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1.
Summary An attempt is made at giving an appraisal of some representative rheological models of both differential and integral type, using the standard rheological measurements of six polymer melts. Experimental data obtained were the steady shear viscosity and the first normal stress difference by means of aWeissenberg rheogoniometer over the range of shear rates: 10–2 ~ 10 sec–1, and by means of aHan slit/capillary rheometer over the range of shear rates: 10 ~ 103 sec–1. Also measured by means of theWeissenberg rheogoniometer were the dynamic viscosity and dynamic elastic modulus over the range of frequencies: 0.3 × 10–2 ~ 3 × 102 sec–1. Rheological models chosen for an appraisal are theSpriggs 4-constant model, theMeister model, and theBogue model.It is found that the capability of the three models considered is about the same in their prediction of the rheological behavior of polymer melts in simple shearing flow. It is pointed out however that, due to the ensuing mathematical complexities, the usefulness of these models is limited to the study of flow problems associated with simple flow situations. Therefore, in analysing the complex flow situations often encountered with various polymer processings, the authors suggest use of the empirical models of the power-law type for both the viscosity and normal stress functions.With 11 figures, 4 schemas and 1 table 相似文献
2.
Mahmoud Rajabian Ghassem Naderi Charles Dubois Pierre G. Lafleur 《Rheologica Acta》2010,49(1):105-118
Transient elongational rheology of two commercial-grade polypropylene (PP) and the organoclay thermoplastic nanocomposites
is investigated. A specifically designed fixture consisting of two drums (SER Universal Testing Platform) mounted on a TA
Instruments ARES rotational rheometer was used to measure the transient uniaxial extensional viscosity of both polypropylene
and nanoclay/PP melts. The Hencky strain rate was varied from 0.001 to 2 s − 1, and the temperature was fixed at 180°C. The measurements show that the steady-state elongational viscosity was reached at
the measured Hencky strains for the polymer and for the nanocomposites. The addition of nanoclay particles to the polymer
melt was found to increase the elongation viscosity principally at low strain rates. For example, at a deformation rate of
0.3 s − 1, the steady-state elongation viscosity for polypropylene was 1.4 × 104 Pa s which was raised to 2.8 × 104 and 4.5 × 104 Pa s after addition of 0.5 and 1.5 vol.% nanoclay, respectively. A mesoscopic rheological model originally developed to predict
the motion of ellipsoid particles in viscoelastic media was modified based on the recent developments by Eslami and Grmela
(Rheol Acta 47:399–415, 2008) to take into account the polymer chain reptation. We show that the orientation states of the particles and the rheological
behavior of the layered particles/thermoplastic hybrids can be quantitatively explained by the proposed model. 相似文献
3.
Yuji Aoki Kentaro Hirayama Koji Kikuchi Masataka Sugimoto Kiyohito Koyama 《Rheologica Acta》2010,49(10):1071-1076
A poly(vinyl chloride) (PVC, Mw = 102×103)(\mbox{PVC,}\;{\rm M}_{\rm w} =102\times 10^3) di-octyl phthalate (DOP) gel with PVC content of 20 wt.% was prepared by a solvent evaporation method. The dynamic viscoelsticity
and elongational viscosity of the PVC/DOP gel were measured at various temperatures. The gel exhibited a typical sol–gel transition
behavior with elevating temperature. The critical gel temperature (Tgel) characterized with a power–law relationship between the storage and loss moduli, G′ and G″, and frequency ω, G¢=G¢¢/tan ( np/2 ) μ wn{G}^\prime={G}^{\prime\prime}{\rm /tan}\;\left( {{n}\pi {\rm /2}} \right)\propto \omega ^{n}, was observed to be 152°C. The elongational viscosity of the gel was measured below the Tgel. The gel exhibited strong strain hardening. Elongational viscosity against strain plot was independent of strain rate. This
finding is different from the elongational viscosity behavior of linear polymer solutions and melts. The stress–strain relations
were expressed by the neo-Hookean model at high temperature (135°C) near the Tgel. However, the stress–strain curves were deviated from the neo-Hookean model at smaller strain with decreasing temperature.
