New School Polymer Physics

The Source of Molecular Motion and Flow in Polymers

2012-01-17T01:48:00.000-08:00

I have just posted a new Video Clip Lecture (#21) which explains how interactive coupling of Dual Phases can be used to describe thermally stimulated molecular motions and flow (rheology).

This subject is closely related to my previous post, yet the information is presented differently and the format (video lecture) is more casual.

This lecture is available on the WIZIQ teaching platform:

http://www.wiziq.com/tutorial/194924-The-Source-of-Molecular-Motion-and-Flow-in-Polymers

Dual Phase Visco-Elasticity

2012-01-16T04:35:00.000-08:00

Polar plot of Modulus vs Phase Angle for the dissipative and Elastic components of the two Dual Phases (red and blue).

I have finished part III of my series ¨ The Great Myths of Rheology¨. The paper is going to be published momentarily. This paper talks about the melt network elasticity, diffusion, shear-thinning and strain softening, in other words melt deformation and flow.

It is a rather long paper, which no one likes to consider reading, yet I write it like a novel, introducing my parameters like an author would introduce his actors. I also make flash backs and replace intuitive images by equations, which themselves produce new conclusions, more intuitive images. I am never far from my subject, which is to describe the experimental data, but I try to innovate not just on the ideas advanced, but also on the style to present them.

Well, the objective was not really to entertain, but to launch new ideas. The style may help the reader swallow this whopper.

My real objective was to lay down the background for the Grain Field statistics, knowing that it would take two or three more lectures before I am ready to expose the mathematical model.

It took me a while (several years) to develop the connection between molecular motion and flow within the framework of the dual-phase concept. Flow induces transport of matter and it was a real challenge to integrate this with interactive local motions, which I thought I had described well in my work on thermal stimulated relaxation (see one of the previous posts of this blog).

I reproduce below the Introduction of my new paper.

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 [1,2], we showed that the existing models valid in the linear visco-elastic deformation range were not adequate to extrapolate to the non-linear 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 visco-elasticity parameters emerge and the new view of the deformation of a polymer melt results in a different definition of the entanglement network.

INTRODUCTION BACKGROUND
The mathematical treatment serves as a way to support the concepts, but the reverse is also true, the concepts of dual-phase naturally led to the search for these mathematical tools. Thus, the concepts are introduced early on, in a qualitative and intuitive way, and refined as the results emerge giving support or challenging the initial ideas. For instance, thermal diffusion in polymer melts is imaged, in our views, by a continuous coherent sweeping motion of “the phase-lines”, defining the boundaries between the dual phases, organized as a continuous network. These phase-lines are constantly in motion, with natural frequency w’o, to insure melt isotropicity and homogeneity despite the free volume difference between the dual-phases. At one stage of melt deformation, the orientation of the phase-lines occurs and creates anisotropicity which is compensated, at least partially, by an increase of the sweeping wave frequency to maintain the homogeneity of the cohesion between the interactive bonds. We describe this mechanism (and other competing ones) mathematically in this article.

We consider a new parameter, wR= w /(G'/G*)^2, where w is the radial frequency, G' is the elastic modulus and G* the amplitude of the complex modulus and study how it correlates to viscosity, suggesting that shear-thinning can be simply expressed in terms of w and (G’/G*)^2. We show that (G’/G*)^2 can be split into two terms, k1 and k2 , i.e. (G’/G*)^2 = k1 + k2 , the variation of k1 and k2 with w and temperature being fundamentally related to the mechanisms of deformation of the network of interactions (inter-and intra-molecular in nature, working coherently and defining the viscous cohesion). We show that the k2 term is related to the energy stored by the network of activated phase-lines (“entanglements”) which may lead to its entropic modification (orientation) resulting in a further increase of the sweep wave frequency, so k2 is a characteristic of the deformation mechanism occurring in the “strand-channel-phase” of the two dual-phases. By contrast, we show that the k1 term is related to the core-phase, the other dual-phase, which participates in the response to deformation by way of compensation with k2, either by diffusion (at low strain) or by a stretch-relax mechanism (at higher strain) similar to what is observed for the k2-phase when shear-thinning is active.

We define w’ as the dynamic frequency of the entanglement network, w’ = w/ k2 , and show that w’ correlates simply with the total stress generated by the flow mechanism in the shear-thinning regime at low strain. At vanishing w, w’ converges to a finite value, w’o, that we associate, as already said, with the fundamental static diffusion of the network of entanglements, i.e. with the natural sweeping wave frequency of the entanglement phase to interpenetrate the core phase, delimiting the contours of the boundaries between the dual-phases. We correlate w’o with the onset of non-Newtonian viscous flow behavior. Subtle differences of the variation of k1 and k2 emerge for various thermo-mechanical treatments of the melt or by varying temperature or the magnitude of the strain applied.

The analysis of the split of (G’/G*)^2 into k1 and k2 suggests to assign a physical dynamic attribute to the elastic entanglement network, whose deformation occurs by an activated mechanism of stretch-relax, and the need to characterize its stability under stress. We also define the elastic cohesive energy of the dynamic network, DELTAw, which varies with both frequency, w, and strain since it directly correlates with the number of activated strands of the dynamic network, k2 . We study the influence of the Talpha transition, the mechanical manifestation of Tg, which varies with w and strain ,and which we write Tg(w,strain), on the visco-elastic behavior, showing that it plays a significant role in the mechanism of shear-thinning and strain softening, and propose a way to evaluate its impact on k1 and k2. Multiple examples are given comparing k1 and k2 for linear low density polyethylene (LLDPE), polymethylmethacrylate (PMMA), polycarbonate (PC), polystyrene (PS), polyethylene terephtalate glycol (PETG) and polypropylene (PP) melts. The influence of temperature on the elasticity of the dynamic network of entanglements suggests a change of the characteristics of the elastic network in the melt above Tg, an observation already foreseen in a previous communication [1].

The effect of strain is an important section of this paper. We show that the essential role of strain is to activate the k1-phase to participate actively (by shear-thinning) in the deformation process. In linear viscoelastic conditions, the conformers[1] in the k1 dual-phase do not deform, their motion is through diffusional reorganization, i.e. delocalization in the structure triggered by the stretch-relax deformation mechanism (shear-thinning) of the k2-phase conformers. When the k1-phase is activated by an increase of the strain, strain softening occurs. In the discussion, we present a new understanding of “the network of entanglement” and show how its orientation and gradual instability gives rise to the mechanisms of deformation observed from very low w to high w, at various strains. We suggest that the network character of deformation is not due to topological considerations but, instead, due to the cooperative coupling nature of the interactions between the macromolecules conformers which organize according to a Dual-Grain Field-Statistics. In this model, the duality aspect comes twice: it comes at the local level of interactions between the conformers, and this duality is dealt with by the introduction of the Grain-Field Statistics applicable to macro-coil systems. The equations of the Grain-Field Statistics predict the dynamic aspect of the interactions between conformers. But the interaction between macro-coils introduces a second level of duality, above a certain size for the macro-coils (which we consider to be the onset of entanglements), responsible for the molecular characteristics of the dynamic network.

In summary, we introduce in this article new methods of analysis of the rheological results which appear to confirm an essential aspect of the cohesion of the interactions between the conformers and the existence of the “entanglements”, the existence of a Dual-Phase structure. The question of the stability of the network of interactions, which was an essential focus of experimental investigation in part II of this series [2] is reviewed here in terms of the Dual-Phase model.

