The Dual-Phase and Cross-Dual-Phase Model of Polymer Interactions to Describe their Physical Properties: Evidence from Spectroscopy , Viscous Flow , PVT Equation of State, and Crystallization.
Fig. 1
Deconvolution of
the 1st cooling peak Tx obtained by DSC for
PET
Fig.2 Fit of the DATA by the dual-phase model
(red:Fit,black:DATA)
At the New School
Polymer Physics, we explain the results of an (ongoing) extensive investigation
of the deformation behavior of amorphous and semi-crystalline polymers in terms
of a new model of interactive coupling between conformers belonging to
interpenetrating coil-macromolecules. The interactions between the conformers
respond to a dual-phase statistics defining a new entity, the b-grains, which
compensate with the local free volume and the conformers state
(cis-gauche-trans): [(b/F) ↔(c,g,t)]. Above
a critical molecular weight Me, the system defining the conformers’
interactive domain splits into two cross-dual-phase systems; that split of the
interactions into two compensating “cross-phases” explains the properties of
entangled macromolecules:
[(b/F) ↔(c,g,t)]1 ↔
[(b/F) ↔(c,g,t)]2
The spectroscopic evidence for the presence of b-grains in polymers (un-entangled
and entangled) was reviewed in an article that examined the work of many
scientists who concluded on the local existence of nodules (or “blobs”) in
glass forming materials. One of the best experimental evidence was presented by
Duval et al. using low frequency Raman spectroscopy. Duval et al assume a
non-continuous structure of glasses to interpret their inelastic neutron
scattering and Raman scattering results.
The boson peak in Raman scattering is related to the vibrational density
of states excess. Duval suggests that
the excess Vibration Density of State (VDS) is the result of vibrations
localized in "blobs" that compose the glass. Size distributions of the blobs can be
deduced from neutron and Raman scatterings. These blobs are frozen-in b-grains
in the glassy state.
-
J.P.
Ibar “Do we Need a New Theory in Polymers
Physics?” J.M.S-Rev. Macromol.
-
Chem.
Phys., C37(3), 389-458 (1997).
-
E.
Duval, N. Garcia, A. Boukenter and J. Serughetti, J. Chem. Phys. 99(3), 2040
(1993)
Both articles
are available on ResearchGate and Academia.edu
Viscous
Flow evidence.
Our investigation of
the deformational properties includes the viscous behavior (capillary,
rotational and dynamic shear viscosity). Flow is induced by the modification of the
interactions between the conformers belonging to the macromolecules due to the
imposed deformation, either by pressure flow or drag flow. Hence the existence
of the b-grains and of the split of the system of interactions into two
dual-phases (for entangled polymers) should have a considerable incidence on
the flow behavior, and vice versa. We use the dual-phase approach to show the
instability of the Newtonian state with respect to the b-grains, explaining the
solid-like characteristics of the Newtonian state evidenced by Noirez et al. (see
the corresponding blog here).
We provide a novel interpretation of
shear-thinning and distinguish the case of un-entangled polymers for which
shear-thinning is simply due to the rate effect of the dual-split equations
governing the interactions, and the case of entangled polymers (the stretch/relax
blinking model), for which the increased number of activated “strands” -sections
of the entanglement network-
sharing an increase of the demand for producing deformation
results in the classical shear-thinning reduction of viscosity with strain rate
or frequency. Hence, below Me, shear-thinning is
an inherent property of the dual-phase model, i.e. of the existence of the
b-grains, and above Me, it is a consequence of the entanglement
network, i.e. of the existence of two cross-dual-phases. We also point out the
deficiency of the prevailing reptation model in its explanation of
shear-thinning because of the contradictions raised by Rheo-SANS experiments of
Laurence Noirez et al. and Hiroshi Watanabe et al. (see
the corresponding blog here: SANS results contradict the Current Understanding
of Deformation)
Based on these new ideas about melt
deformation, a major part of our experimental work has consisted in studying
the strain conditions that trigger the instability of the network of
entanglements, leading to the “disentanglement technology”. In particular, we have combined, using “Rheo-Fluidification”,
the shear-thinning viscosity reduction and the strain softening decrease of
modulus to induce meta-stable melt
states with the ability to store as pellets the viscosity reduction triggered
by the time dependent non-linear processing conditions.
This is exposed in a series of papers all available on ResearchGate
& Academia.edu, also collected as a new book “The Great Myths of
Polymer Melt Rheology (SLP Press, 2016)”.
