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.