[1] Conformers are defined in refs. 33-35. Also see Fig. 12a.

Dependence of Viscosity on Molecular Weight at constant Free Volume

2011-09-04T03:45:00.000-07:00

I already expressed my interest in determining if the famous 3.4 exponent that characterizes the melt viscosity dependence on molecular weight (for entangled polymers) would be different when the rheological data are determined at constant free volume.

In particular, I wanted to know if de Gennes had been right in the first place, coining the exponent at 3.0 in his famous 1971 paper.

The analytical technique to analyze rheological data at constant free volume is presented in a WIZIQ lecture found at http://www.wiziq.com/NewSchoolPolymerPhysics977161

(class#2: On the incidence of Tg and Talpha on the formulation of rheolgical equations)

I have now addressed and completed a series of monodispersed polystyrene grades and the result is shown in the figure above:

THE EXPONENT IS NOT 3.0, NOR 3.4, IT IS 5.3

Besides, in the Vogel-Fulcher's expression of the temperature dependence of the friction factor, the famous T2 - for which viscosity becomes infinity- is raised from 55 oC to 123 oC, when the free volume is accounted for.

These results show how important it is to correctly describe the effect of the free volume on molecular mobility when analyzing dynamic rheological data. The mythical constants, 3.4 for the viscosity exponent, T2=Tg-52.5 for the WLF equation, are the results of cooperative contributions from free volume and conformer rotations. The influence of free volume is not separable the way it is traditionally presented: in our analysis, free volume influences both the T and M factors in the viscosity expression.

Interestingly, the temperature of 123 oC is 23 oC above the Tg of polystyrene, determined by DSC, for instance. And this temperature is precisely the temperature of compensation for this polymer for all the relaxation modes occuring below Tg. Refer to a previous blog page on "Interactive Coupling between Relaxation Modes". One knows that the coupling between the molecular motions below Tg, resulting in compensation, occurs in a very restricted free volume environment, compared to what is assumed to occur above Tg. It is, therefore, somewhat satisfying to find that the T2 obtained after removing the effect of free volume is the same as the compensation temperature found from a study of motions in the solid state.

It is also remarkable to see how the free volume is intrinsically coupled with the effect of molecular chain length above Tg: mobility is much more reduced (by a factor 100) than what one thought was only due to molecular weight alone. The influence of molecular weight is described by the exponent 5.3, an extraordinary large number. This is only because the free volume is interactively coupled with the configurational effect that we observe the 3.4 exponent. As said before, viscosity does not separate into a term that varies with T only and a term that is function of M only. This formulation is only a convenient approximate representation.

So, unfortunately, the brilliant demonstration by Prof. de Gennes to explain the restrictive mobility in polymer melts will remain, in my mind, incomplete, perhaps even "un faux pas".

The Optimist: the little man at instant t

2011-04-03T07:26:00.000-07:00

The Optimist by Baptiste Ibar (2001)

I am looking at a painting across the room, above the fireplace, “the Optimist” it is called. It is a large painting, showing just a few elements, a black dead tree with branches, a red ladder that folds up in the air in a bizarre way, leaves that fly like butterflies and seem to pass by, disappearing towards the horizon, and a little man suspended from a rope, posing his feet at the intersection of the ladder and the tree. The whole scene is overlaid on top of a background color divide between just two colors, gold and burgundy. The flying leaves are all colored in aqua green.

It is breathtaking, mysterious, deep but simple, naïve but profound, it brings me peace and a sense of existing, as if time was passing in front of me, like fishes in an aquarium...

There are several basic concepts I relate to in this painting. The structure of the painting is this basic split between two colors, although note that these two colors are not complementary. What makes it work, it seems, is the presence of the aqua green stains which spread on boths sides, ignoring the divide, giving the appearance that the two colors are much more compatible than they actually are. The aqua green color turns out to be beautifully contrasted with each background color, gold and burgundy, giving that appearance. This may be a basic principle: get a compatibilizer, a diffuser, it will blur a divide. A divide is a split, like a discrete quantum event, either 0 or 1, not a smooth variation between 0 and 1. The leaves are also a set of discrete objects, yet their presence, as a transversal spread, smoothes out the discontinuity, renders the divide more continuous.

Perhaps this illusion also comes from the fact that the leaves are independent objects, present in the picture but without belonging, since they seem to ignore the main story of the painting, the little man, the rope, the tree and the ladder, they are parallel to the event, yet they play an essential role in the overall aspect of the painting. The size of the butterfly leaves decreases when they approach the horizon divide line, which gives them the apparence of being in motion across the scenery towards infinity. This adds to the picture a dynamic dimension, introduces time as a reference, making the event of the suspended man a space event, at instant t. Perhaps the little man on his tree is watching the passing of the butterflies and, during his time of observation, his position in space is stable.

This is the other concept that I see coming out of this painting. Consider the chances for this exceptional event consisting of this moment of coincidence where the branch of the tree, the ladder step and the feet of the little man suspended from his rope exactly meet. This event is like an interaction in space and time. The painting is a snapshot of this coincidence. The tree has many branches, filling space, increasing the chances that events of this sort will occur. Branching permits to duplicate the possibilities, expanding the area for the reaches with little expansion demands from the tree itself, a very efficient way to increase the chances to reach out (create interactions), but the search is done randomly, at irregular intervals, it symbolizes unpredictability. The ladder is like a one dimension space filling, it explores space by changing direction, the whole ladder is redirected in the new direction, this is a different approach than branching. The presence of rungs, transversal to the main direction, provides a second degree of space filling, it symbolizes regularity, periodicity, the order dimension. And our little man is there, in equilibrium between the tree, the last bar of the ladder and he holds himself from the rope above him. What a coincidence! None of the other tree branches could do that, none of the other ladder configurations, no other rungs could do that, no other position of the little man on the rope would work. The occurrence of the event has to be very sparse, almost unique. How long will it last?

This occurrence reminds me of the way nature works, it tries and tries, fails a million times, continues to try until a coincidence occurs, a node, an interaction, and the important question is its stability, the durability of the interaction. Matter emerges from that mechanism, which I call chrono-condensation. Structuring can occur at different scales, depending on the stability of past solutions, increasing the inertia to create new coupled interactions. The ladder of solutions interlocks like a chinese lantern,from small to large, from 1 small to 1 large, yet still through the same mechanism, repeated over and over again. We are part of those interlocked cycles, we are part of why it stands. We are hanging to our rope, just for the time to let the butterfly leaves pass by.

All of these ideas emerge from this beautiful painting. I assure you, I see all these things: physics is everywhere!

This is what the artist said about his painting:
“I decided to call it "The optimist" after thinking about our talk and how all of the elements and events meet up at a certain point in space/time.... the optimist believes in these events happening perfectly in the present moment. Therefore feeling fearless of the future and free from the past.”

Here is a portrait of the artist in his studio in Brooklyn, NY

On the Incidence of Tg and Talpha on the Formulation of Rheological Equations

2011-03-01T05:37:00.000-08:00

One often uses Frequency sweeps at constant temperature to analyse the rheological characteristics of polymer melts. But, I suggest, it would be preferable to popularize Temperature sweeps at constant frequency w instead.

Why?

Because frequency plays two roles and it would be easier to deconvolute their respective influence:

- Frequency increases the value of Tg (or Talpha) and therefore decreases free volume when T remains constant; this increases viscosity.

- Frequency plays a significant shear-thinning role in reducing viscosity.

