The transient shear and extensional properties of ethylene vinyl acetate nanocomposites containing two geometrically different nanoparticles (spheres of CaCO3 and platelet of clay) were investigated experimentally and the data were compared to the rheological predictions of the modified molecular stress function (MSF) theory as recently proposed by Abbasi et al. [Rheol. Acta 51, 163–177 (2012)]. While good agreement was obtained for spherical particles, deviations were observed for platelet particles at concentrations higher than 2.5 wt. %. The limitation of MSF theory for such compositions was related to the domination of the linear rheological response by the presence of particle nanonetworks over polymeric chains' contribution. This particle network contribution was also found to increase nonlinearity under large deformation, a phenomenon which was quantified via Fourier transformed rheology on data obtained under large amplitude oscillatory shear.

1.
Abbasi
,
M.
,
N.
Golshan Ebrahimi
,
M.
Nadali
, and
M.
Khabbazian Esfahani
, “
Elongational viscosity of LDPE with various structures: Employing a new evolution equation in MSF theory
,”
Rheol. Acta
51
,
163
177
(
2012
).
2.
Akcora
,
P.
,
H.
Liu
,
S. K.
Kumar
,
J.
Moll
,
Y.
Li
,
B. C.
Benicewicz
,
L. S.
Schadler
,
D.
Acehan
,
A. Z.
Panagiotopoulos
,
V.
Pryamitsyn
,
V.
Ganesan
,
J.
Ilavsky
,
P.
Thiyagarajan
,
R. H.
Colby
, and
J. F.
Douglas
, “
Anisotropic self-assembly of spherical polymer-grafted nanoparticles
,”
Nature Mater.
8
,
354
359
(
2009a
).
3.
Akcora
,
P.
,
S. K.
Kumar
,
J.
Moll
,
S.
Lewis
,
L. S.
Schadler
,
Y.
Li
,
B. C.
Benicewicz
,
A.
Sandy
,
S.
Narayanan
,
J.
Ilavsky
,
P.
Thiyagarajan
,
R. H.
Colby
, and
J. F.
Douglas
, “
‘Gel-like’ mechanical reinforcement in polymer nanocomposite melts
,”
Macromolecules
43
,
1003
1010
(
2009b
).
4.
Anderson
,
B. J.
, and
C. F.
Zukoski
, “
Rheology and microstructure of entangled polymer nanocomposite melts
,”
Macromolecules
42
,
8370
8384
(
2009
).
6.
Chatterjee
,
T.
, and
R.
Krishnamoorti
, “
Steady shear response of carbon nanotube networks dispersed in poly(ethylene oxide)
,”
Macromolecules
41
,
5333
5338
(
2008
).
7.
Chen
,
B.
, and
J. R. G.
Evans
, “
Nominal and effective volume fractions in polymer–clay nanocomposites
,”
Macromolecules
39
,
1790
1796
(
2006
).
8.
Ci
,
L.
,
J.
Suhr
,
V.
Pushparaj
,
X.
Zhang
, and
P. M.
Ajayan
, “
Continuous carbon nanotube reinforced composites
,”
Nano Lett.
8
,
2762
2766
(
2008
).
9.
Crosby
,
A. J.
, and
J. Y.
Lee
, “
Polymer nanocomposites: The “nano” effect on mechanical properties
,”
Polym. Rev.
47
,
217
229
(
2007
).
10.
Dealy
,
J. M.
, and R.
G.
Larson
, “
Tube models for nonlinear viscoelasticity of linear and branched polymers
,” in
Structure and Rheology of Molten Polymers: From Structure to Flow Behavior and Back Again
(
Hanser Gardner
,
Cincinnati, OH
,
2006
), Chap. 11, pp.
415
471
.
11.
Doi
,
M.
, and
S. F.
Edwards
,
The Theory of Polymer Dynamics
(
Clarendon
,
New York
,
1989
).
12.
