The
End of an Era in Polymers
There is new Rheo-SANS evidence, just published (July 17th),
which strongly suggests that our current understanding of the flow and relaxation of entangled polymers, based on
the reptation theoretical model of motions pioneered by de Gennes (1971) and
Doi-Edwards (1979) is fundamentally wrong:
“This
result calls for a fundamental revision of the current theoretical picture for
nonlinear rheological behavior of entangled polymeric liquids…the predictions
by the tube model are not experimentally
observed in a well-entangled polystyrene melt after a large uniaxial step
deformation” conclude the authors.
and
if you wonder about the credibility of these authors, they are all scientists
working at the most reliable international institutions in the world: the 1,2Oak
Ridge National Laboratory, Oak Ridge, Tennessee (USA), the 4Center
for Neutron Research, National Institute of Standards and Technology, in
Gaithersburg, Maryland, the 3Department
of Polymer Science of the University of Akron in Ohio(USA), the 6Institut
Laue-Langevin, in Grenoble France, and the 5Department of Chemical
and Biomolecular Engineering, University of Delaware (USA).
The
paper in question is remarkably well written, based on explicit and well
explained experimental procedure, an innovative analysis, and is easy and
fascinating to read:
Fingerprinting Molecular
Relaxation in Deformed Polymers
Selected for a Viewpoint in Physics
PHYSICAL REVIEW X 7, 031003 (2017)
by
Zhe Wang,1,* Christopher N. Lam,2 Wei-Ren Chen,1 Weiyu
Wang,2 Jianning Liu,3 Yun Liu,4,5 Lionel Porcar,6
Christopher B. Stanley,1 Zhichen Zhao,3 Kunlun Hong,2 and Yangyang Wang2,†
I extract below
a few excerpts from this paper to highlight the procedure and conclusions for
my purpose on this blog #32. I have chosen not to paraphrase their text and
decided to literally quote entire sentences and paragraphs, because either I
happened to agree with the content of the statements made (which I could not
have expressed in a better way myself), or because of the clarity and the
quality of the writing, which I found rare these days. Not to mention the use
of the scientific method to present their new data and the new analysis
(spherical harmonics deconvolution). I have also left the references’ marks in
the brackets, but the reader will need to go to the paper to access those.
PAPER OVERVIEW
“The entanglement phenomenon is one of the most important and
fascinating characteristics of long flexible
chains in the liquid state [1–3]. Our
current understanding of the dynamics of entangled polymers is built on the
tube theoretical approach pioneered by de Gennes [4] and Doi and Edwards [5–9]."
“The advent of the tube model has revolutionized the field of
polymer dynamics, and the predictions of the model about both the linear and
nonlinear viscoelastic properties of entangled polymers have been significantly
improved over the years, by incorporating additional molecular mechanisms such
as contour length fluctuation [10–12], constraint release [13–17], and chain stretching [18–20].”
"The GLaMM model (after Graham, Likhtman, Milner, and McLeish [20]),is widely considered the state-of-the-art version of the tube
theory, as it incorporates the effects of reptation, chain stretch, and
convective constraint release on the microscopic level through a stochastic
partial differential equation for the contour dynamics."
“In an effort to account for the nonlinear rheological behavior,
Doi and Edwards [6] proposed a unique microscopic deformation mechanism
for entangled polymers, which asserts that the external deformation acts on the
tube, instead of the polymer chain [21]. The chain retraction within
the affinely deformed tube would lead to nonaffine evolution of chain conformation
beyond the Rouse time, with entanglement strands being oriented but hardly stretched.
This hypothesis, being a keystone of the tube model, stands in stark contrast
to the elastic deformation mechanisms of many other alternative theoretical
approaches such as the transient network model [22–24], where the affine deformation mechanism is adopted.”
“How can we critically test the chain retraction hypothesis of
the tube theory for entangled polymers? The investigations in the past have
been focused on the analysis of the radius gyration tensor in step-strain
relaxation experiments, following the original strategy outlined in the
celebrated 1978 paper of Doi and Edwards [6].”
"The chain retraction along the tube around the Rouse time would
reduce all components of R2g. After the retraction, the
chain continues to relax towards the equilibrium state through reptation."
“In principle, one should be able to critically test the chain
retraction hypothesis by performing SANS experiments on uniaxially stretched
entangled polymer melts and comparing the measured Rg with theoretical predictions.
In reality, experimentalists have encountered tremendous difficulty in following
this approach.
…it is practically impossible to reliably determine the radius of
gyration tensor through model independent Guinier analysis, because of the limited Q range and flux of existing SANS instruments and the large
molecular size of entangled polymers.”
“Here, we present a general approach for extracting microscopic
information about molecular relaxation in
deformed polymers using small-angle scattering (SAS).”