By working at (T-Tg(w)) constant one can study how the rheological parameters vary at constant free volume. There are surprising and interesting results from such an analysis, but it requires to correct the data obtained at constant T and to know the variation of Tg(w), i.e. the frequency map for the Talpha relaxation.

By working at constant w, Tg(w) is fixed, and one can obtain shear-thinning results by simply sweeping the temperature (cooling or heating) at a given rate.

In the video-lecture available from the following link, we study the incidence of working at constant free volume on the classical relationships found in rheology, such as the Maxwell fits at low w of G'(w) and G"(w), or the evaluation of the terminal time from the maximum of G'/w vs logw etc.

http://www.eknetcampus.com/videopresentation/On the incidence of Tg and Talpha on the formulation of rheological equations2.avi

This work suggests the importance of incorporating the influence of several parameters: w Frequency, T temperature, P Pressure, M molecular weight, L lambda, the elongational stretch ratio, on the value of Tg, i.e.

Talpha (w,T,P,M,lamda)

A New Understanding of Entanglement -The Quizz

2011-02-01T07:30:00.000-08:00

I launched a series of 12 classes on January 13th 2011 on the WIZIQ teaching platform.

Here is the link: http://www.wiziq.com/online-class/430878-the-need-for-a-new-understanding-of-entanglement-in-polymer-physics

The video recording of the class is available to people who access the above link. I post (below) another direct link to view the class, without the need to register with WIZIQ. It appears, though, that viewers need to be online in order to view the recording, saved or not, meaning that if the file is saved on a computer, it still needs to be watched on-line!

http://www.eknetcampus.com/WIZIQ/Class1_video_recording/634305601542868750.exe

In any case, I like to communicate, before, during, and after the class, and I have enjoyed the many exchanges and discussions by email.

I preceeded the announcement of the class by a quizz, THE ENTANGLEMENT QUIZZ, with 22 questions (http://www.wiziq.com/online-tests/22446-the-entanglement-quizz).

I had 56 students who tried the test, with an average of 8 out of 22 good answers. Of course, "good answer" depends where one stands with respect to the entanglement concept. What it really shows is how different I stand on the topic.

Like Boris Vian once said (about something else): "My views are right since I made them up".

I have posted a pdf file with my answers and comments to the entanglement quizz:

http://www.eknetcampus.com/WIZIQ/ANSWERS%20to%20the%20Entanglement%20Quizz.pdf

The main idea to remember from my first class is that "entanglement" manifests the reality of the physics of dual-phases and how it changes scales with the number of interactive units involved. It is a "slow motion" example of how energy of interaction and population size interact to define the scale of a statistics. It's the chance of a lifetime for statisticians, who normally deal with very fast relaxation processes, therefore solutions for steady state problems. With polymers, motions are considerably slower, giving the opportunity to conceive and adapt simpler models to describe "scaling" , hence to illustrate complex mathematical abstract concepts by using common language: Ah... writing a Renormalization Group Theory for Dummies... using polymer entanglements!

It is true that de Gennes initially thought of that idea, but he stayed too far from Prigogine to set up his initial statistical frame, and got stuck with single chain dynamics in steady state.

Here is a picture of entangled dual-phases. The duality is at two levels for M > Me. This is why there is a critical molecular weight. Below it, there is only one duality, the one responsible for the compensation phenomena below Tg and for the Boson peak observed for glasses.

My next class is scheduled for February 17th, 10:30 am Eatern US standard Time.

check it out: http://www.wiziq.com/online-class/454992-molecular-weight-and-frequency-dependence-of-tg-on-rheological-data

The Great Myths Part II: Abstract, Summary, Conclusions

2010-11-24T12:47:00.000-08:00

Drawing by Baptiste Ibar (2009)

Some of the students have asked me to put a link to the Abstract, a short Summary of the paper and the Conclusions. Here it is:

ABSTRACT
https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B1EGViD3w4U0NzU5NTQ2NDEtODQzNS00NTk4LTkzOTItMDU0NTI0ZWM5ZjVm&hl=en

SUMMARY

To summarize some of the findings and thoughts expressed in this paper:

- Transients and steady states must be described by a unique theory of the deformation of interactive conformers. We suggest it is necessary to understand non-linear effects first and to have linear viscoelasticity derived by extrapolation to infinite time. In other words, time, frequency (or strain rate) and strain should be involved in the mathematical description of the deformation process (in the quantification of the moduli).

- A melt can be brought out of equilibrium with respect to its entanglement state. The return to equilibrium explains the transient properties. New entanglement states can be made quasi-stable, even at high temperature in the melt, by coupling entropic and enthalpic effects produced under specific conditions of melt processing.

- The currently accepted descriptions of rheology only apply to a stable entanglement state, which is not general enough. For instance, the WLF-Carreau equation of viscosity-strain rate does not correctly describe the rheology of an unstable entanglement network. The modelization of the influence of a network of entanglement on the melt deformation mechanism in terms of parameters introduced in linear viscoelasticity (tauo, GoN, Me) provides the wrong answers when the entanglement network has become transient.

- The influence of strain on the rheological equations is currently not addressing the issue of its influence on the stability of the network of entanglement, and therefore is incomplete.

- The interpretation of the phase angle between stress and strain in terms of a dissipative and an elastic component represents an over-simplification of the mechanism of deformation which, we believe, mischaracterizes the relative influence of a network of strands on the elasticity / relaxation process versus the influence of the local bond orientation (the conformer statistics). The difference between the two permits to define the amount of interactive coupling reorganization due to entropic vs enthalpic drives and under what conditions of strain rate and strain they occur. An entropic driven coupling mechanism of deformation can be viewed as an activation, then orientation process of the active network of strands. We have made the suggestion, in this paper, that the active number of system strands (defining the EKNET network) is proportional to (G'/G*)^2. In fact, the active number of strands is not exactly proportional to (G'/G*)^2 but can be calculated from (G’/G*)^2 , and is almost exactly equal to (G’/G*)^2 shifted by a constant when its value is approximately less than 80% of the maximum of (G'/G*)2 .The enthalpic contribution starts beyond that.point and corresponds to the orientation of the network. We suggest that only certain compensations of enthalpic and entropic contributions result in stable “sustained oriented entanglement states”. This set of conditions would be the equivalent of “plastic yielding” and implies highly anisotropic samples.

- An increase or decrease of G* (t) and thus of viscosity can be produced when the network of strands is unchanged (Figs 1a to d of the paper) and local orientation/relaxation is responsible for the transient behavior, and the relaxation times relate to the properties of this network. In order to obtain a modification of the network, one needs to add energy to it until it yields. Strain rate or frequency are capable of reaching that point for any strain % deformation, but the value of the strain % allows to decrease the frequency or strain rate at which the network starts to deform.

CONCLUSION

The deformation of a polymer melt in shear mode is the main subject of interest in the science of rheology of such materials. It is a crucial topic for successfully processing these materials. As illustrated in part I of this series and in the above examples, it is a complex and rich subject which is far from being fully understood.

