Polymer viscoelasticity from an orientational closure with implicit stretch

Abstract

We propose a deviatoric-stress constitutive equation derived from orientational kinetics, while implicitly retaining contributions from conformational stretch. Starting from the dumbbell model, we show that conformational stretch affects orientational dynamics through an effective stress scale and rotational diffusivity, which determine an effective relaxation time. The orientation-based equation is derived by assuming an approximate relation between orientational anisotropy and the stretch state. Within the proposed framework, constant effective coefficients yield steady-oscillatory shear correspondences closely related to the empirical Cox-Merz and Gleissle-Osaki relations. For model-specific effective coefficients, the upper-convected Maxwell model is characterized by a constant relaxation time and an increasing modulus under steady shear, whereas finite extensibility with Peterlin preaveraging shortens the relaxation time and suppresses the modulus increase. With coefficients determined from steady-shear states, the proposed equation successfully reproduces stress responses under transient shear, large-amplitude oscillatory shear, and uniaxial extension. These results show that the effects of conformational stretch on orientational kinetics can be retained implicitly, providing a constitutive description based on a deviatoric-stress state reconstructable from standard rheometry and a physical interpretation of how stretch enters polymer viscoelasticity.