Re-Formulation of the Rheological Equations of Polymer Melts Pursuant to the Dual-Phase and Cross-Dual-Phase Model of Dissipative interactions. Description of the Dual-Phase Rheology Protocol (DPRP).

The current equations describing the dynamic rheology of polymer melts provide the correlations between the modulus of visco-elasticity, G*(w), split into its elastic and viscous moduli, G’(w) and G”(w), respectively, and the frequency of the shear deformation applied to the melt, w. The dynamic viscosity of the melt, h* = G*/w is usually used to compare melts of different chemical nature or to study the effect of molecular weight, M, its dispersity, and the presence or the absence of branches, short or long. The equations also describe the influence of external variables on the rheological state of the melt: temperature and pressure. The terms and constants that enter the equations of rheology have themselves been interpreted, to a large extent, by molecular mechanisms triggered by the changes occurring to the statistical description of the individual chains: the dynamic molecular models of Rouse (for un-entangled melts) and of de Gennes (reptation) for entangled melts illustrate the current formulation and understanding of the rheology of polymer melts. On the other hand, we have pointed out in several publications the problems surfacing in the classical molecular interpretation of the rheological data when revisited by our analysis, and the contradictions arising from these models when they are applied to the understanding of new experimental work on “the strain-induced time dependence of the melt viscosity” leading to the technologies of “Rheo-Fluidification” of melts and of their “sustained-Orientation”. In short, we have concluded that the current comprehension of the visco-elasticity of polymers, in particular of the entanglement concept, is not compatible with the reality of new experimental facts and, therefore, that the current accepted theories should be debated and revised; more generally, that a different approach to the physics of interactions in polymers should be considered. We have already introduced the principles of such a theory of interactions of Dual-conformers in which the statistical system is no longer a single macromolecule, but a self-generated collective network of Dual-Conformers belonging to the macromolecules. The local deformation of the Dual-conformers and the collective network enthalpy and entropy are interactively emerging from the solution of the Grain-Field Statistics applied to the interactions between the Dual-conformers, demonstrating the dissipative character of the solutions: this is our new foundation to explain the observed experimental facts, old and new, regarding the visco-elastic effects of melts under shear-deformation, linear or non-linear. This paper presents the Dual-Phase Rheology Protocol (DPRP) i.e. how to derive the parameters of the new statistical approach from the visco-elastic moduli G’(w,T) and G”(w,T) in dynamic rheology. In particular, it is shown that a completely different empirical presentation of the rheological results can be expressed in terms revealing the relevance of the Dual-Phase and Cross-Dual-Phase concepts. We introduce, for the 1st time, an empirical analysis of the data that permits to relate the rheological properties of an entangled melt (M > Mc, the entanglement molecular weight) to the stability of the solution presented by the split of Dual-Phases into Cross-Dual-Phases. In other words, the “entanglement” of the macromolecules can be quantified in terms of the viscosity, h, and the intrinsic elasticity, c=(G’/G*)2 of the individual interactive Dual-Phases emerging from the split to re-establish a new rheological stability of the melt as M increases. This paper also introduces a roaster of new rheological markers that can be traced to analyze phenomena visible in rheology, widening the panel of analytical tools available to characterize difficult situations (blends, branches etc.).