In part I of this series, we suggested that even the linear visco-elastic behavior of polymer melts (at low strain rate and low strain) was not satisfactorily described by the accepted theoretical models, when carefully comparing experiments and theoretical predictions. In the non-linear range, at high strain rate and strain, the subject of this part II, it is generally admitted that the current theoretical developments that successfully predict the main characteristics of polymer melts in the linear range come short but merely need improvements. The improvements proposed generally consist in tweaking certain assumptions of the linear viscoelastic model to be able to extrapolate to the non-linear behavior. There is no current theoretical challenge to the dominant reptation model of melt deformation in polymer physics. The aura this model has reached among polymer scientists makes it more difficult to search for other explanations for visco-elasticity and rubber elasticity. Yet, as we suggest, it is possible that the experiments described in this paper challenge the reptation school to its limits, to the edge of usefulness.

As already concluded in part I of this series of papers dedicated to flow, the theory seems to be fine in the linear range in appearance only. The “devil is in the details” says the old saying. The present understanding of the physics of macromolecules is based on an analysis of the properties of a single chain. The presence of the other chains is perceived as a mean field influence on the properties of that chain. The reptation school considers that this mean-field can be described as a topology, an homogeneous field of obstacles restricting the motion of the single chain and explaining the molecular weight dependence of viscosity. The mobility is constrained within an imaginary tube and the chain “reptates” within that tube. The shortcomings of the predictions of that model made the initial static tube evolve into a more dynamic tube, capable of evolution, in time and as a consequence of the various modes of deformation of the melt. The tube was therefore thought to have a stability of its own, it could fluctuate in length, and, to address some of the non-linear issues, it could get thinner and elongate in length. In other words, the tube itself had evolved into a “super macromolecule” capable of deformation very similar to what early polymer scientists would assign to macromolecular chains themselves. Perhaps, at the horizon of the reptation school, also lies the concept of entanglement of the tubes themselves!. We are not suggesting this idea totally ironically, because it illustrates another concept that we will develop in a follow up article of this series, that of the need to not only define the scale of the basic unit that participates in the deformation process, but also to determine the link and the modulation between cooperative scales.

In explaining several figures of this paper, we made reference to a “network of strands” to describe the cooperative interactive process resulting from the macroscopic deformation. We obviously referred to a basic unit of deformation that involved the cooperative motion of a group of bonds responding as a set. We must define what cooperation means, how many bonds cooperate in an active strand and where they are located, on a single chain or on several chains?. The physics of dealing with all the chains at once is the model that we have adopted to describe the deformation of polymer melts and solids, above Tg and below Tg. The theory not only addresses the interaction between the conformers of a single chain to assume the shape of a macro-coil (which can be deformed), but also defines why entangled macro-coils exhibit the response of a network of active strands when all the chains participate cooperatively in the deformation process. The link between the deformation of a conformer, of a macro-coil and of a network of strands must be fully described.

The Great Myths of Rheology, Part II: Transient and Steady State

2010-11-24T06:01:00.000-08:00

Should I start by saying that this long article just got published?

"The Great Myths of Rheology, Part II: Transient and Steady State Melt Deformation: the Question of Melt Entanglement Stability".

Journal of Macromolecular Science, Part B(Physics), Volume 49, issue 6, November 2010, pp 1148-1258.

You can find the links to the published paper, the Abstract and the Table of content by going to my teaching course on-line at:
http://www.WIZIQ.com/NewSchoolPolymerPhysics977161
go to the bottom of the page where I have several downloadable lectures listed. If the one you are looking for is not displayed (it rotates every week), you need to register to wiziq.com to have access to all courses, or send me an email and I will send you the free sign-up invitation. Also, check out the Eknetcampus website http://sites.google.com/a/eknetcampus.com/the-great-myths-of-rheology/

You will be able to connect with me on line through a series of classes which I will present LIVE on Tuesdays and Thursdays to enrolled students. Some of the class material is already available.

How did this idea of teaching on-line got started?

I was facing a panel of scientists (all French professors) this past September for my HDR (qualification to University Professorship) and was presenting my views on this new polymer physics, which I said I wanted to teach to graduate students. One of the reviewers had strong eyes, had been quite agitated during my presentation, and had been given the lead start to question my qualifications:

He said: "so, are you suggesting that what I taught my students for the last 30 years is wrong, worth tossing to the bin".

He had a mustache much thicker than mine (see picture below), and, I have to add, I had reviewed with my niece Pauline, on the morning of the HDR, a short memorandum written by Cardinal Mazzarin on the art of convincing an audience (to achieve success?);

I replied:"... not to the bin, no Sir, absolutely not to the bin, but, may I suggest we could all honor it in a nice room of the history museum?"

Darn, I just thought of that answer, it's good, I should have said that, but, instead, I probably said "Heu, ..., well,..., but, ...heu, yes,..., well not really...". I am like Jean-Jacques Rousseau who had "l'esprit d'escalier", always thinking of what he should have said when he was running down the stairs afterwards, not when he was there, mumbling a stupid answer.

In any case, OK, I can now teach, the President of my HDR Panel said so, reading the verdict: "and now..., you have been given the ability to guide students to research the truth", ...or something like that.

Quite a responsability. I take it seriously.

My next move was to make available on-line to the community of students a few of my hundreds of courses which I have prepared, but not finished, like a painting without a signature. I have finished a few. They are on-line at the address given above.

I have another anecdote about my HDR: I finished my presentation by giving two quotes, one from Ilya Prigogine and one from Scott Page:

" All models are wrong, and that's why you want a diversity of models" (S. Page, Social Scientist, U. of Michigan, Time, June 1, 2009 p.40)

and

"L'ecart a l'equilibre conduit a des comportements collectifs, a un regime d'activite coherent impossible a l'equilibre...Pour donner une signification dynamique a cet ecart d'equilibre, nous devons incorporer l'instabilite au niveau dynamique" (I. Prigogine, Nobel 1977, in "La Fin des Certitudes", Editions Odile Jacob (1996), p. 183,184.)

The mustached Panelist urged me to explain myself about this crazy intention to teach to students that "all models are wrong". "I will not give you my daughter as a student", he said. Yet, the panelist next to him elbowed him and said:" but he can certainly have my son..."

My intention is to teach to graduate students first, those engaged in their doctoral research. They must learn all the models and make up their mind so that they can create new ones. What is beautiful in science is the "experimental method" (Claude Bernard). Undergraduate students must learn how to apply the experimental method and models are just a part of the story on how to master this.

Models open up new ideas for new experiments, the truth is in the next experiment.

"Disentanglement "of Polymer Melts in a Dynamic Rheometer. YEAR + 14 Perspectives

2010-10-30T02:12:00.000-07:00

In this video presentation , we introduce the subject of "disentanglement" to describe triggered transients in dynamic experiments. In part II of the Great Myths of Rheology (J. of Macromol. Sci. Part B, 49, 6, 1149-1258 (2010), I explain why these transients cannot be resulting from surface effects or artifacts. Middway through this lecture (~26 min to the end) I discuss the basic assumptions of my new model of interactive coupling leading to the Dual-Phase split and the definition of the entanglement network. Part II and Part IV of the Great Myths of Rheology are devoted to the description of the network elasticity and of Dual-Phase Viscoelasticity.

http://www.google.com/url?q=http%3A%2F%2Fwww.eknetcampus.com%2Fvideopresentation%2FN29_017_Disentanglement_of_Polymer_Melts_using_a_lab_dynamic_rheometers_APS_%2520presentation.avi&sa=D&sntz=1&usg=AFrqEzdn2vBtlmaI4k5sjzOgFdN51d9qZg

Grain-Field-Statistics Applied to Conformers in Interactions

2010-10-29T10:21:00.000-07:00

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).

