Analysis of medium amplitude oscillatory shear data of entangled linear and model comb polymers

Abstract

Studying the mechanical response of nearly monodisperse linear and comb polystyrene (PS) melts to medium amplitude oscillatory shear (MAOS), Hyun and Wilhelm [Macromolecules 42, 411 (2009)] identified two important scaling relations: (1) The relative intensity I3/1 of the third harmonic compared to the first harmonic scales with the strain amplitude according to γ02. Consequently, a new nonlinear coefficient Q≡I3/1/γ02 as well as the so-called intrinsic nonlinearity Q0≡limγ0→0 Q was introduced. (2) In the terminal relaxation regime, the intrinsic nonlinearity Q0(ω) scales with ω2 and was found to be a very sensitive measure regarding molecular topology by identifying and separating relaxation processes in model branched polymers. A constitutive analysis based on a general single integral constitutive equation, which includes the Doi–Edwards model without (DE) and with (DE IA) independent alignment assumption as well as the molecular stress function (MSF) model, confirms both scaling relations. We show tha...