The Great Myths of Rheology Part III: Elasticity of the Network of Entanglements

Abstract

The dynamic data of polymer melts are analyzed in a novel way, presenting new correlations between the viscosity, G′ and G′′ (the elastic and loss moduli), and strain rate and the implications of the new formulas on our understanding of melt entanglement network elasticity are discussed. In the two previous articles of this series, Part I and Part II, we showed that the existing models valid in the linear viscoelastic deformation range were not adequate to extrapolate to the nonlinear regime, suggesting that the stability of the network of entanglements was at the center of the discrepancies. In this article, we introduce new tools for the analysis of the dynamic data and suggest new ideas for the understanding of melt deformation based on this different focus. In particular, we express classical concepts, such as shear-thinning, melt diffusion or melt elasticity and viscosity, in a different context, that of the existence of a dual-phase interaction, essential to our treatment of the statistics of interaction of the bonds responsible for the system coherence and cohesion. It is within this framework that viscoelasticity parameters emerge and the new view of the deformation of a polymer melt results in a different definition of the entanglement network.

Keywords:

• cross dual-phase model
• entanglement
• grain-field-statistics
• new polymer physics
• visco-elasticity theory

Acknowledgments

The author is thankful to the Fulbright Foundation and the Ikerbasque Foundation for sponsoring this research. This work has also been made possible by an award to the author of the IRG Marie-Curie Grant 200342 (European FP7 framework). Many thanks to the Editor-in-Chief, Prof. P. H. Geil, for his patience and his guidance during the corrections of this paper, leading to many improvements.

Notes

Conformers are defined in refs.^[ 33–35 ^] Also see Fig. 12a.

The treatment was mechanically done, mostly consisting of the superposition of pressure flow and cross-lateral drag flow (combining rotational and vibrational shear).

The results will be presented in a separate article.

Note that for PMMA there are not enough data points in Figs. 24(c) and (d) to eliminate the possibility that 2 Arrhenius lines should be defined instead of one. However, based on other results (not shown), there is only one Arrhenius line in that temperature span. A wider temperature span might show the need for two Arrhenius lines.

The intercepts are given on a log scale.