These results indicated that this physical gel behaves as the neo-Hookean model at low cross-linking point, and is deviated
from the neo-Hookean model with increasing of the PVC crystallites worked as the cross-linking junctions. 相似文献
4.
5.
Self-consistent modeling of entangled network strands and linear dangling structures in a single-strand mean-field slip-link model 总被引:1,自引:0,他引:1
Linear viscoelastic (LVE) measurements as well as non-linear elongation measurements have been performed on stoichiometrically
imbalanced polymeric networks to gain insight into the structural influence on the rheological response (Jensen et al., Rheol
Acta 49(1):1–13, 2010). In particular, we seek knowledge about the effect of dangling ends and soluble structures. To interpret our recent experimental
results, we exploit a molecular model that can predict LVE data and non-linear stress–strain data. The slip-link model has
proven to be a robust tool for both LVE and non-linear stress–strain predictions for linear chains (Khaliullin and Schieber,
Phys Rev Lett 100(18):188302–188304, 2008, Macromolecules 42(19):7504–7517, 2009; Schieber, J Chem Phys 118(11):5162–5166, 2003), and it is thus used to analyze the experimental results. Initially, we consider a stoichiometrically balanced network,
i.e., all strands in the ensemble are attached to the network in both ends. Next we add dangling strands to the network representing
the stoichiometric imbalance, or imperfections during curing. By considering monodisperse network strands without dangling
ends, we find that the relative low-frequency plateau, G0/GN0G_0/G_N^0, decreases linearly with the average number of entanglements. The decrease from GN0G_N^0 to G
0 is a result of monomer fluctuations between entanglements, which is similar to “longitudinal modes” in tube theory. It is
found that the slope of G′ is dependent on the fraction of network strands and the structural distribution of the network. The power-law behavior of
G
″ is not yet captured quantitatively by the model, but our results suggest that it is a result of polydisperse dangling and
soluble structures. 相似文献
6.
In this article, we present a device for rapid quenching of elongated polymer melts. The tool is an accessory to the uniaxial
elongational rheometer RME of Meissner and Hostettler. It is intended to be used for microscopic and other investigations
of stretched polymers. The device allows us to solidify a polymer melt by pouring liquid nitrogen on it and to cut it at the
nearly same instant of time. Then the sample can be easily removed from the stretching apparatus. Solving the heat diffusion
equation for a polymer melt, which is cooled by liquid nitrogen, we theoretically estimate the quenching time of this method.
To demonstrate that this quenching procedure indeed rapidly cools a polymer melt, the stress birefringence of elongated and
subsequently quenched polystyrene melts is measured and the stress-optical coefficient C is determined. The experimental value of the stress-optical coefficient is |C|= 4.65×10−9 Pa−1, which agrees well with the data in literature. Using this tool for elongation experiments with the RME, polymer melts can
be solidified in between approximately 0.2 and 2.0 s, depending on the thickness of the sample. 相似文献
7.
Víctor Hugo Rolón-Garrido Radek Pivokonsky Petr Filip Martin Zatloukal Manfred H. Wagner 《Rheologica Acta》2009,48(6):691-697
Experimental data of two low-density polyethylene (LDPE) melts at 200°C for both shear flow (transient and steady shear viscosity
as well as transient and steady first normal stress coefficient) and elongational flow (transient and steady-state elongational
viscosity) as published by Pivokonsky et al. (J Non-Newtonian Fluid Mech 135:58–67, 2006) were analysed using the molecular stress function model for broadly distributed, randomly branched molecular structures.
For quantitative modelling of melt rheology in both types of flow and in a very wide range of deformation rates, only three
nonlinear viscoelastic material parameters are needed: Whilst the rotational parameter, a
2, and the structural parameter, β, are found to be equal for the two melts considered, the melts differ in the parameter describing maximum stretch of the polymer chains. 相似文献
8.
