Application of a constitutive equation to polymer melts

Yamamoto's integral constitutive equation in which the memory function is dependent on the second invariant of the rate of deformation tensor at past times has been found to be successful in predicting many of the nonlinear viscoelastic functions from the linear viscoelastic data for melts of linear polyethylenes, polypropylenes, and polystryene but not for those of branched polyethylenes with high level of long‐chain branching. A specific functional form for the rate‐dependent relaxation spectrum is used and is based on the physical meaning resulting from the molecular entanglement theory of Graessley on steady shearing flow. No arbitrary constant is involved in such an interconversion scheme. The data examined are dynamic storage modulus and loss modulus, steady flow viscosity, first normal stress difference, and parallel superimposed small oscillations on steady shear flow. The theory predicts that in such parallel superimposed experiments, storage modulus G ′(ω, \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document} ) divided by the square of frequency shows a maximum under finite shear and that G ′(ω, \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document} ) would itself become negative at a frequency whose value is about one third the superimposed rate of shear. The experiments are in line with such predictions. Possible reasons for the failure of the theory for branched polyethylenes are considered, and a possible approach is suggested so that the interconversion scheme may be successful for such resins.