J.P. Ibar, Z. Zhang,
Z.M. Li, A. Santamaria, “Investigation of the Dynamic Rheological
Properties of a Polycarbonate melt presenting solid‐like characteristics and a
departure from pure liquid Newtonian behavior at long relaxation times., J.
Macromol. Sci. Phys. Volume 54, Issue 6, pp. 649-710 (2015).
J.P Ibar, “ The Great
Myths of Polymer Rheology. Part I.: Comparison
of Experiment and Current Theory', J. Macromol. Sci., Part B, 48: 6, 1143 —
1189 (2009).
J.P. Ibar “ The Great
Myths of Polymer Rheology” Part II.: Transient
and Steady State. The question of the entanglement stability. J. Macromol.
Sci., Part B, 49, 1148 -1258 (2010).
J.P. Ibar, “The Great Myths in Polymer
Rheology, Part III: Elasticity of the
Network of Entanglements”, J. Macromol. Sci. Part B, Phys. 52:222-308 (2013).
J.P. Ibar, “ Processing
polymer melts under Rheo-Fluidification flow conditions: Part 1. Boosting
shear-thinning by adding low frequency non-linear vibration to induce strain
softening.”. J. Macromol. Sci. Part B, Phys, 52:411-445 (2013).
Evidence
from the Equation of State (PVT)
All existing models
analyzing pressure-volume-temperature (PVT) results (Rachel, Simha, Prigogine,
Tait, etc.) always assume a homogeneous and isotropic distribution of free
volume or density in glasses and melts.
This is true of many prevailing models in physics which describe (well) homogeneous
statistically mean-averaged closed systems of interactions.
We show that the free
volume (and thus the b-grain location) in polymers is not evenly distributed, has
a structure, in fact has many “polymorphic structures”, depending
on the temperature and the pressure range. A visual analogy could be the more
familiarly known patterns showing the “Bessel function mode states” for a
resonating vibrating table starting from a homogeneous spread of sand grains.
For specific frequencies the grains assemble in fundamental patterns resulting
from the solution of the vibration produced wave propagation equations.
We advocate, via a
new analysis of the PVT data, that determining the average free volume is not
enough to determine the physical properties such as the viscosity or the impact
strength. To understand why Polycarbonate and Polystyrene differ so much in
impact strength, not just the amount of free volume counts but also the free
volume structure. These polymorphic
structures are a direct consequence of the dual-phase model of the
interactions.
Fig. 3a
Intercept of PV/T vs r (density) at various Pressure (0-200 MPa) and T (25-250 oC) for PETG.
The zones I to IV represent polymorphic states; When Intercept is plotted against slope for each P range (A,B, or C) of the PV/T vs r lines, a perfect straight line determines the common originating compensation coordinates (Nc, rc) for this P range (see Fig. 3b below for range [70-150 MPa, 25-250 oC].). The (Nc, rc) coordinates for the 3 P ranges themselves compensate (not shown), suggesting the global correlation and its origin from a common source: [ (b/F) ↔ (c,g,t)].
Fig. 3b
Nc is the total number of conformers involved in the formation
of a stable polymorphic volume structure in the P range {70-150 MPa, 25-250 oC,
range B}. Range A,B,C all compensate (Nc vs rc is linear). One can comprehensively
describe the PVT behavior of melts and glasses with this concept of polymorphic
packing states for the free volume structure within stable P,T zones.
Figures 3 are extracted from “Chengdu 12 Lectures on Physics of
Interactions in Polymers: Application to Processing –Lecture 2 (follow
this link).
Thermal
Analysis evidence.
Yet, not just the viscoelastic and mechanical
properties can be explained by this new model. Recently, we investigated the
solidification process from the melt in amorphous and semi-crystalline polymers
using thermal analysis (DSC, TMA) showing that discrepancies in the evaluation of
the degree of crystallinity calculated from the peaks on heating and cooling could
be resolved quantitatively by applying the dual-phase concept of b-grains vs
crystallization to fit and deconvolute the thermal peaks.
The thermal activity
analysis does not simply consist of the determination of the amount of
crystallinity and of the heat capacity, but also of the dynamics of change of
the b-grains, either their formation (exothermic) or their melting
(endothermic). Hence, the area under thermal peaks is not entirely devoted to
the phenomenon of crystallization or crystal melting, which is the reason for
the noticed discrepancies reported in a previous blog (link
to: Do we really understand crystallization in polymers?).