Dykes
,
L. M. C.
,
J. M.
Torkelson
, and
W. R.
Burghardt
, “
Shear-induced orientation in well-exfoliated polystyrene/clay nanocomposites
,”
Macromolecules
45
,
1622
1630
(
2012
).
13.
Guth
,
E.
, and
O.
Gold
, “
On the hydrodynamical theory of the viscosity of suspensions
,”
Phys. Rev.
53
,
322
(
1938
).
14.
Han
,
Z.
, and
A.
Fina
, “
Thermal conductivity of carbon nanotubes and their polymer nanocomposites: A review
,”
Prog. Polym. Sci.
36
,
914
944
(
2011
).
15.
Harton
,
S. E.
,
S. K.
Kumar
,
H.
Yang
,
T.
Koga
,
K.
Hicks
,
H.
Lee
,
J.
Mijovic
,
M.
Liu
,
R. S.
Vallery
, and
D. W.
Gidley
, “
Immobilized polymer layers on spherical nanoparticles
,”
Macromolecules
43
,
3415
3421
(
2010
).
16.
Hobbie
,
E.
, “
Shear rheology of carbon nanotube suspensions
,”
Rheol. Acta
49
,
323
334
(
2010
).
17.
Hyun
,
K.
, and
M.
Wilhelm
, “
Establishing a new mechanical nonlinear coefficient Q from FT-rheology: First investigation of entangled linear and comb polymer model systems
,”
Macromolecules
42
,
411
422
(
2009
).
18.
Hyun
,
K.
,
M.
Kempf
,
D.
Ahirwal
,
V. H.
Rolón-Garrido
,
M. H.
Wagner
, and
M.
Wilhelm
, “
A new non-linear parameter for polymer melts, using FT-rheology
,”
Ann. Trans. Nordic Rheol. Soc.
19
,
247
(
2011
).
19.
Hyun
,
K.
,
M.
Wilhelm
,
C. O.
Klein
,
K. S.
Cho
,
J. G.
Nam
,
K. H.
Ahn
,
S. J.
Lee
,
R. H.
Ewoldt
, and
G. H.
McKinley
, “
A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS)
,”
Prog. Polym. Sci.
36
,
1697
1753
(
2011
).
20.
Inoue
,
T.
,
Y.
Yamashita
, and
K.
Osaki
, “
Viscoelasticity of an entangled polymer solution with special attention on a characteristic time for nonlinear behavior
,”
Macromolecules
35
,
1770
1775
(
2002
).
21.
Jancar
,
J.
,
J. F.
Douglas
,
F. W.
Starr
,
S. K.
Kumar
,
P.
Cassagnau
,
A. J.
Lesser
,
S. S.
Sternstein
, and
M. J.
Buehler
, “
Current issues in research on structure-property relationships in polymer nanocomposites
,”
Polymer
51
,
3321
3343
(
2010
).
22.
Kagarise
,
C.
,
K.
Koelling
,
Y.
Wang
, and
S.
Bechtel
, “
A unified model for polystyrene–nanorod and polystyrene–nanoplatelet melt composites
,”
Rheol. Acta
47
,
1061
1076
(
2008
).
23.
Kairn
,
T.
,
P. J.
Daivis
,
I.
Ivanov
, and
S. N.
Bhattacharya
, “
Molecular-dynamics simulation of model polymer nanocomposite rheology and comparison with experiment
,”
J. Chem. Phys.
123
,
194905
(
2005
).
24.
Kallus
,
S.
,
N.
Willenbacher
,
S.
Kirsch
,
D.
Distler
,
T.
Neidhöfer
,
M.
Wilhelm
, and
H. W.
Spiess
, “
Characterization of polymer dispersions by Fourier transform rheology
,”
Rheol. Acta
40
,
552
559
(
2001
).
25.
Kim
,
H.
,
A. A.
Abdala
, and
C. W.
Macosko
, “
Graphene/polymer nanocomposites
,”
Macromolecules
43
,
6515
6530
(
2010
).