Interactive Coupling of Conformers studied by Thermally Activated Depolarization

2010-03-05T05:35:00.000-08:00

The use of "thermal-windowing" methods to decouple molecular motions in polymeric materials was in the nineties a very popular method to characterize polymers, as a result of the introduction of the automated TSC/RMA spectrometer from Solomat Instruments on the thermal analysis market [282]. The decoupling of the relaxation modes responsible for internal motion leads to a better understanding of their coupling characteristics which often relate to the state of the material itself.

Originally, thermal stimulated current depolarization techniques were used to measure charge detrapping in low-molecular-weight organic and inorganic compounds. Ever since 1967 they have been applied to the study of structural transitions in polymers.

The credit for the initial development must be given to Professor C. Lacabanne and her co-workers at the University of Toulouse, France. She pioneered the use of the technique of " thermal-windowing polarization" as early as 1974, and has applied it to the study of a wide variety of macromolecular materials.

Several techniques exist to analyze the molecular response of materials to physical or chemical inputs, in order to determine their specific performance. Differential Scanning Calorimetry (DSC), and Differential Thermal Analysis (DTA) are among the most popular in laboratories and on production sites. Other techniques include Thermal Mechanical Analyzers (TMA), Dynamic Mechanical Analyzers (DMA), stress relaxation or creep analyzers, thermal expansion coefficient devices, and dielectric analyzers (DEA). The method of thermo-stimulated current (TSC) consists in putting the specimen rapidly at high temperature (above the transition temperature at which the relaxation phenomena is expected), orient the dipoles at that temperature and freeze-in the orientation thus produced by quenching at low temperature (Fig. 0-1).

Fig. 0-1

The voltage field applied is then removed and the temperature is ramped linearly back up to reveal the polarization induced at high temperature. TSC is therefore a thermally stimulated recovery experiment. An electrometer is connected to the sample to record the short-circuit current while heating . A current is created when the material depolarizes. This thermally stimulated current reveals the molecular mobility of the material's structure. The rate of depolarization is related to the relaxation times of the internal motions providing a new opportunity to study the physical and morphological structure of materials.

The depolarization current, J, flowing through the external circuit is measured by a very sensitive electrometer (capable of measuring currents 10 million times smaller than those measured by a tunnelling microscope), and allows determination of the "dipole conductivity".

The current peaks recorded this way (Figs. 0-2a and 0-2b) are found to correlate well with the transition temperatures measured by mechanical relaxation (DMA), by DSC or by conventional (a.c.) dielectric spectroscopy (DETA). A TSC output looks like a tan δ versus temperature plot, showing maxima at the transitions occurring inside the material. In fact, TSC provides very similar results to those obtained from other analytical instruments operating at the same low frequency equivalent (10-4 Hz), with the addition of an accrued sensitivity, and a separating power unseen in other technologies.

Fig. 0-2a

Fig. 0-2b

The concept of "thermal-windowing" gives the TSC another dimension. Windowing consists of polarizing only a fragment of the full spectrum of relaxation and depolarizing it partially to isolate or "window" a single relaxation process. There are two types of possible windowing techniques: the first method, which can be called "partial isothermal recovery" or "isothermal windowing", consists of the following: first, polarize the sample at temperature Tp for a time tp adjusted to allow orientation only of a certain fragment of the dipoles. At the same temperature Tp, cut off the polarizing voltage and stay at Tp for a time td. This allows the depolarization of a fragment of the oriented dipoles. Finally, quench the sample to To << Tp. Reheat at constant rate and measure the current of depolarization. Δt = (tp - td) is the "time-window" and can vary between 1 min and about 1 hour.

The most practical and commonly used thermal deconvolution method is the "thermal-windowing" experiment (Fig. 0-3), because it essentially gives identical results and it is the fastest.

Fig. 0-3

In this option, a constant voltage is applied at Tp for a time tp, commonly of the order of 2 minutes. The temperature is then lowered to Td at which the voltage is removed and the specimen allowed to recover partially for a time td, usually equal to tp. ΔT = (Tp - Td) is the temperature window and can vary between 1 oC and about 10 oC. The specimen is then quenched by 50 to 100 oC to a sub-temperature To where the amount of polarization induced in the material is frozen. A linear heating-up is then performed, and the variation of current due to thermally induced depolarization or other current discharges is observed as a function of time (i.e. temperature). Since the current J(t) is the derivative of polarization, the ratio P(t) divided by J(t) is a quantity with the dimension of time and represents, according to Bucci [56], the elementary relaxation time τi typical of the relaxing system. Figure 0-4 shows the result of thermal-windowing on the TSC output.

Fig. 0-4

When tp, td, and (Tp - Td) are conveniently chosen, the depolarization current is supposed to represent the relaxation of a single Debye relaxation mode isolated from the spectrum of relaxation modes. By varying the value of the temperature of polarization Tp, and repeating the above thermal-windowing process, one can isolate the elementary modes one by one (Fig. 0-5).

Fig. 0-5

The computer in the TSC/RMA spectrometer integrates the current vs temperature peak for each temperature, and calculates the value of the relaxation time at each temperature. The analysis, according to the Bucci's equation, of each resolved Debye peak obtained at various polarization temperature gives a temperature dependent retardation time τi(T) which often follows an Arrhenius dependence (Fig. 0-6).

Fig. 0-6

The relaxation time is the inverse of the frequency of jump between two activated states. According to Eyring, the intercept of the Arrhenius equation is proportional to the Entropy of activation for the activated process involved, and the slope is proportional to the Enthalpy of activation. If a structure is "loose" the contrary of "ordered" or "compact", i.e. when molecular mobility is less hindered by the interactive intra-intermolecular surrounding, the Entropy of activation will be "larger". Conversely, any parameter which acts to "organize" the structure and create a tighter environment for the bonds will cause a decrease of the Entropy of activation. So, the activated Entropy calculated from the intercept of Figure 0-6 gives an indication of "the degree of disorder" (DOD) of the structure.

The technique of TSC/RMA is used to determine the degree of cooperativeness between the relaxation modes responsible for internal motions at the main transitions occurring in non-conductive materials, revealing the state of the structure and the morphology.

Fig. 0-7

A relaxation map (Fig. 0-7) is the collection of relaxation lines obtained for each deconvoluted Debye peak, and analyzed according to Bucci's equation. Relaxation maps can be looked at as "fingerprints" of the material, being representative of its chemical structure, morphology, and non-equilibrium structure (Fig. 0-8).

Fig. 0-8

Relaxation Map Analysis (RMA) determines the elementary Enthalpies of activation, and the pre-exponential factors (related to the Entropy of activation) for all the relaxation modes obtained by varying the temperature of polarization Tp.

In summary, the relaxation observed during the recovery stage of TSC reveals the kinetics, and the powerful method of "thermal-windowing" deconvolutes the individual relaxation modes. This allows the study of their coupling characteristics, reflecting the structure and the physical state of the material. Constitutive equations can be used thereafter to reconstruct the material dielectric behavior (Fig. 0-9) by calculation of the fundamental physical parameters from the spectrum of relaxation (dielectric permittivity, etc) .

Fig. 0-9

The various Arrhenius lines obtained by thermal-windowing at different polarization temperature Tp often converge to a common point, the compensation point (Fig. 0-10).

Fig. 0-10

The essential focus of interest in the work of thermal stimulated process analysis seems to lie around this phenomenon of compensation, the determination of its coordinates, the interpretation of its origin, its practical use to characterize the degree of coupling in the amorphous phase of polymeric matter, and its relationship with the state of (non) equilibrium.