EXPERIMENTAL PROCEDURE
“Rectangular samples (of PS) are uniaxially stretched at 130 °C to a stretch ratio λ=1.8,
with a constant crosshead velocity v=40l0 /τR, where l0 is the initial length of the sample, tR the Rouse relaxation time (~10 min). The samples
are allowed to relax for different amounts of time (from 0 to 20τR) at 130 °C and then immediately
quenched by pumping cold air into the oven. At 130 °C, the Rouse time of the
sample is about 10 min, whereas the terminal relaxation time is on the order of
7 h. Furthermore, since the test temperature is only about 30 °C above Tg, the relaxation time increases sharply with decreasing
temperature. In our experiment, it takes less than 10 s for the temperature to
drop from 130 °C to 125 °C, at which point the chain
relaxation is already exceedingly slow. Therefore, we are able to effectively
freeze the conformation of the polymer chain with negligible stress relaxation
during the quenching procedure.”
A
NEW ANALYSIS APPROACH: THE SPHERICAL HARMONIC EXPANSION.
“In the polymer community, Roe and Krigbaum have already
conceived the idea of spherical harmonic expansion of the orientation
distribution function of statistical segments in deformed polymer networks and
discussed the potential application of this technique in analyzing the
variation of x-ray intensity of the amorphous halo observed for stretched
polymers [72]. However, it was not until the work of Mitchell
and co-worker almost 20 years later [84–86] that a more formal treatment of the measured scattering
intensity in terms of Legendre expansion for the uniaxial extensional geometry
was developed. Despite the widespread use of this method, the polymer community
has so far mainly looked at the problem of scattering of deformed polymers
through the lens of rheology, where the major interest is to extract an order
parameter to compare with stress. Consequently, the previous works in this area
fell short at recognizing the value of spherical harmonic expansion as a
general approach for characterizing Q-dependent deformation
anisotropy and chain conformation at different length scales.”
“This approach helps to distill the “hidden” information about molecular deformation from the
distorted 2D spectrum.”
“The spherical harmonic expansion analysis permits a direct and
unambiguous comparison of SANS experiments with the theoretical picture of the
tube model.”
“It has also been
recognized that the model-independent nature of the harmonic analysis not only
enables quantitative characterization of materials but also allows one to
challenge constitutive relations. From this perspective, our spherical harmonic
expansion approach to SAS and the widely used (generalized) Fourier analysis in
the complex fluids community share a similar philosophical root.”
.
EXPERIMENTAL EVIDENCE CONTRADICTS THE TUBE MODEL
PREDICTIONS
“In the case of uniaxial extension geometry, the above-mentioned
mechanism (the GLaMM’s tube retraction)
is expected to lead to a nonmonotonic change of radius of gyration in the
perpendicular direction during the stress relaxation. Figure 3(b) gives an example for the evolution of the radius of gyration in
the parallel and perpendicular directions to stretching, calculated according
to the GLaMM model.”
Compare the reptation model prediction (Fig. 3(b)) with the
experimental results (Fig. 6(a)):
“It is (also) evident
from Fig. 5 that the unique scattering patterns [Fig. 3(c)] associated with chain retraction are not experimentally
observed.” Compare Fig. 3(c), the tube model prediction of a shift of the
minimum. Fig. 5 shows that the experimental minima at various relaxation times
do not shift.”
CONCLUSIONS OF THE PAPER
“Unlike the previous investigations, there is no ambiguity
associated with model fitting and no room for human bias. Therefore, our
critical test clearly demonstrates that the chain retraction hypothesis of the
tube model is not supported by small-angle neutron scattering experiments.”
“We show that the two prominent spectral features associated
with the chain retraction—peak shift of the leading anisotropic spherical harmonic expansion coefficient
and anisotropy inversion in the intermediate wave number (Q) range around Rouse time—are not experimentally observed in a well-entangled polystyrene melt after a large uniaxial step deformation. This result calls
for a fundamental revision of the current theoretical picture for nonlinear
rheological behavior of entangled polymeric liquids.”
“Therefore, without an alternative mechanism for molecular
relaxation, the idea of nonaffine deformation alone does not seem to be able to
explain the experimental observation.”
“…the lack of evidence for chain retraction does not imply that
the chains do not relax. On the contrary, both the stress measurements Fig. 4(b)] and SANS patterns (Fig. 5) suggest that the system
does continuously relax towards the equilibrium state. Therefore, the issue of
chain retraction is about the pathway
through which the chain
relaxes.”
“The spherical harmonic expansion analysis permits a direct and
unambiguous comparison of SANS experiments with the theoretical picture of the
tube model. The chain retraction hypothesis of the tube model is not supported
by the new SANS measurements of well entangled polystyrenes after a large step
uniaxial extension.”
“Since the tube theory is of paramount importance for our current
understanding of the flow and deformation behavior of entangled polymers, the
invalidation of the chain retraction hypothesis has immense ramifications.”
