Establishing a New Mechanical Nonlinear Coefficient Q from FT-Rheology: First Investigation of Entangled Linear and Comb Polymer Model Systems

Abstract

The nonlinear response of monodisperse linear and comb polymer melts has been investigated under oscillatory shear with Fourier-transform rheology (FT-rheology). The relative intensity of the third harmonics ( I 3/1 ), which quantify nonlinearity, was found to depend on the strain amplitude (γ 0 ) at small and medium strain amplitudes quadratically regardless of the excitation frequency, temperature, and polymer topology. From these results, for the first time, we proposed new nonlinear coefficient Q, which is defined as Q ≡ I 3/1 / γ 0 2, and we also defined zero-strain nonlinearity, Q 0, as a constant value at relatively small strain amplitude (lim γ 0 →0 Q ≡ Q 0; e.g., the zero shear viscosity). In the case of the linear polymer melt, the Q value displays a constant value at small and medium strain amplitude. At large strain amplitude, we detect that the value of Q is finally reduced ( Q (γ 0 ) is decreasing). The investigated comb polymer shows very different behavior; the value of Q displays an overshoot ( Q (γ 0 ) is increasing). The Q 0 (ω) shows time−temperature superposition (TTS) behavior that is very similar to that of the linear viscoelastic properties. Using TTS, we create master curves of Q 0 (ω) over a wide range of frequency. The Q 0 (ω) for linear PS displays a relaxation process of disentanglement of polymer chains such as linear viscoelastic properties. Experimentally, we find that Q 0 (ω) displays very different results for monodisperse linear and comb polymer melts. More specifically, Q 0 (ω) of comb polymers with entangled branches robustly exhibits two relaxation processes that are currently related to the relaxation process of branches and the backbone chain. In this article, for the first time, we proposed this new nonlinear coefficient Q and the zero-strain nonlinearity Q 0 from FT-rheology. This analysis is applied to the investigation of the entangled linear monodisperse polymer and comb polymer melts. In the current stage, we assume that polymer topology has a strong influence on these nonlinear coefficients ( Q and Q 0 ). This coefficient Q 0 (ω) additionally opens up the possibility for quantitative comparisons between experiments and simulations under nonlinear oscillatory shear.