In a certain sense, one could say that a new type of thermal analysis is born with the understanding of "thermal-windowing", since compensation phenomena apparently reflect the coupling between relaxation motions occurring cooperatively, and also because this new thermal analysis technique can describe WLF type of behavior susceptible to comparison with results observed in rheological experiments (upper temperature curve, T > Tg, in Fig. 0-8).

In subsequent blogs, we concentrate on many aspects of the depolarization phenomena. We compare the TSC results with those obtained by other techniques. We cover theoretical topics, such as the origin of the polarization, or the possible interpretations for the effect of voltage field. We use computer modelling to curvefit the depolarization curves, and give the equations which describe the effect of voltage, temperature of polarization or depolarization, etc.

Most importantly, We explore in depth the technique of thermal-windowing and use it to deconvolute the cooperative response of polymers at their main transitions, mainly the glass transition. We provide a new method to characterize the glass transition, and determine the respective contribution to the Entropy of the electronic and atomic vibrations.

The presence of multi-compensations in a material might be linked to the existence of multi-phases, and we dedicate a full blog to analyze blends, block copolymers and the other applications of RMA to which the concept of DOD (degree of disorder) applies its full force. But the presence of multi-compensations also occurs in cases where the material is known to be monophasic. The comparison of the multiple compensation RMA spectra for brittle and ductile polymers, or between annealed and quenched liquid crystal polymers is intriguing and will be explored in depth, because, we believe, it expresses the heart of "interactive coupling between conformers".

Interlude blog: PAINTINGS from New York Show (May 2009)

2009-06-12T08:31:00.000-07:00

1st INTERLUDE: Swans Realms

RELAX: Beautiful art can be seen on this link (from New York Studio School):

http://maiaibar.blogspot.com/

Art is the ultimate free expression of emotions. Its interactive aspect with the viewer is most interesting. Talking about a painting reveals the person as much as what the painting immortalizes. The interpretation of the emotions from looking at a painting is what's makes me so attracted to art, beyond the crafting skills.

The paintings by my daughter Maia drag me deep inside them with a force that exhausts me. This may be due to a sensation of whirl created by an harmony interplay between two or three layers, a local level with small details, and a large scale level that consolidates the colors, overpowers the details, integrates, fuses the small pieces together, as the image is defocused, concentrating on the overall piece. In my world of thoughts, I always see high frequency components part of a larger integrated system in a moving environment, a system and its twin shadow, the distorted and fading mirror image of itself, like if the past was the present that had started to dissolve.

Of course, you will say, I am using words of physics to relate to art, and I will answer that it is precisely my point, it reveals who I am.

I discovered, for instance, an art piece that Maia did, "Swans Realms" that reminded me estrangly a sketch that I once did , before she was born, which described my Dual-Statistics concept of interlocked kinetics (which I call Energetic Kinetics Duality). I spent hours looking at this painting at the New York Studio School, where she exhibited last month:

http://4.bp.blogspot.com/_P8NDk779MP4/SgCTDbBshBI/AAAAAAAAAJc/4qcjPZrQjKE/s1600-h/IMG_3884.jpg

and could not understand why this painting attracted me like glue, until I realized the analogy with my own ideas in physics of interactive coupling, and the strange resemblance it evoked with my cartoon sketch of those ideas (see the Figure below).

I wanted to know what my daughter meant in the painting. The whole show was about her immense misery and sufferance after the tragic loss of her boyfriend, her love, Charlie, in January this year. How come one dies at 24? The exhibit was about Charlie, where is Charlie now, does he still communicate?

In the Swans Realms, Maia was of course making the portrait of herself reaching out to Charlie, in his new world, the connect being somewhat diffuse, as death and life after death are still not well defined. The swan from the top is "touching" the swan below through this narrow uncertain chanel, but definitely influencing its existence, defining its boundaries. The space occupied by the swans is moving, depending on their respective influence: who influences who?

This is the way I saw the painting: a 1st layer, the triangle containing the drawing, expresses the continuity of time, the fluidity of things, the arrow of time. A 2nd layer is a split between two domains that each contain a figure, a swan, a fine line separating the two domains. A symmetry between the upper and lower swans puts them in a sort of connected position, but the beakers join in what looks like a spark discharge, not a single point. One of the swans is smaller than the other, the symmetry being scaled by the size of the confining domains; the details of the swans skirts are not identical, just similar in appearance, but quantitatively distinct.

All these particular features take a special meaning when one now looks at the sketch of "a Dual Split Kinetic diagram":

I defined "conformers", an entity that could represent many small systems in physics, but that I applied to parts of macromolecules in that sketch (a macromolecular chain being a series head-to-tail of conformers). The overall shape of the sketch is not a triangular figure, like in Maia's painting, but an oval, but what matters in the analogy is that it actually defines an overall confinement system, splitted into two domains, limited by a loosely defined line, the serpent in the oval. The b-conformers and the F-conformers "occupy" each domain, and one sees details within domains, for instance two horizontal lines of the b-domain are designated tF and cgF. The same details, but looking like miniature horizontal lines, are repeated within small circles drawn inside the b-domain, and if one zooms on those details, one can read tb and cgb. Identical letter symbols, t and cg, are used to represent the same conformation of the conformers in either the b-or the F-domain. The analogy with the Swans Realms picture starts to emerge. The reality of the conformers, labelled by the letters c, t, g to describe the spatial position of its atoms, also called their intramolecular conformation, as a cis, a trans or a gauche conformation, can be found in two interactive coupling "worlds", the b and the F domain, b standing for "bonded" and F for "free".

The Dual-Phase Statistics is a set of assumptions to describe the cross-kinetics between all these conformers, the tF and tb states, the cgF and cgb states in one hand, and between the t and cg states in the other hand. All these states co-exist, and because they are assumed to stabilize in an equilibrium state where they all exist, one needs to define an inhomogeneous field of interaction, actually "a granular" field of interaction would be a better description.

In classical physics, a homogeneous field of attraction/repulsion between particles, described as a mean field, is assumed to control the statistics, and it is taken as the average value of the field over spatial and temporal scales. So, if fluctuations of the interactions exist, their influence is co-linear in spatial and temporal dimensions and in phase with the mean value, in classical stastistical theory, meaning there is no need to worry about the possibility that averaging in the space or time domain is going to provide different results. I call this a smooth one dimensional statistical theory of interactions, as opposed to my new cross-statistics, the result of this granular Dual dimension statistics, the subject of my research starting in my Ph-D thesis at MIT.

So, back to the New York Studio School. Here is the scene: I have been standing and exploring for twenty minutes the details of the Swans Realms. A secret chill is emerging from inside of me as I see the analogy with the granular statistics. I sweat and smile, I want to dance.

At that point, everything takes a magical spin, as I am living the intense experience that people could connect in spaceless and timeless spheres to reach the same emotions or ideas from completely different angles.

But the next moment I panick with a new thought: perhaps this drawing by my daughter is the proof that what I conceived in physics years ago, what I consider perhaps my greatest theoretical achievement, is purely conceptual, has no physics "reality" behind it: perhaps it's just the expression of a human conceptualisation of reality, like art, perhaps it is art, just another theory, just another sketch with equations, the cover up for BS! Oh my God!

My wife taps my shoulder and asks if I am allright, and I immediately blame the jet lag for refusing the bit of cheese on a piece of bread that she is handing me.

