The viscosities of miscible blends of 1,4-polyisoprene (Mn=78kgmol)/poly(vinylethylene) (Mn=10kgmol and 120kgmol) and polystyrene (Mn=30kgmol)/poly(vinyl methyl ether) (Mn=105kgmol) were measured as a function of temperature and composition. These results, along with literature data for poly(ethylene-alt-propylene)/head-to-head polypropylene [Gell (1996)] and molecular weight blends of 1,4-polybutadiene [Wang et al. (2003)], were compared to the predictions of a previously published model [Haley and Lodge (2004a)]. The agreement between theory and experiment is generally good, though some quantitative discrepancies are apparent. A new tube dilation model that predicts the terminal relaxation time of the slower moving component in a blend as a function of composition is presented. This model enables improved viscosity predictions, and in several cases produces near quantitative predictions.

1.
Aoki
,
Y.
, “
Viscoelastic properties of blends of poly(acrylonitrile-co-styrene) and poly[styrene-co-(N-phenylmaleimide)]
,”
Macromolecules
23
,
2309
2312
(
1990
).
2.
Aoki
,
Y.
, and
T.
Tanaka
, “
Viscoelastic properties of miscible poly(methyl methacrylate)/poly(styrene-co-acrylonitrile) blends in the molten state
,”
Macromolecules
32
,
8560
8565
(
1999
).
3.
Arrhenius
,
S.
, “
Über die innere Reibung verdünnter wässeriger Lösungen
,”
Z. Phys. Chem., Stoechiom. Verwandtschaftsl.
1
,
285
298
(
1887
).
4.
Balsara
,
N. P.
,
D.
Perahia
,
C. R.
Safinya
,
M.
Tirrell
, and
T. P.
Lodge
, “
Birefringence detection of the order-to-disorder transition in block copolymer liquids
,”
Macromolecules
25
,
3896
3901
(
1992
).
5.
Bank
,
M.
,
J.
Leffingwell
, and
C.
Thies
, “
Thermally induced phase separation of polystyrene-poly(vinyl methyl ether) mixtures
,”
J. Polym. Sci., Polym. Phys. Ed.
10
,
1097
1109
(
1972
).
6.
Composto
,
R. J.
,
E. J.
Kramer
, and
D. M.
White
, “
Matrix effects on diffusion in polymer blends
,”
Macromolecules
25
,
4167
4174
(
1992
).
7.
De Gennes
,
P. G.
, “
Reptation of a polymer chain in the presence of fixed obstacles
,”
J. Chem. Phys.
55
,
572
579
(
1971
).
8.
De Gennes
,
P. G.
, “
Dynamics of entangled polymer solutions. I. The Rouse model
,”
Macromolecules
9
,
587
593
(
1976
).
9.
des Cloizeaux
,
J.
, “
Double reptation vs. simple reptation in polymer melts
,”
Europhys. Lett.
5
,
437
442
(
1988
).
10.
Doi
,
M.
, and
S. F.
Edwards
,
The Theory of Polymer Dynamics
(
Oxford University Press
, Oxford,
1986
).
11.
Doi
,
M.
,
W. W.
Graessley
,
E.
Helfand
, and
D. S.
Pearson
, “
Dynamics of polymers in polydisperse melts
,”
Macromolecules
20
,
1900
1906
(
1987
).
12.
Friedman
,
E. M.
, and
R. S.
Porter
, “
Polymer viscosity-molecular weight distribution correlations via blending: For high molecular weight poly(dimethyl siloxanes) and for polystyrenes
,”
Trans. Soc. Rheol.
19
,
493
508
(
1975
).
13.
Gell
,
C. B.
, Ph.D. thesis,
Princeton University
,
1996
.
14.
Gilman
,
H.
, and
F. K.
Cartledge
, “
The analysis of organolithium compounds
,”
J. Organomet. Chem.
2
,
447
454
(
1964
).
15.
Graessley
,
W. W.
, “
Entangled linear, branched and network polymer systems—Molecular theories
,”
Adv. Polym. Sci.
47
,
67
117
(
1982
).
16.
Graessley
,
W. W.
, and
M. J.
Struglinski
, “
Effects of polydispersity on the linear viscoelastic properties of entangled polymers. 2. Comparison of viscosity and recoverable compliance with tube model predictions
,”
Macromolecules
19
,
1754
1760
(
1986
).
17.
Green
,
P. F.
,
P. J.
Mills
,
C. J.
Palmström
,
J. W.
Mayer
, and
E. J.
Kramer
, “
Limits of reptation in polymer melts
,”
Phys. Rev. Lett.
53
,
2145
2148
(
1984
).
18.
Haley
,
J. C.
, and
T. P.
Lodge
, “
A framework for predicting the viscosity of miscible polymer blends
,”
J. Rheol.
48
,
463
486
(
2004a
).
19.
Haley
,
J. C.
, and
T. P.
Lodge
, “
Failure of time-temperature superposition in dilute miscible polymer blends
,”
Colloid Polym. Sci.
282
,
793
801
(
2004b
).
20.
Haley
,
J. C.
,
T. P.
Lodge
,
Y.
He
,
M. D.
Ediger
,
E. D.
Von Meerwall
, and
J.
Mijovic
, “
Composition and temperature dependence of terminal and segmental dynamics in polyisoprene/poly(vinylethylene) blends
,”
Macromolecules
36
,
6142
6151
(
2003
).
21.
Han
,
C. D.
, and
H. H.
Yang
, “
Rheological behavior of compatible polymer blends. I. Blends of poly(styrene-co-acrylonitrile) and poly(e-caprolactone)
,”
J. Appl. Polym. Sci.
33
,
1199
1220
(
1987
).
22.
He
,
Y.