Beginning with a formal statement of the conservation of probability, we derive a new differential constitutive equation
for entangled polymers under flow. The constitutive equation is termed the Partial Strand Extension (PSE) equation because
it accounts for partial extension of polymer strands in flow. Partial extensibility is included in the equation by considering
the effect of a step strain with amplitude E on the primitive chain contour length. Specifically, by a simple scaling argument we show that the mean primitive chain contour
length after retraction is L=L
0
E
1/2, not the equilibrium length L
0 as previously thought. The equilibrium contour length is infact recovered only after a characteristic stretch relaxation
time λ
s
that is bounded by the reptation time and longest Rouse relaxation time for the primitive chain. The PSE model predictions
of polymer rheology in various shear and extensional flows are found to be in good to excellent agreement with experimental
results from several groups.
Received: 16 July 1997 Accepted: 22 January 1998 相似文献
9.
Shifang Han 《Acta Mechanica Sinica》2007,23(2):149-158
A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid–liquid
crystalline (LC) polymers. A concept of anisotropic viscoelastic simple fluid is introduced. The stress tensor instead of
the velocity gradient tensor D in the classic Leslie–Ericksen theory is described by the first Rivlin–Ericksen tensor A and a spin tensor W measured with respect to a co-rotational coordinate system. A model LCP-H on this theory is proposed and the characteristic
unsymmetric behaviour of the shear stress is predicted for LC polymer liquids. Two shear stresses thereby in shear flow of
LC polymer liquids lead to internal vortex flow and rotational flow. The conclusion could be of theoretical meaning for the
modern liquid crystalline display technology. By using the equation, extrusion–extensional flows of the fluid are studied
for fiber spinning of LC polymer melts, the elongational viscosity vs. extension rate with variation of shear rate is given
in figures. A considerable increase of elongational viscosity and bifurcation behaviour are observed when the orientational
motion of the director vector is considered. The contraction of extrudate of LC polymer melts is caused by the high elongational
viscosity. For anisotropic viscoelastic fluids, an important advance has been made in the investigation on the constitutive
equation on the basis of which a series of new anisotropic non-Newtonian fluid problems can be addressed.
The project supported by the National Natural Science Foundation of China (10372100, 19832050) (Key project). The English
text was polished by Yunming Chen. 相似文献
10.
Hideyuki Uematsu Yuji Aoki Masataka Sugimoto Takashi Taniguchi Kiyohito Koyama 《Rheologica Acta》2008,47(2):237-242
We investigated the dynamic viscoelasticity and elongational viscosity of polypropylene (PP) containing 0.5 wt% of 1,3:2,4-bis-O-(p-methylbenzylidene)-d-sorbitol (PDTS). The PP/PDTS system exhibited a sol–gel transition (T
gel) at 193 °C. The critical exponent n was nearly equal to 2/3, in agreement with the value predicted by a percolation theory. This critical gel is due to a three-dimensional
network structure of PDTS crystals. The elongational viscosity behavior of neat PP followed the linear viscosity growth function
3η
+
(t), where η
+
(t) is the shear stress growth function in the linear viscoelastic region. The elongational viscosity of the PP/PDTS system
also followed the 3η
+
(t) above T
gel but did not follow the 3η
+
(t) and exhibited strong strain-softening behavior below T
gel. This strain softening can be attributed to breakage of the network structure of PDTS with a critical stress (σ
c) of about 104 Pa. 相似文献
11.
