I am currently writing a book dedicated to the understanding of the physics of polymers from a different point of view from the admitted models. In the classical views, the chain is particularized and its interaction with its surrounding is described in terms of a mean field of interactions. The entropy of a single chain is calculated from its intra-molecularly linked covalent bonds and the deformation-to express flow properties, for instance- is due to a modification of the entropy. The presence of the other chains is perceived as a restriction on the entropy, in particular, in de Gennes’s well praised model, by the confinement of the motion of the chain within a tube in which the chain can reptate. The sophistication of the “reptation” model comes from the refinement of the definition of the tube itself.
In my new model, I consider all the chains at once in their state of interaction, whether it is from multiple inter-molecular or intra-molecular origins. Thus the need to create a statistics which accounts for this global scale. I imagine that the field of interaction is not a mean field, and that it is “granular” due to thermal local fluctuations. The granular-field statistics defines the integration of the inter and intra molecular interactions, which are no longer two separate entities. I call this statistics a grain-phase statistics and study its properties in the first few chapters of the book. The novelty from my MIT thesis is the recent (last few years) understanding of the influence of long chain length on the properties of the grain-field statistics, in particular its split into dual phases beyond a certain value of the molecular weight, thus the definition of the entanglement network in terms of a dual-grain-field statistics. New calculations show that the increase of the relaxation times, naturally occurring as systems of interaction become bigger, becomes critically bigger when the threshold of molecular chain length is reached. This result, I have assumed, give rise to entanglement effects. I study this new complexity in subsequent chapters of the book, showing that it explains viscoelastic properties of melt in a novel way and perhaps predicts the reduced (and controllable?) stability of the entanglements with numerous applications to the polymer field.
I want to illustrate below with a few graphs the application of the Dual Phase model to linear visco-elasticity. I have written two articles "The Great Myths of Rheology, part I and part II" (published in the J. of Macromol. Sci. Phys, in 2009 and 2010) which inquire about the accuracy of the predictions by the current theories of the linear visco-elastic phenomena (part I) and about the transient and steady state rheology as it relates to the stability of the entanglement network(part II). These are big articles, perhaps too big for the modern reader who likes to "tweet" in 164 characters long messages. But, hold on, Part III (network elasticity)and part IV (Dual-Phase viscoelasticity) are on their way and also contribute their hundreds of more pages filled with graphs and equations. So, bear with me with these 3 graphs, if they can convince you that something is cooking, it's worth all the tweeters in the world, and, as you know, "a picture is worth a thousand words".
One more word about linear visco-elasticity: I was frankly not interested in digging the subject further and admitted, like most of us, that it was the area of achievement of the reptation modelists, their reason for power and glory. When I arrived at the University of Pau and Pays de l'Adour for my Fulbright Scholarship, I was told that linear viscoelasticity was the jewlry of polymer science, that it was complete, well described, a polished piece ready for the MOMA in New York. Fine.
I spent two years studying the theses of the rheology group in this inspiring institution and learned a lot about the classical models. I must say, at first glance, it looked good, impressive even. But, I noticed a few discrepancies, especially at low w (in dynamic data) for long polymer macromolecules. I saw a systematic deviation with the models' predictions and was not convinced by the explanations. I asked for the data, scanned and digitized the figures of G'(w) and G"(w) when I could not get the raw data, and here I was, comparing fitting residuals, implementing the parameters found in the theses and checking the accuracy of the predictions. This is why I wrote the first article of the Great Myths of Rheology: even the sacro-saint linear viscoelasticity needed some hey-not-so-fast comments.
In part II, I investigated the transition to non-linear behavior, at higher strain, which is a subject much more complex, but actually this is the range of deformation used by processors, the real world. Part of the problem lies in our profoundly anchored vision of molecular motions expressed in terms of a spectrum of relaxation times, a fantastic fitting tool in the linear range of viscoelasticity, but very difficult to handle in the non-linear range. Turner Alfrey (who I consider as one of the great minds in polymer physics) once wrote beautiful pages on this delicate departure to the world of non-linearity. What if the real world had to be explained first and the world of linearity derived from it? Would we need to throw out the idea of a spectrum of relaxation times?
Here are my three graphs, just to give you the feeling that other concepts can lead to a totally different approach to understanding deformation in polymer melts.
This is a typical G'(w) and G"(w) plot in rheology, obtained with a dynamic rheometer using a Polystyrene melt at T=235 oC. The Mw is ~ 300,000, the polydispersity 2. A classic. The lines passing through the data are the curvefitted lines obtained by applying the Dual-Phase model, not the reptation model (which would also provide an excellent fit).
Using analytical tools which I describe in the book one can determine the separate viscoelastic properties of the two phases: "phase 1", shown in this Fig. is one of the Dual-Phases. In this graph, it appears that phase 1 looks very much like an "unentangled phase " (such as found for M < Me)).
This Figure provides the viscoelastic properties of "Phase 2" of the Dual-Phases.
The cross-over point is now visible. The magnitude of the moduli is more consistent with what is usually considered a M > Me melt.
QUESTIONS
1. How do the Dual-phases vary with temperature?
An example can be seen in the picture at the top of this post, which applies to a Polycarbonate melt, at w= 10 rad/s, various temperatures. The cross-over of one of the phases (the low moduli one) extrapolates to the Tg of PC ! The other cross-over extrapolates to the NO-FLOW temperature for PC.
2. How do the Dual-phases vary with the MWD of the polymer?
3. Are the Dual-phases STABLE?
4. Can one modify (mechanically for instance) the proportion of the Dual-Phases?
5. Are the Dual-phases "reversed" for PS and PC?
These are some of the questions I raise and try to figure out in my writings, especially in my book and lectures. The book starts with this fundamental question: what kind of statistics do we need to describe these fluctuating interactive coupled Dual-Phases?
I have conceived a new set of kinetic equations which work on open systems and converge to classical formulas at equilibrium, but behave like Prigogine's dissipative systems as the size of the system increases. The size can increase as an alternative mechanism to a modification of the potential energy of interaction by the stress: this creates anisotropicity (preferred concentration of a type of conformers, say the trans, in the deformation direction) via a stretch-relax process: in that scenario, the macromolecule "rotates" (does not change its rms distance) while the phase-lines re-organize into a different net pattern.
Speaking of dissipative structures, I have just finished the book by Prigogine "La fin des Certitudes" and ask myself: Did he know that polymer entanglements could have been one of his topics of application?
Or is it the opposite which applies: could polymer physics teach us anything about dissipative systems? The study of the stability of entanglements may bring a lot of new ideas and new light onto the subject.
Ultimately, the understanding of why strain triggers transient behavior in melt must be resolved (see Part II of the Great Myths of Rheology).