The two Figures at
the top of this blog show the deconvolution of the exothermal peak observed by Differential
Scanning Calorimetry (DSC) on cooling (@ 10 oC/min) for a sample of
PET, the so-called “crystallization peak”. PET is always chosen as the “model polymer” to
explain the DSC features in polymers. The deconvolution in Fig. 1 provides 6 peaks which,
pursuant to our model, we couple in two groups corresponding to the M and the S
phase (see later); each phase has one crystallization peak and 2 b-grain peaks,
one positive and one negative. The larger elementary peaks (red, blue) are
crystallization peaks (exothermic), one for each phase. The smaller elementary
peaks refer to thermal activity related to b-grain forming or melting: the
positive peaks are exotherms (purple, dark cyan) and correspond to the
formation of b-grains (F --> b conformers). The negative peaks are endotherms
(magenta, green) corresponding to the melting of b-grains (b -->F).
The combined thermal
activity of all the elementary peaks is compared with the data in Fig. 2. It is a quasi-perfect fit (r2=1.0).
While most of the thermal response, in this particular case of a Virgin PET, is
due to crystallization, 5% of the surface area under the peak is not due to
crystallization but reflects thermal activity from b-grains variations. Notice,
in passing, that some of the b-grain activity cancels out since there are both
exo and endo terms: in other words the total b-grain activity is
more 10% than 5%.
For some treated melts which have been brought
into non-equilibrium states by Rheo-Fluidification processing, the amount of
thermal activity due to the b-grains can be much higher, up to 20-30% of the
surface area. In fact, if one wants to compare the effect of a certain process
or treatment on the degree of crystallinity, the classical approach to determine
the crystallinity in the sample by simple integration of the surface area fails
(see the blog link above). We have found many examples for which the surface
area was smaller than the reference, yet the crystallinity was actually
greater.
The deconvolution of
the thermal peaks varies with the state of the melt before crystallization/melting
takes place. To be able to compare the crystallinity between samples and the
crystallinity between several thermal peaks (crystallization vs melting), one
needs to perform for each thermal peak their deconvolution and identify each
elementary peak to be either a crystallization peak or a peak due to the
b-grain activity: b-grain vs crystallization. Furthermore, the identification
of the phase in which the thermal activity takes place is also important,
either the M or the S phase. For instance in Fig.1, the M-phase corresponds to
the red, green and purple curves, and its compensating phase, the S-phase is
described by the blue, dark cyan and magenta curves.
The M-phase is a
primary stage for the nucleation and growth of st-t conformers (yielding a sort
of micelle-morphology) whereas in the S-phase more structured morphologies such
as sherulites develop in parallel to and/or compensating for the M-phase (we
recognize the S-phase by the slower rates occurring in the dynamics of change
of its elementary peaks). In the
dual-phase model, such splitted activity is the consequence of the equations
describing the dynamics of the interactions. Properties are only extensive
until a certain size of its evolution is reached, inducing the split. When
dealing with equilibrium or quasi-equilibrium states, the results are different
than under non-equilibrium conditions. Hence, annealing the samples affects the
deconvolution results: not just the crystallization vs b-grain formation in
each phase evolves, but also the compensation between the two phases M and S is
kinetically involved. Note that the morphological changes occurring in the
S-phase fall under what other theories call “secondary crystallization”).
It is clear that the mechanical properties
(diffusion, viscous flow, tensile strength, impact strength and modulus) are
all derived from what happened to the crossed dual-two splits: between the
crystallinity and the b-grains in one hand, and between the M and S phases in
the other hand.
All our results analyzed
can be interpreted within a picture of the amorphous state suggested by the dual-phase
and Cross-Dual-Phase model of interactions. The crystallization process from
the amorphous state is incorporated in the model.
In summary, spectroscopic evidence, Newtonian and Non-Newtonian viscosity evidence,
PVT equation of state evidence, Thermal Analysis evidence and the effect of
molecular weight on these parameters can be quantitatively described by
new formulas consistent with the New School Polymer Physics basic concept of
b-grains statistics, [(b/F) ↔(c,g,t)], and a split of the system of
interactions to explain the properties:
[(b/F) ↔(c,g,t)]1 ↔
[(b/F) ↔(c,g,t)]2
MORE INFORMATION CAN BE FOUND BELOW
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