Alexander Semenov Aurélia Charlot Rachel Auzély-Velty Marguerite Rinaudo 《Rheologica Acta》2007,46(5):541-568
Dynamics of associating polymer solutions above the reversible gelation point are studied. Each macromolecule consists of
a soluble backbone (B) and a small fraction of specific strongly interacting groups (A or C stickers) attached to B. A mixture
of B–A and B–C associating polymers with 1:1 stoichiometric ratio is considered. As a result of AC association, the polymers
reversibly gelate above the overlap concentration. It is shown that (1) the network strands are linear complexes (double chains)
of B–A and B–C; (2) “diffusion” of the network junction points is characterized by an apparent activation energy, which can
be significantly higher than the energy of one AC bond; (3) most importantly, the randomness of sticker distribution along
the chain can significantly slow down the network relaxation leading to a markedly non-Maxwellian viscoelastic behavior. The
theory elucidates the most essential features of rheological behavior of polysaccharide associating systems (with A = adamantyl
moiety, C = β-cyclodextrin, B = either chitosan or hyaluronan) including similar behavior of G
′ and G
″ in a wide frequency range, strong temperature dependence of the characteristic frequency ω
x
, and an extremely strong effect of added free stickers (fC) on the dynamics.
This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006. 相似文献
12.
Werner-Michael Kulicke Ulf Reinhardt Gerald G. Fuller Oliver Arendt 《Rheologica Acta》1999,38(1):26-33
Sodium carboxymethylcellulose (NaCMC) in solution represents a complex rheological system, since it forms aggregates and
associations and hence higher-level structures and, depending on the synthesis, is only found in a molecularly dispersed form
in exceptional cases. Rheo-mechanical investigations of the viscoelasticity showed that the Cox-Merz rule is not fulfilled.
The aim was therefore to examine whether rheo-optics could be employed to provide more detailed conclusions about the parameters that influence the flow behavior of NaCMC than
has hitherto been available with mechanical methods. The flow birefringence, Δn
′, rises as the degree of polymerization increases, and exhibits the same dependence on molar mass as does the viscosity: Δn
′∝M
w
3.4. As the degree of polymerization increases while the shear rate remains constant, the polymer segments become more distinctly
aligned in the direction of shear. Hence increasing the degree of polymerization also affects the solution structure, i.e.
the interaction of the molecules with one another. The stress-optical rule only applies to a limited extent for this system.
The stress-optical coefficient, C, is almost independent of the shear rate, but is strongly influenced by the concentration and attains a limiting value of
3 × 10−8 Pa−1. C was determined for a polymer in dilute solution and the curve obtained also enabled transitions in the solution structure to be recognized.
Received: 1 May 1998 Accepted: 5 October 1998 相似文献
13.
Creep and recovery experiments have been used to investigate the behaviour of heat set protein gels exemplified by those
prepared from β-lactoglobulin (β-Lg). Some initial experiments were also performed on heat set BSA gels to establish appropriate
experimental conditions. The latter illustrated the importance of a well-controlled thermal regime and the use of an appropriate
solvent trap.
Results from the concentration dependence of compliance for β-Lg were in good agreement with previously published results
for the long time extrapolated storage modulus, G
′
∞
we introduced previously, especially considering the necessarily different experimental conditions. The exponent of creep
and recovery phase viscosity vs concentration was extremely high, ∼30, but reflects the nature of such gelling systems close
to their critical concentration. In this respect, the behaviour of the creep phase viscosity was in qualitative agreement
with our recently postulated viscosity vs concentration state diagram for a gelling system.
Received: 12 July 2001 Accepted: 29 October 2001 相似文献
14.
Different blending laws have been proposed in the literature to describe the polydispersity effect on the rheological behavior
of polymer melts. In this paper predictions of linear viscoelastic properties of entangled polydisperse polymers have been
derived from the double reptation mixing rule. The results in terms of the relaxation modulus, the zero shear-rate viscosity,
η0, and the steady-state compliance, J
e
0, have been obtained using three different relaxation functions for the monodisperse fractions, namely the Tuminello step
function, the single exponential function and the BSW function. Both discrete and continuous molecular weight distributions
(MWDs) have been investigated. The Generalized Exponential Function (GEX) has been considered in the continuous case.
