Modeling of rheological properties of polyethylene melts during uniaxial stretching

The paper considers the use of the modified Vinogradov and Pokrovskii rheological model to describe the occurrence of stresses in a polymer melt during uniaxial stretching. One of the changes introduced in the model concerns the anisotropic law of internal friction, which makes it possible to take into account the nonmonotonic dependence of the stationary elongational viscosity on the extension rate. Another change is associated with the multimode nature of the relaxation processes accompanied the deformation of the polymer melt. The above changes made it possible to evaluate an increase in the longational viscosity of the melt, which was found to be three times higher than its shear viscosity in the linear deformation mode. A comparison between the results of calculation and the experimental data available in the literature was performed for five industrial samples of polyethylene with a branched structure of macromolecules. The calculations according to the mathematical model were carried out by the Runge-Kutta method. The components of the relaxation spectrum were similar to those used in the experiment. Other parameters of the model were selected on the premise that there is the best possible fit of the theoretical and experimental time dependences of the elongational viscosity of the melt during stretching. Despite the fact that the proposed multimode model was a development of theoretical concepts of the dynamics of linear polymer chains, it allows us to accurately describe the nonstationary time dependences of the viscosity of branched polymer melts under uniaxial tension. A comparison between the results of calculations made in the framework of the above model and the models described in the literature shows that the predictions of the former are comparable with the predictions of such advanced models as the Leonov and Prokunin model, the multimode Giesekus model, the “pom-pom” model, and the extended “pom-pom” model, MSF model, and significantly better than the results of its single-mode approximation.