Fourier transform rheology of branched polyethylene: Experiments and models for assessing the macromolecular architecture

Fourier transform rheology (FTR) consists of analyzing the frequency spectrum of the nonlinear torque response obtained during large-amplitude oscillatory shear. In the present work, the analysis has been carried out in the whole complex space and was especially focused on the study of the third complex harmonic 1*(3)/I-1 (= I*(3 omega(1))/I-1 where I, is the spectrum intensity at the fundamental frequency omega(1)), the intensity I-3/I-1(= |I*(3)/I-1|), and the phase shift Phi(3) of I*(3)/I-1. The accuracy of FTR to characterize the architecture of linear, sparsely, and densely branched polyethylene regarding the number of branches and their length has been shown. A modified Wagner integral model and a differential multimode pompom model were used to simulate FTR experiments. Nonlinear parameters of each model were determined by fitting the curve of the third complex harmonic I*(3)/I-1 versus the strain amplitude gamma(0) with the experimental data. Good results have been obtained with the modified Wagner model. Whereas, the pompom model accounts for the experimental intensity of the third harmonic, discrepancies remain for the phase shift behavior Phi(3) for the polymers showing the highest nonlinear behavior regarding the level of I-3/I-1. Nevertheless, when fitting was possible, the results have been correlated with the supposed structure expected from the type of synthesis.