for entangled linear polymers, that is, the Rolie-Poly and cDCR-CS models, displayed a second sign change in third-harmonic elastic MAOS modulus when finite chain extensibility was introduced. These results suggest that chain relaxation dynamics can be reflected in signatures of MAOS moduli. We extended singlemode predictions into multimode versions to predict the behavior of weakly or moderately entangled polystyrene solutions (effective entanglement number < 5). All models described the two elastic MAOS moduli well, but different predictability was obtained for viscous MAOS moduli. Therefore, viscous MAOS moduli can be a measure of evaluating the predictability of constitutive models for MAOS.