In 2007, I started an academic career, dedicating my time understanding what I thought were extraordinary results which the current theoretical models could not predict nor explain. My first task was to understand in depth the existing rheological models and question the meaning of the experiments I had conducted. This is why I studied with a lab dynamic rheometer the effect of strain and how it differed or coupled with the effect of strain-rate (frequency). By focusing more and more on the way entanglements were mathematically described by the current models, I realized the limitations and shortcomings of their definition, especially under deformation conditions which brought the melt into the “non-linear” visco-elastic region, i.e. at higher strain.
By the end of 2009 I had read and studied all the theses of the University of Pau which dealt with polymer flow and rheology. I also studied the relevant references. I was now totally convinced that the established models of entanglements were too simplistic and missed the fundamental understanding of the concept of chain components interactions. I started to believe and suggest that a new theory of polymer physics had to be presented not only to account for the spectroscopy results discussed in my paper of 1997 (Brillouin scattering, RMA results, Low frequency Raman), but also to account for rheology in the non-linear region.
I generalized the equations of the Dual-Phase statistics, which applied to a macro-coil system of conformers of size M<Me to the case of interpenetrating macro-coils of size M>Me and discovered that it gave birth to another level of split, the two dual-phase statistics, which I coined the Cross-Dual-Phase Statistical model. The interesting result was that the cross-dual-phases would only hold stable if the interpenetrating macro-coils were of a size superior to a critical value Me. This provided a definition of Me as the critical system size for a split of the dual-phase to occur and remain stable, an entirely new concept. The network of entanglement resulted from the interpenetration of one of the two dual-phases into the other, defining a network of channeling boundaries perpetually in motion.
Using that definition of the entanglement network, I was able in 2011 to develop the rheological equations responsible for linear and non-linear effects such as shear-thinning, normal force and strain softening. The width of the rubbery plateau with molecular weight, as well as the very existence of the rubbery plateau itself, could also be understood and derived from the same concepts. Finally, I showed in 2012 that the sacred-saint exponent 3.4 found empirically for the molecular weight dependence of the Newtonian viscosity, which had driven so much attention from the de Gennes school of reptation, was in fact ill-defined since it did not represent the sole influence of the molecular weight alone, incorporating also a mix of free volume contribution. The real molecular weight dependence was characterized by an exponent 5.3, not 3.4, at constant free volume contribution.
All in all, it appeared that the new physics which gave birth to the new concept of entanglement network through the stability of the crossed-dual-phase, was better adapted to the description of the experimental results I had obtained combining the effect of shear-thinning and strain softening, which I had called “Rheo-Fluidification”.
The innovation really came from the new statistics of the conformers I created to describe the interplay between the inter and intra molecular interactions between the conformers. Initially, in my thesis, I had described the conformational state of the bonds by a series of circularly bounded chained kinetic equations, the way it is used in chemistry in the case of multi-stage chemical reactions. But, a few years later, after dropping the assumption that local order could stabilize thermodynamically the systems of interactions, I introduced a dissipative term between two “splitted” kinetic equations that provided the rate dependence of the population of the conformers. The presence of the dissipative term coupled the (b/F) statistics with the conformational statistics (trans<--> gauche<-->cis). This became the Dual-Phase statistics (the two phases being the b and F “local” phases), also called the Dual-Split Kinetics, which described the properties of single macro-coils and of interpenetrated macro-coils for M<Me. The solution of the dual nature of the interactions between the conformers (which were covalently intra-molecularly bonded along the chain and inter-molecularly interacting with neighboring conformers) was therefore represented by the formation and the fluctuation of bb-grains surrounded by F-conformers. The grain structure of the b-conformers came about intuitively from the notion that they locally interacted, forming, at least temporarily, a cooperative unit. The cohesion of the melt resulted from the local fluctuation of the grain formation and dissolution, giving the appearance of the delocalization of the grain structure in space (this was not true, of course, below Tg).
At first, I associated the fluctuation with the thermal motion, but I recently understood, with the introduction of the Grain-Field Statistics, that this was not a trivial issue at all, that it was, in fact, the most important theoretical problem I had to address and understand (with ramifications in all branches of physics).
Consider a “normal statistics”: the energy level between two states is constant, say Eo , which defines an homogeneous field. I define a Granular-Field a fluctuating field, for instance a series of Eo and 0 values over dt time intervals. The Grain-Field parameters would be associated with the amplitude Eo and the frequency corresponding to dt. This field is not homogeneous, it is granular. The granular aspect, in time, of the field can be described via a Fourier transform into a series of sine waves, so the problem of studying the response generated by a granular field is, in fact, equivalent to studying a variable field such as E= Ea sin(wt+Q). This is a fascinating research on its own, which I will publish separately.
What interests me, in this communication, is the impact of introducing a grain-field into the dual-split kinetic equations, especially to describe the interactions between two interpenetrating macro-coil systems, leading to their self-diffusion. As I said above, the stability of the Cross-Dual-Phase solution is the consequence of the existence of the Granular Field.
The very existence of entanglements would be due to the granular aspect of the field defining the
conformational statistics!
Also, to make a long story short, it can be shown that the local grain structure, giving rise to the localization or delocalization of the b-grains, derives from the fluctuation of the conformational field. The frequency of the local fluctuation of density (due to the (b/F) <-->(c, g, F) statistics) is not simply due to thermal fluctuations, it is correlated to the parameters of the Grain-Field.
The Pink-Flow technology originated from this new understanding of the interactions between the conformers (summarized as “entanglements”) which came about from the theoretical work I conducted , making granular the conformation field of the dual-split equations. This was 2010-2011.
It now appears possible to determine a specific set of processing conditions which can modify “plastically” the network of phase-entanglement (versus “visco-elastically” in the 1st generation of disentanglement processors) so that the major drawbacks of the first generation of machines could be overcome. The 2nd generation Rheo-Fluidification technology is compact and adapted to the high throughput rates of the industry. Its efficiency no longer depends on the residence time in the Rheo-Fluidizer. Validation tests are the next phase.