The results showed that, in systems with a large number of components, the predictions of linear viscoelastic properties mainly
depend on the double reptation mixing rule assumption, while the choice of the relaxation function is not crucial. In particular,
the mathematical simplicity of the Tuminello step relaxation function has allowed analytical computation of the linear viscoelastic
properties in closed form. Indeed, the analytical results indicated a dependence of η0 on the MWD that could be expressed in terms of (M
z/M
w)0.8, in agreement with experimental results reported in the literature. In the case of J
e
0, the analytical model defines a dependence on (M
z/M
w)5.5, i.e. as expected a strong dependence on the MWD is predicted for the steady-state compliance. Finally, dynamic moduli have
been computed from the relaxation modulus and their predictions have been favorably compared with experimental results from
the literature.
Received: 19 July 1999/Accepted: 24 November 1999 相似文献
15.
In this research experiments were performed to examine the hydrodynamic diffusion of spherical particles in a highly filled
suspension. The suspension consisted of nearly monodisperse polymethylmethacrylate spheres in a density matched polymer solution.
The polymer solution was prepared by dissolving 0–700 ppm of polyacrylamide in a mixture of ethyleneglycol and glycerine.
The polymer solution did not show appreciable shear thinning. The particle loading was varied from 30 to 55%. The hydrodynamic
diffusivity was estimated by measuring the time-dependent viscosity when the suspension was subjected to a circular Couette
flow with an air bubble trapped under the rotor of the Couette apparatus. The results show that the dimensionless diffusivity
(D/γ˙a
2) of particles in polymer solution is not proportional to shear rate (γ˙), as in the case of a Newtonian fluid, but that it
decreases with increasing shear rate. The diffusivity also decreases with increasing polymer concentration. It is suggested
that the elongational thickening behaviour and the increased lubrication force due to the first normal stress difference may
be responsible for the reduction of diffusivity in the polymer solution.
Received: 18 January 2000 Accepted: 6 April 2000 相似文献
16.
Summary An apparatus has been designed and constructed to measure the dynamic viscoelastic properties of polymer melts over the frequency range 10–2–103 Hz. The measurements made on two samples of polythene are discussed, the samples differing in their molecular weight distributions. Some fractions from these two parent polymers have also been studied. The results are compared with the modifiedRouse (3) theory for polymer melts, and with the liquid model proposed byBarlow,Erginsav andLamb (4).
Zusammenfassung Mit Hilfe einer neuentwickelten Apparatur wurden Messungen der dynamischen viskoelastischen Eigenschaften von polymeren Schmelzen im Frequenzbereich 10–2 bis 10–3 Hz durchgeführt. Die Meßergebnisse, die an zwei Polyäthylenproben unterschiedlicher Molekulargewichtsverteilung erhalten wurden, werden diskutiert. Einige Fraktionen dieser beiden Polymeren wurden auch untersucht. Es wurden schließlich die Ergebnisse mit derRouseschen Theorie über polymere Schmelzen (3) und mit dem vonBarlow, Erginsav undLamb (4) vorgeschlagenen Flüssigkeitsmodell verglichen.相似文献
17.
Effect of melt viscosity of polypropylene on fibrillation of thermotropic liquid crystalline polymer in in situ composite film 总被引:1,自引:0,他引:1
Various grades of polypropylene were melt blended with a thermotropic liquid crystalline polymer, a block copolymer of p-hydroxy benzoic acid and ethylene terephthalate (60/40 mole ratio). The blends were extruded as cast films at different values
of draw ratio (slit width/film thickness). Fibrillation of TLCP dispersed phase with high fiber aspect ratio (length/width)
was obtained with the matrix of low melt flow rate, i.e., high viscosity and with increasing film drawing. Melt viscosities
of pure components and blends measured using capillary rheometer were found to decrease with increasing shear rate and temperature.