Like Shakespeare said, the main question remains: BS or not BS?

PS:

I turned around and grabbed that cheese, I will tell you why in a future blog.

Here is a picture of the artist, Maia Ibar:

The Great Myths of Polymer Rheology Part I

2009-06-12T08:10:00.000-07:00

Viscosity of polymers is key to their behavior in the molten state and thus to their processing. The well known equations of rheology giving the temperature, strain rate, frequency and molecular weight dependence of viscosity are the basic equations that theories must explain. This is what de Gennes and other theorists before him had tried to explain (among other properties of course).

In a paper that will be published very soon (J. Macro. Sci. Phys, issue 6, 2009) I show that the admitted view that molecular weight and temperature separate in the expression of viscosity is only an approximation that theoretical models should not therefore succeed to explain. Furthermore, the classical 3.4 exponent for the variation of Newtonian viscosity with molecular weight is shown to represent another curve fitting approximation of the effect of entanglements on the viscosity.

“Shear-Thinning”, the lowering of viscosity with an increase of shear rate, demarking the Newtonian regime, is a fundamental property of polymer melt. I review the use of scaling variable on log-log axes to describe shear-thinning, such as Vinogradov’s plots, and show the limitations of such an approach, which often leads to very wrong extrapolations and predictions when “unwinded”, and the results compared to reality. I also review, using statistical tools from regression analysis, the validity of the time temperature superposition principle, another fundamental concept of rheology, and demonstrate that the principle is not valid, even when a graphical fit “ looks good”.

The WLF equation (due to Williams Landel and Ferry in the sixties) describes well the temperature dependence of the horizontal shift factor, log aT. This well admitted equation is also critically reviewed and compared to other simple curvefitting equations which provide as good results, although offering a very different insight into the physics responsible for melt or rubber deformation. In particular, it can be shown that the interpretation of the shift factor in terms of the ratio of Newtonian viscosity is an approximation limited to a narrow temperature range. Same such approximation also applies to the ratio of the terminal times, calculated from plots of G’/w vs w in dynamic experiments. The vertical shift factor, log bT, is not equal to (T1 p1/Tp), as predicted by the temperature dependence of modulus, according to rubber elasticity. This is clearly coming out of accurate shifting done analytically, instead of graphically.

The concept of relaxation time and spectrum of relaxation times, another mammoth concept in rheology, is critically examined to show that it is fundamentally wrong to apply it directly to polymer melt deformation (unless it is accepted as a curvefitting tool, on the same basis that polynomials or Fourier series descnbe well any type of curves). In that context, it is shown that models such as the Rouse model, de Genne’s, Doi & Edwards’, and all their improved versions (for instance by Klein, Montfort, Graessley, Larson, Wagner, Marrucci, or MacLeich), that describe (well?) the molecular weight and temperature dependence of relaxation times, are necessarily limited in their description of melt deformation to the linear regime where the curvefitting power of such mathematical tools gives the impression of their success.

I suggest that these Pantheonic models are not capable (without an extreme demonstration of mathematical modeling skills, that looks more and more like an exercise of cover-up) to describe the non-linear regime, which is the only regime important to real life, i.e. to processors of plastic melts. In particular, the present understanding of shear-thinning, normal stresses and strain-hardening of polymer melts in terms of chain reptation / renewal deserves critical attention.

Forty years ago, the polymer field was dominated by chemists and physical chemists who understood linear visco-elasticity in terms of networks of dashpots and springs, but were puzzled by large amplitude strain rates and strain behavior, especially by the effect of strain. Their interest and success in describing rubber elasticity and swelling” molecularly” (under equilibrium conditions) in terms of Gaussian chains whose length could affinely be related to macroscopic strain, can be viewed as the birth mark of modem physics, "a la" de Gennes, but also, perhaps, the source of the mis-understanding of what entanglements are, and how their existence affect the melt deformation, in particular what entropic deformation means. I critically review the present classical understanding of the influence of entanglements on melt deformation, and expose its limitations.

Another model of melt deformation and of the influence of entanglements will be presented in a series of articles and blogs. This model elaborates a profound different understanding of the source of viscoelastic behavior and of rubber elasticity.

If you want to be emailed the following paper (1.44MB): “The Great Myths of Polymer Melt Rheology Fart I.pdf” insert your email address in the comments box for this blog. You can also find it in issue #6 (2009) of the I. of Macromolecular Physics.

Part II of the Great Myths deals with transient and steady state, and the stability of the entanglement network, the subject of my next blog.

Why a new School in Polymer Physics?

2009-06-12T07:24:00.000-07:00

Is this the place to expose new foundation for polymer physics?

Warum nicht?

It may sound odd to use a public blog to discuss a subject interesting mostly to specialists. I agree, but, after publishing over 100 peer-reviewed articles, most of them never referenced nor read, the direct exposure to the public via a different route takes some justification. At least, I hope this blog will be read by those students intrigued by its title.

Why would anyone need to create a new school of thoughts in polymer physics?

1. “Timing is every thing”, people say (I have seen Agassi’s commercial), and it’s the right timing. 30 years of intense research on the subject is not enough to have exhausted my investigation, but now is time to communicate.

2. Sometimes in science, an established school of thoughts has enough control over the publishing channels that it prevents, although in a subtle way, publication of new or controversial ideas that may shaken its stable grounds, or lead to the impression that its understanding is at best shaky, that the subject is not as well known as it should, after all these years of publications and awards to praise the important people who constantly write about them (the H-rating obliges...) The pity is that despite the fact that important results were, indeed, obtained, there seems to be a cover up now to avoid exposing the limitations reached by the models, and their ramifications, which led to these achievements.

3. Fundamentally, I advocate, the science of polymer physics is now working in circles, patching up with more and more band-aids a model of polymer deformation, the reptation model, that has prevailed for the last 35 years, and now stands like a crippled soldier returning from the first world war, with scars everywhere, crotches and a black eye, after all the modifications to make its stand. Support from the establishment consists in the protection at all cost of the POW returning home: no one is allowed to say bad things about heroes. So here we are. The generals will not allow a tolerant debate, because the subject is so deeply rooted in terms of classical reptation polymer physics that showing a different approach looks useless or insulting, which, in the polite way of saying things in science, means “wrong”, unpublishable.

4. If the experiments you show (or re-analyse) cannot be explained by the established model, it’s not the model to question, Monsieur, “these experiments are wrong”, say the Generals. They must be. Period. No discussion. Paper rejected: “these results contradict our present knowledge on the subject”.

5. If you can explain with your new model the features described by the established model, but you use a different statistics, place a new focus on what defines your thermodynamic system of interactive units, or define entropy of deformation in new ways, then the comments take the subtle tone of irony (“who do you think you are?”), with an elegant gesture of the full arm that says: "here is the Exit door, mon cher".

6. The Generals’ tolerance Chart reads like this: Yes, we are tolerant to controversy, the best proof is that your paper is allowed to be presented at our international convention on Thurday night (when every body has left) around 6: 30 pm (when the few left are hungry and tired), or in Poster Sessions. Yes, Sir, Posters are extremely well-attended, don’t disagree please. By the way, send a check for $ 750 for being part of this well organized meeting. Do you need a receipt? And the Circus of the Establishment rolls on.

7. I have only reached 5 minutes into this writing, and am experiencing this sense of freedom in style which is so far away from the congested, “constipated” style we normally use in scientific publication, where we feel obliged to quote references every two lines, as if someone was there to justify the validity or the importance of what we write. I want to be able to put anecdotes into my story, make the scientists I have met live through recollection of meetings with them, or courses tought by them.