“It should be emphasized, however, that the current
investigation is only concerned with the tube approach in the nonlinear rheological regime. In other words, our work does not question
the linear part of the tube theory.”
THE END OF AN ERA
“Our work does not question the linear part of the tube theory”
say the authors. I do; its interpretation of shear-thinning, for instance, has
been discussed in previous blog posts (#22,#23), and proven wrong by Rheo-SANS
evidence, once again. Refer to the experimental work of Noirez et al and
Watanabe et al, who independently showed that for shear deformation at high
shear rate, triggering an intense shear-thinning effect, RG remains
constant, in total contradiction with the tube model prediction.
Remember what Karl Popper once said:
"Good tests kill flawed theories; we remain
alive to guess again".
I understand there is a comprehensive apprehension in abandoning
a concept which has reached, after over 47 years of subtle improvements, the status
of a scientific truth, trusted like an established dogma. But there is no such
a thing as a dogma in science and only experimental results can establish
themselves as scientific truth, not theories (the “guess again” of Popper).
I proposed it before, I will say it again: the reptation model
must be buried!
With Honors, certainly, yet buried in the annals of the great
wrong achievements like the Ptolemaic system and its great wrong description of
the solar system planets motion.
What could replace this “knowledge”?
THE DUAL-PHASE AND CROSS-DUAL PHASE MODEL OF THE AMORPHOUS PHASE.
I
can’t proclaim that this new model of the interactions in polymers will ever
reach any status of recognition among my peers, but I am convinced that some of
the fundamental ideas embedded in its foundation could lead to new advances in
polymer physics, and, more generally, in physics, especially for understanding
dynamic systems in non-equilibrium.
“This book describes a new understanding of the
interactions between polymer macromolecules and a new interpretation of
entanglements as the chain length increases. The eight chapters of the book
focus on the flow properties of melts (rheology) and offer a new basis to
describe the classical experiments performed to determine the viscosity and the
elasticity of polymeric melts. It is suggested in this work that the classical
concepts of rheology (relaxation time, Me, GoN, Newtonian
viscosity) may be useful parameters at low rates only, becoming deficient and
being responsible for the difficulty to describe non-linear effects
(shear-thinning, strain softening) as the strain rate or the strain increases.
A new model of visco-elasticity is presented which is applied to linear and
non-linear regimes. This work is the result of 40 years of intense research on
this subject.
…the new
model used to describe the source of molecular motions and flow is termed the Dual-Split
Statistics of the conformers; this model provides a quantitative way to determine
stress and strain from the variation of the conformational state of the
conformers. Grain-Field Statistics, which generalizes the application of the
Dual-Split Statistics of conformers to “open dissipative systems”, is
responsible for the existence of “entanglements”, i.e. the split of the system
of interactions between conformers into two open dissipative systems, which we
call Cross-Dual Phases. This is the core of the originality of this work.”
There
is a need to better understand the amorphous state, and by this I mean the
interactions within the amorphous state resulting in molecular motions,
orientation and the flow behavior.
There is a need to comprehend the thermo-kinetics
duality of the amorphous state, profoundly impacting its (free volume) structure
and generating its instability, the source of non-equilibrium properties.
In
addition to its application to melt deformation, helping to re-invent our
understanding of melt rheology, as explained in the book, this new “knowledge” has
pertinent consequences on understanding crystallization from a new dynamic
point of view: from the state of non-equilibrium of the amorphous melt point of
view.
There are as many different iso-amorphous
states as crystalline forms, and their co-existence in semi-crystalline
polymers remain essentially in non-equilibrium conditions, all the time, even
above Tm.
This new knowledge is of paramount importance to determine
and control the mechanical properties of plastic materials.
A
new theory of crystallization accounting for the dual-phase aspect of the melt
must be created and implemented (see Blog #29: Do We Really Understand
Crystallization in Polymers? ).
The
simplest evidence of melt instability and its inherent properties comes from
realizing that what we call “entanglements” is actually the expression of
interactive coupling interactions defining non-equilibrium states.
The
reptation model is failing the Rheo-SANS evidence, both in shear and in high
strain elongation, because it is incorrectly understanding “entanglements” in
polymers. In the reptation views, the singular chain is the center of attention.
In contrast, in the Dual-Phase model, the statistical system to describe the
interactions is not the macromolecule, it is the conformer, although the
increase of the macromolecular weight is determinant to trigger the changes of
properties that we perceive as caused by “entanglements”.
The question of the
stability of the entanglements is totally missing in the current molecular
dynamic models, and thus those models are confined to describe quasi-static
experiments corresponding to linear visco-elastic conditions.
It is time to provide processing engineers,
compounders, resin processors with the right mathematical concepts to tackle
the high speed rates they face in their manufacturing craft.