26.
Knauert
,
S. T.
,
J. F.
Douglas
, and
F. W.
Starr
, “
The effect of nanoparticle shape on polymer-nanocomposite rheology and tensile strength
,”
J. Polym. Sci., Part B: Polym. Phys.
45
,
1882
1897
(
2007
).
27.
Krishnamoorti
,
R.
, and
E. P.
Giannelis
, “
Rheology of end-tethered polymer layered silicate nanocomposites
,”
Macromolecules
30
,
4097
4102
(
1997
).
28.
Krishnamoorti
,
R.
, and
K.
Yurekli
, “
Rheology of polymer layered silicate nanocomposites
,”
Curr. Opin. Colloid Interface Sci.
6
,
464
470
(
2001
).
29.
Letwimolnun
,
W.
,
B.
Vergnes
,
G.
Ausias
, and
P. J.
Carreau
, “
Stress overshoots of organoclay nanocomposites in transient shear flow
,”
J. Non-Newtonian Fluid Mech.
141
,
167
179
(
2007
).
30.
Li
,
Y.
,
M.
Kröger
, and
W. K.
Liu
, “
Nanoparticle geometrical effect on structure, dynamics and anisotropic viscosity of polyethylene nanocomposites
,”
Macromolecules
45
,
2099
2112
(
2012
).
31.
Likhtman
,
A. E.
,
S. T.
Milner
, and
T. C. B.
McLeish
, “
Microscopic theory for the fast flow of polymer melts
,”
Phys. Rev. Lett.
85
,
4550
4553
(
2000
).
32.
Ma
,
P. C.
,
M.-Y.
Liu
,
H.
Zhang
,
S. Q.
Wang
,
R.
Wang
,
K.
Wang
,
Y. K.
Wong
,
B. Z.
Tang
,
S. H.
Hong
,
K. W.
Paik
, and
J. K.
Kim
, “
Enhanced electrical conductivity of nanocomposites containing hybrid fillers of carbon nanotubes and carbon black
,”
ACS Appl. Mater. Interfaces
1
,
1090
1096
(
2009
).
33.
Mahi
,
H.
, and
D.
Rodrigue
, “
Linear and non-linear viscoelastic properties of ethylene vinyl acetate/nano-crystalline cellulose composites
,”
Rheol. Acta
51
,
127
142
(
2012a
).
34.
Mahi
,
H.
, and
D.
Rodrigue
, “
Relationships between linear and nonlinear shear response of polymer nano-composites
,”
Rheol. Acta
51
,
991
1005
(
2012b
).
35.
Marrucci
,
G.
, and
G.
Ianniruberto
, “
Interchain pressure effect in extensional flows of entangled polymer melts
,”
Macromolecules
37
,
3934
3942
(
2004
).
36.
Marrucci
,
G.
, and
N.
Grizzuti
, “
Fast flow of concentrated polymers: Predictions of the tube model on chain stretching
,”
Gazz. Chim. Ital.
118
,
179
185
(
1988
).
37.
McLeish
,
T. C. B.
, and
R. G.
Larson
, “
Molecular constitutive equations for a class of branched polymers: The pom-pom polymer
,”
J. Rheol.
42
,
81
110
(
1998
).
38.
Mead
,
D. W.
,
R. G.
Larson
, and
M.
Doi
, “
A molecular theory for fast flows of entangled polymers
,”
Macromolecules
31
,
7895
7914
(
1998
).
39.
Mobuchon
,
C.
,
P.
Carreau
, and
M.-C.
Heuzey
, “
Effect of flow history on the structure of a non-polar polymer/clay nanocomposite model system
,”
Rheol. Acta
46
,
1045
1056
(
2007
).
40.
Mohraz
,
A.
, and
M. J.
Solomon
, “
Orientation and rupture of fractal colloidal gels during start-up of steady shear flow
,”
J. Rheol.
49
,
657
681
(
2005
).