Viscosity ratios (dispersed phase to matrix phase) of the systems being investigated at 255 °C at the shear rate ranged from
102 to 104 s−1, were found to lie between 0.04 and 0.15. The addition of a few percent of elastomeric compatibilizers; a tri-block copolymer
SEBS, EPDM rubber and maleated-EPDM, was found to affect the melt viscosity of the blend and hence the morphology. Among these
three compatibilizers, SEBS was found to provide the best fibrillation.
Received: 10 January 2000/Accepted: 24 January 2000 相似文献
18.
Constitutive relationships for polymeric materials with power-law distributions of relaxation times 总被引:1,自引:0,他引:1
R. G. Larson 《Rheologica Acta》1985,24(4):327-334
The linear relaxation modulus of polydisperse polymer melts and solutions can often be approximated by a power law,ct
–m over some range of time,t. If, in addition, the nonlinear rheology is given by a separable integral equation, with a strain-dependent factor typical of those observed experimentally, then some commonly observed empirical rules and equations can be readily derived as approximations, namely the Cox-Merz relationship between complex viscosity and steady-state shear viscosity, Bersted's predictions of steady shear stress and first normal-stress difference from a truncated spectrum of linear relaxation times, and the observation of Koyama and coworkers that the ratio of the nonlinear to the linear time-dependent elongational viscosity is independent of strain rate, over a range of strain rates outside the linear regime. 相似文献
19.
V. F. Shumsky I. Getmanchuk T. Ignatova Yu. Maslak P. Cassagnau G. Boiteux F. Melis 《Rheologica Acta》2010,49(8):827-836
The viscoelastic characteristics of the blends of poly(methyl methacrylate)/poly(styrene-co-acrylonitrile) (PMMA/SAN) were investigated at various temperatures below, near, and above the phase separation temperature.
The investigated polymer system is characterized by a lower critical solution temperature. Rheological behavior of the blends
in the region of a phase separation was compared with change of the light scattering intensity. The presence of nanofillers
in the blend results in that the phase separation occurs at a higher temperature. At the isothermal conditions, the phase
separation begins earlier and proceeds with a higher rate as compared with the same blend without filler. The results of the
study show the considerable change of the viscoelastic characteristics of PMMA/SAN when the polymer system passes from the
homogeneous state to the heterogeneous one. Such characteristics as the dependence of the storage modulus (G
′) on the loss modulus (G
″), the dependence of the loss viscosity (η
″) on the dynamic viscosity (η
′), the dependences of the complex viscosity (η*), and the free volume fraction (f) on the blend composition are the most sensitive to the phase separation. The phase separation affects the characteristics
G
′(ω), where ω is the frequency only in a low-frequency range. Temperatures of phase separation were estimated using dependence G
′(T) at ω, which is the constant in the range of low frequencies. 相似文献
20.
Giovanni Romeo Giovanni Filippone Alberto Fernández-Nieves Pietro Russo Domenico Acierno 《Rheologica Acta》2008,47(9):989-997
We investigate the relation between the structure and the viscoelastic behavior of a model polymer nanocomposite system based
on a mixture of titanium dioxide (TiO2) nanoparticles and polypropylene. Above a critical volume fraction, Φ
c, the elasticity of the hybrids dramatically increases, and the frequency dependence of the elastic and viscous moduli reflects
the superposition of the independent responses of the suspending polymer melt and of an elastic particle network. In addition,
the elasticity of the hybrids shows critical behavior around Φ
c. We interpret these observations by hypothesizing the formation of a transient network, which forms due to crowding of particle
clusters. Consistent with this interpretation, we find a long-time, Φ-dependent, structural relaxation, which emphasizes the transient character of the structure formed by the particle clusters.
For times below this characteristic relaxation time, the elasticity of the network is Φ-independent and reminiscent of glassy behavior, with the elastic modulus, G′, scaling with frequency, ω, as G′∼ω
0.3. We expect that our analysis will be useful for understanding the behavior of other complex fluids where the elasticity of
the components could be superimposed. 相似文献