Probing Nonlinear Viscoelasticity of Polymer Melts by Medium Amplitude Oscillatory Shear (MAOS)

MAOS is shown to be a powerful tool to investigate the inception of nonlinear viscoelasticity of polymer melts. A constitutive analysis based on a general single integral constitutive equation, which includes the Doi-Edwards model without (DE) and with independent alignment assumption (DE IA) as well as the molecular stress function (MSF) model, confirms two important scaling relations found experimentally by Hyun and Wilhelm: (1) The relative intensity of the 3rd harmonic compared to the 1st harmonic scales with the square of the strain amplitude according. Consequently, a new nonlinear coefficient, the so-called intrinsic nonlinearity was introduced. (2) In the terminal relaxation regime, the intrinsic nonlinearity scales with the square of the angular frequency, and was found to be a very sensitive measure regarding molecular topology by identifying and separating relaxation processes in model branched polymers. We show that the nonlinear viscoelastic moduli can be expressed as sums of their linear-viscolelastic counterparts at angular frequencies of omega, 2 omega, and 3 omega. The absolute value of the intrinsic nonlinearity depends on the difference (alpha - beta) between the 3rd order orientational effect (parameter alpha) according to the DE or DE IA model and the 2nd order isotropic stretching effect (parameter beta) according to the MSF model. The measured apparent values of the intrinsic nonlinearity measured in parallel-plate geometry are rescaled in order to take the non-uniform shear deformation into account, and are compared to constitutive models. While both the DE and DE IA model fail to describe the experimental data, the data of linear and comb-like PS melts are quantitatively described by the MSF model. However, the model predicts a plateau at the level of the maximum of the experimental data, while for comb polymers with entangled branches, a minimum in the intrinsic nonlinearity is observed, followed by a second increase of the intrinsic nonlinearity at higher frequencies, which correspond to the terminal relaxation times of the branches. Surprisingly, this can be modelled quantitatively if only the terminal relaxation modes of the backbone and the branches are assumed to be deforming non-affinely and to respond to the nonlinearity.