41.
Moniruzzaman
,
M.
, and
K. I.
Winey
, “
Polymer nanocomposites containing carbon nanotubes
,”
Macromolecules
39
,
5194
5205
(
2006
).
43.
Neidhöfer
,
T.
,
M.
Wilhelm
, and
B.
Debbaut
, “
Fourier-transform rheology experiments and finite-element simulations on linear polystyrene solutions
,”
J. Rheol.
47
,
1351
1371
(
2003
).
44.
Neidhöfer
,
T.
,
S.
Sioula
,
N.
Hadjichristidis
, and
M.
Wilhelm
, “
Distinguishing linear from star-branched polystyrene solutions with Fourier-transform rheology
,”
Macromol. Rapid Commun.
25
,
1921
1926
(
2004
).
45.
Nusser
,
K.
,
S.
Neueder
,
G. J.
Schneider
,
M.
Meyer
,
W.
Pyckhout-Hintzen
,
L.
Willner
,
A.
Radulescu
, and
D.
Richter
, “
Conformations of silica–poly(ethylene–propylene) nanocomposites
,”
Macromolecules
43
,
9837
9847
(
2010
).
46.
Pattamaprom
,
C.
,
J. J.
Driscroll
, and
R. G.
Larson
, “
Nonlinear viscoelastic predictions of uniaxial-extensional viscosities of entangled polymers
,”
Macromol. Symp.
158
,
1
14
(
2000
).
47.
Paul
,
D. R.
, and
L. M.
Robeson
, “
Polymer nanotechnology: Nanocomposites
,”
Polymer
49
,
3187
3204
(
2008
).
48.
Pearson
,
D.
,
E.
Herbolzheimer
,
N.
Grizzuti
, and
G.
Marrucci
, “
Transient behavior of entangled polymers at high shear rates
,”
J. Polym. Sci., Part B: Polym. Phys.
29
,
1589
1597
(
1991
).
49.
Pearson
,
D. S.
,
A. D.
Kiss
,
L. J.
Fetters
, and
M.
Doi
, “
Flow-induced birefringence of concentrated polyisoprene solutions
,”
J. Rheol.
33
,
517
535
(
1989
).
50.
Picu
,
R. C.
, and
A.
Rakshit
, “
Dynamics of free chains in polymer nanocomposites
,”
J. Chem. Phys.
126
,
144909
(
2007
).
51.
Pujari
,
S.
,
S. S.
Rahatekar
,
J. W.
Gilman
,
K. K.
Koziol
,
A. H.
Windle
, and
W. R.
Burghardt
, “
Orientation dynamics in multiwalled carbon nanotube dispersions under shear flow
,”
J. Chem. Phys.
130
,
214903
(
2009
).
52.
Rajabian
,
M.
,
G.
Naderi
,
P. J.
Carreau
, and
C.
Dubois
, “
Flow-induced particle orientation and rheological properties of suspensions of organoclays in thermoplastic resins
,”
J. Polym. Sci., Part B: Polym. Phys.
48
,
2003
2011
(
2010
).
53.
Ren
,
J.
, and
R.
Krishnamoorti
, “
Nonlinear viscoelastic properties of layered-silicate-based intercalated nanocomposites
,”
Macromolecules
36
,
4443
4451
(
2003
).
54.
Riggleman
,
R. A.
,
G.
Toepperwein
,
G. J.
Papakonstantopoulos
,
J.-L.
Barrat
, and
J. J.
d. Pablo
, “
Entanglement network in nanoparticle reinforced polymers
,”
J. Chem. Phys.
130
,
244903
(
2009
).
55.
Robertson
,
C. G.
, and
C. M.
Roland
, “
Glass transition and interfacial segmental dynamics in polymer-particle composites
,”
Rubber Chem. Technol.
81
,
506
522
(
2008
).
56.