8. My philosophy at this point on polymer physics and polymer processing stands like this: in order to continue to progress, i.e. imagine new experiments, explore new commercial applications, especially based on non-linear effects in visco-elasticity and melt deformation, we need to pause and step back, re-evaluate the work done for the last 70 years, and go back to Treolar, Bueche, Kuhn, Alfrey, Boyer, Flory, Gibbs Di Marzio and other giants from the 60’s and 70’s. Is it possible that de Gennes’s extraordinary insight in coining “reptation” has lead to 35 years of too-fast forwarding which now needs a total rewind. The situation is the same in many disciplines, not just in science of course (the string theory has reached in theoretical physics this same situation of dogma, which is equally intolerable), but also in other activities organized by humans. The total surprise is that scientists behave like human beings. Who thought otherwise?

I remember, back in the early 60s, in Courchevel, skiing was taught by instructors de l’Ecole Francais de Ski (EFS)who told you to plant your pole, adjust your skies to have one move forward and turn around your pivot. Then came Grunberg, Falcose and other instructors who presented a very different style, invented “la godille”, were not allowed to teach this different method to ski, were fired as instructors from the established EFS school, and had to create their own “Nouvelle Ecole de Ski Francais”. That eventually became the “ski moderne” with Perillat, Killy and all the other champions illustrating the success of this technique. The tension and confusion between who was the real school lasted for several years. Humans at work, “same same but different” , as the Vietnamese say.

This is why I have created this blog. I want to expose an entirely new way to explain polymer physics. I started this work a long time ago, actually in 1972 as I had started Graduate studies at MIT. Of course, I have not finished, but I am now intensely focused.

Let’s rewind polymer physics back to 1971. The big name was Flory. There are two things that pop-up in my mind when I remember the man, Paul Flory: one is a picture of him at the blackboard while he was teaching Prof. Edward Merril’s class at MIT for a semester, as a Visiting professor from Stanford: he was obstructing with his body what he was writing on the board, and at the same time mumbling with a very inaudible voice some comments about it. We were all making gestures to each other, stopping writing our notes, and wondering if this guy was the same great Flory from the “Principles of Polymer Chemistry”( 1953), a book that we all considered the equivalent of the Bible in the field. He did get the Nobel price a little bit later (1974), to show you how well Flory was considered at the time (the last person to receive the Nobel in the field of polymers was Staudinger himself, the inventor of the concept of macromolecules, decades earlier). De Gennes would be next.

My second recollection of Flory dates back to 1979, I believe, attending an international conference on polymer networks in Jablonna, Poland. At the end of the several days conference, there was a piano recital, and I was sitted near Flory in the first row. I noticed his beautiful fingers resting on his knees, and I could also admire the size of his jaw. It is kind of weird to observe someone’s jaw, but people were saying that he was shredding, “eating alive” they said, every one who stood against his ideas. Apparently, Prof. Corradini once stood up to Flory and disappeared in these powerful jaws. So, I was on the watch, carefully examining my chances. Of course, Chopin in the background was re-assuring, but, nevertheless, I had asked Flory a question, during one of the breaks between sessions, which I considered a little dangerous. The question was controversial, but I had used my best “I am a stupid-idiot” look to raise it, and had avoided to remind him that I had been one of his students at MIT:

Me (shaking): “Professor Flory, you once determined, through volume-temperature data in the melt, that there was a higher than Tg transition, later designated TIl by Dr. Ray Boyer of MMI, could you tell me what physical significance one should assign to this transition-relaxation”.

Flory: “ None. It does not exist, I don’t know any Boyer.”

End of the discussion, he had already turned around, after closely reading my name off my tag (putting a chill in my back, I was thinking of Corradini’s fate...Jaws III? ).

I heard of Flory’s death from Boyer himself. I had told Boyer that Flory denied knowing him, which amused him greatly, and he had called me to assure me that it was now safe to walk in the streets. I must add that I was somewhat shocked by this phone call. After all, I considered Flory as one of the giants in my field, and his second book, “Statistical Mechanics of Chain Molecules” (1969), on conformational computation, was one of my favorite classics (although some had said that he had “borrowed” many ideas from Volkenstein). Cf course, it would be fair to also add that Flory’s fame, when he received the Nobel, was indirectly negative to my reputation, because I had written a long paper in Prof. Uhlmann’s class about the uncertainty of Small Angle Neutron Scattering results to the determination of whether or not a polymer glass was in a theta-solvent condition, the same results (from Benoit) that got him the Nobel. Houps!

My contention was that there was enough uncertainty in the scattering resolution, especially demonstrated when temperature varied, to accept both Flory’s views, that the chains were Gaussian like in a Theta-solvent condition, or Boyer’s views, that there was local order present.

I had built a model in my thesis that could explain Boyer’s views. It explained rubber elasticity and visco-elasticity, and many properties of the glass, including crazing and yielding in terms of cooperative systems of "interactive conformers", and whether the radius of gyration was that of the chain in theta conditions or not was irrelevant to my new definition of entropic changes. BUT, if there was no local order to maintain my “EKT systems” thermodynamically stable in the melt, below Tll to be precise, how could my systems exist? My MIT thesis supervisor, Prof. Fred McGarry, started to gasp for air after Flory got the Nobel price! I was placed in a vaccum box and went into a deep coma shortly thereafter (I said in my profile that I like to maintain a good humor on things...).

If only I could find a way to make these systems of interactive units stable, without the need of local order. I searched for such a solution for several years, almost non-stop. The solution came to me in 1981. Of course, by then, the school of polymer physical chemists, the Flory, Boyer, Bueche, Volkenstein, Mark, Alfrey, Ward, Ferry, McCrum was long forgotten ( I learned later). Graessley had survived and had endorsed the new reptation ideas.

So, while I was creating a new statistical model to describe stable systems of interactive-coupling units (the Dual-phase statistics), the buzz word had become “de Gennes” in my back. His reptation model had been coined in 1971, but his success had started only in 1979, when Doi had fluctuated the tube’s length to stretch the exponent of the molecular weight dependence of viscosity from 3 to 3.4. The book by Doi and Edwards has become a classic, de Gennes’s beautiful mind, his elegance and charism convinced the world community.

In the next blog, I will focus on ‘the Myths of polymer rheology”, re-examining the basic experimental knowledge (the facts) that led de Gennes and others to introduce their model and claim that it described well those results. We will see that Myths can mislead even great scientists.

Basically, THE problem with the current established view stems from the focus to describe the motion of individual chains. In my proposed research the active system is not the single individual macromolecule, embedded in a sea of interactions. I use a different statistics bearing on the whole system of conformers in interactions, from all the macromolecules at once, and try to determine the coupling laws which makes this canonical ensemble react to a macroscopic influence, a deformation for instance. Entropy of deformation is different when the system is redefined. I call this new physics of polymers "poly-conformers physics". It leans on the presence of the chains, of course, but understands the specific particularities of polymers from a statistical approach which applies to smaller chain molecules as well.

The transition to polymers involves the famous concept of "entanglements", which is at the heart of the misconceptions, I believe, of the present state of understanding. I will present experimental results on polymers that are going to shake up the established views to such a point that the immediate reaction will be as I expect it to be. But I will continue to present the evidence, step by step, like the famous inspector of Agatha Christie. I already have the mustache, anyway...