Rolón-Garrido
,
V.
, and
M.
Wagner
, “
The MSF model: Relation of nonlinear parameters to molecular structure of long-chain branched polymer melts
,”
Rheol. Acta
46
,
583
593
(
2007
).
57.
Rolón-Garrido
,
V.
,
R.
Pivokonsky
,
P.
Filip
,
M.
Zatloukal
, and
M.
Wagner
, “
Modelling elongational and shear rheology of two LDPE melts
,”
Rheol. Acta
48
,
691
697
(
2009
).
58.
Sarvestani
,
A. S.
, “
Modeling the solid-like behavior of entangled polymer nanocomposites at low frequency regimes
,”
Eur. Polym. J.
44
,
263
269
(
2008
).
59.
Schlatter
,
G.
,
G.
Fleury
, and
R.
Muller
, “
Fourier transform rheology of branched polyethylene: Experiments and models for assessing the macromolecular architecture
,”
Macromolecules
38
,
6492
6503
(
2005
).
60.
Schneider
,
G. J.
,
K.
Nusser
,
L.
Willner
,
P.
Falus
, and
D.
Richter
, “
Dynamics of entangled chains in polymer nanocomposites
,”
Macromolecules
44
,
5857
5860
(
2011
).
62.
Sentmanat
,
M.
, “
Miniature universal testing platform: From extensional melt rheology to solid-state deformation behavior
,”
Rheol. Acta
43
,
657
669
(
2004
).
63.
Sinha Ray
,
S.
, and
M.
Okamoto
, “
Polymer/layered silicate nanocomposites: A review from preparation to processing
,”
Prog. Polym. Sci.
28
,
1539
1641
(
2003
).
64.
Sternstein
,
S. S.
, and
A.-J.
Zhu
, “
Reinforcement mechanism of nanofilled polymer melts as elucidated by nonlinear viscoelastic behavior
,”
Macromolecules
35
,
7262
7273
(
2002
).
65.
Utracki
,
L. A.
,
M. M.
Sepehr
, and
P. J.
Carreau
, “
Rheology of polymers with nanofillers
,” in
Polymer Physics: From Suspensions to Nanocomposites and Beyond
(
John Wiley & Sons
,
Hoboken
,
2010
), pp.
639
670
.
66.
van Dusschoten
,
D.
, and
M.
Wilhelm
, “
Increased torque transducer sensitivity via oversampling
,”
Rheol. Acta
40
,
395
399
(
2001
).
67.
Vermant
,
J.
,
S.
Ceccia
,
M. K.
Dolgovskij
,
P. L.
Maffettone
, and
C. W.
Macosko
, “
Quantifying dispersion of layered nanocomposites via melt rheology
,”
J. Rheol.
51
,
429
450
(
2007
).
68.
Via
,
M. D.
,
F. A.
Morrison
,
J. A.
King
,
J. A.
Caspary
,
O. P.
Mills
, and
G. R.
Bogucki
, “
Comparison of rheological properties of carbon nanotube/polycarbonate and carbon black/polycarbonate composites
,”
J. Appl. Polym. Sci.
121
,
1040
1051
(
2011
).
69.
Vittorias
,
I.
, and
M.
Wilhelm
, “
Application of FT rheology to industrial linear and branched polyethylene blends
,”
Macromol. Mater. Eng.
292
,
935
948
(
2007
).
70.
Wagner
,
M. H.
, and
J.
Schaeffer
, “
Rubbers and polymer melts: Universal aspects of nonlinear stress–strain relations
,”
J. Rheol.
37
,
643
661
(
1993
).
71.
Wagner
,
M. H.
, and
V.
Rolón-Garrido
, “
The interchain pressure effect in shear rheology
,”
Rheol. Acta
49
,
459
471
(
2010
).
72.
Wagner
,
M. H.
,
H.
Bastian
,
P.
Hachmann
,
J.
Meissner
,
S.
Kurzbeck
,
H.
Münstedt
, and
F.
Langouche
, “
The strain-hardening behaviour of linear and long-chain-branched polyolefin melts in extensional flows
,”
Rheol. Acta
39
,
97
109
(
2000
).
73.
Wagner
,
M. H.
,
J.
Hepperle
, and
H.
Munstedt
, “
Relating rheology and molecular structure of model branched polystyrene melts by molecular stress function theory
,”
J. Rheol.
48
,
489
503
(
2004a
).
74.
Wagner
,
M. H.
,
M.
Yamaguchi
, and
M.
Takahashi
, “
Quantitative assessment of strain hardening of low-density polyethylene melts by the molecular stress function model
,”
J. Rheol.
47
,
779
793
(
2003
).
75.
Wagner
,
M. H.
,
P.
Rubio
, and
H.
Bastian
, “
The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release
,”
J. Rheol.
45
,
1387
1412
(
2001
).
76.
Wagner
,
M. H.
,
S.
Kheirandish
, and
M.
Yamaguchi
, “
Quantitative analysis of melt elongational behavior of LLDPE/LDPE blends
,”
Rheol. Acta
44
,
198
218
(
2004b
).
77.
Wagner
,
M. H.
,
S.
Kheirandish
, and
O.
Hassager
, “
Quantitative prediction of transient and steady-state elongational viscosity of nearly monodisperse polystyrene melts
,”
J. Rheol.
49
,
1317
1327
(
2005a
).
78.
Wagner
,
M. H.
,
S.
Kheirandish
,
J.
Stange
, and
H.
Münstedt
, “
Modeling elongational viscosity of blends of linear and long-chain branched polypropylenes
,”
Rheol. Acta
46
,
211
221
(
2006
).
79.
Wagner
,
M. H.
,
S.
Kheirandish
,
K.
Koyama
,
A.
Nishioka
,
A.
Minegishi
, and
T.
Takahashi
, “
Modeling strain hardening of polydisperse polystyrene melts by molecular stress function theory
,”
Rheol. Acta
44
,
235
243
(
2005b
).
81.
Wapperom
,
P.
,
A.
Leygue
, and
R.
Keunings
, “
Numerical simulation of large amplitude oscillatory shear of a high-density polyethylene melt using the MSF model
,”
J. Non-Newtonian Fluid Mech.
130
,
63
76
(
2005
).
82.
Watanabe
,
H.
, “
Viscoelasticity and dynamics of entangled polymers
,”
Prog. Polym. Sci.
24
,
1253
1403
(
1999
).
83.
Wilhelm
,
M.
, “
Fourier-transform rheology
,”
Macromol. Mater. Eng.
287
,
83
105
(
2002
).
85.
Wilhelm
,
M.
,
P.
Reinheimer
, and
M.
Ortseifer
, “
High sensitivity Fourier-transform rheology
,”
Rheol. Acta
38
,
349
356
(
1999
).
86.
Wohlfarth
,
C.
, “
PVT data of molten copolymers
,” in
CRC Handbook of Thermodynamic Data of Copolymer Solutions
(
CRC
,
New York
,
2001
), Chap. 6.
87.
Yoonessi
,
M.
, and
J. R.
Gaier
, “
Highly conductive multifunctional graphene polycarbonate nanocomposites
,”
ACS Nano
4
,
7211
7220
(
2010
).
88.
Zhou
,
T.
,
J. W.
Zha
,
Y.
Hou
,
D.
Wang
,
J.
Zhao
, and
Z. M.
Dang
, “
Surface-functionalized MWNTs with emeraldine base: Preparation and improving dielectric properties of polymer nanocomposites
,”
ACS Appl. Mater. Interfaces
3
,
4557
4560
(
2011
).
61.
See supplementary material at http://dx.doi.org/10.1122/1.4798559 for fs2 values in shear and elongation deformations.

Supplementary Material

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