,
T. R.
Lutz
, and
M. D.
Ediger
, “
Segmental and terminal dynamics in miscible polymer mixtures: Tests of the Lodge-McLeish model
,”
J. Chem. Phys.
119
,
9956
9965
(
2003a
).
23.
He
,
Y.
,
T. R.
Lutz
, and
M. D.
Ediger
, “
Comparison of the composition and temperature dependences of segmental and terminal dynamics in polybutadiene/poly(vinyl ethylene) blends
,”
Macromolecules
37
,
9889
9898
(
2004
).
24.
He
,
Y.
,
T. R.
Lutz
,
M. D.
Ediger
, and
T. P.
Lodge
, “
Prediction of segmental and global dynamics in disordered styrene-isoprene tetrablock copolymers
,”
Macromolecules
36
,
9170
9175
(
2003b
).
25.
Hirose
,
Y.
,
O.
Urakawa
, and
K.
Adachi
, “
Dielectric study on the heterogeneous dynamics of miscible polyisoprene/poly(vinyl ethylene) blends: Estimation of the relevant length scales for the segmental relaxation dynamics
,”
Macromolecules
36
,
3699
3708
(
2003
).
26.
Hoffmann
,
M.
, “
Rheological behavior and molecular structure of polymers and their solutions. Interdependence of quantitative relations
,”
Makromol. Chem.
153
,
99
124
(
1972
).
27.
Kataoka
,
T.
, and
S.
Ueda
, “
Viscosity of poly(dimethylsiloxane) blends
,”
J. Polym. Sci., Polym. Chem. Ed.
5
,
3071
3089
(
1967
).
28.
Kendall
,
J.
, and
K. P.
Monroe
, “
Viscosity of liquids. II. Viscosity-composition curves for ideal liquid mixtures
,”
J. Am. Chem. Soc.
39
,
1787
1802
(
1917
).
29.
Klein
,
J.
, “
The onset of entangled behavior in semidilute and concentrated polymer solutions
,”
Macromolecules
11
,
852
858
(
1978
).
30.
Leroy
,
E.
,
A.
Alegria
, and
J.
Colmenero
, “
Quantitative study of chain connectivity inducing effective glass transition temperatures in miscible polymer blends
,”
Macromolecules
35
,
5587
5590
(
2002
).
31.
Liu
,
C.
,
J.
Wang
, and
J.
He
, “
Rheological and thermal properties of m-LLDPE blends with m-HDPE and LDPE
,”
Polymer
43
,
3811
3818
(
2002
).
32.
Lodge
,
T. P.
, and
T. C. B.
McLeish
, “
Self-concentrations and effective glass transition temperatures in polymer blends
,”
Macromolecules
33
,
5278
5284
(
2000
).
33.
Lutz
,
T. R.
,
Y.
He
,
M. D.
Ediger
,
M.
Pitsikalis
, and
N.
Hadjichristidis
, “
Dilute polymer blends: Are the segmental dynamics of isolated polyisoprene chains slaved to the dynamics of the host polymer?
,”
Macromolecules
37
,
6440
6448
(
2004
).
34.
Marrucci
,
G.
, “
Relaxation by reptation and tube enlargement: A model for polydisperse polymers
,”
J. Polym. Sci., Polym. Phys. Ed.
23
,
159
177
(
1985
).
35.
Milner
,
S. T.
, and
T. C. B.
McLeish
, “
Reptation and contour-length fluctuations in melts of linear polymers
,”
Phys. Rev. Lett.
81
,
725
728
(
1998
).
36.
Milner
,
S. T.
,
T. C. B.
McLeish
,
R. N.
Young
,
A.
Hakiki
, and
J. M.
Johnson
, “
Dynamic dilution, constraint-release, and star-linear blends
,”
Macromolecules
31
,
9345
9353
(
1998
).
37.
Miwa
,
Y.
,
T.
Tanabe
,
K.
Yamamoto
,
Y.
Sugino
,
M.
Sakaguchi
,
M.
Sakai
, and
S.
Shimada
, “
Segmental dynamics and self-concentration around chain ends in miscible blends of poly(cyclohexyl methacrylate) and poly(cyclohexyl acrylate) as studied by the spin-label technique
,”
Macromolecules
37
,
8612
8617
(
2004
).
38.
Miwa
,
Y.
,
K.
Usami
,
K.
Yamamoto
,
M.
Sakaguchi
,
M.
Sakai
, and
S.
Shimada
, “
Direct detection of effective glass transitions in miscible polymer blends by temperature-modulated differential scanning calorimetry
,”
Macromolecules
38
,
2355
2361
(
2005
).
39.
Ndoni
,
S.
,
C. M.
Papadakis
,
F. S.
Bates
, and
K.
Almdal
, “
Laboratory-scale setup for anionic polymerization under inert atmosphere
,”
Rev. Sci. Instrum.
66
,
1090
1095
(
1995
).
40.
Park
,
S. J.
, and
R. G.
Larson
, “
Tube dilation and reptation in binary blends of monodisperse linear polymers
,”
Macromolecules
37
,
597
604
(
2004
).
41.
Pathak
,
J. A.
,
S. K.
Kumar
, and
R. H.
Colby
, “
Miscible polymer blend dynamics: Double reptation predictions of linear viscoelasticity in model blends of polyisoprene and poly(vinyl ethylene)
,”
Macromolecules
37
,
6994
7000
(
2004
).
42.
Prest
,
W. M.
, Jr.
, “
Viscoelastic properties of blends of ‘entangled’ polymers
,”
J. Polym. Sci., Polym. Phys. Ed.
8
,
1897
1908
(
1970
).
43.
Roovers
,
J.
, and
P. M.
Toporowski
, “
Rheological study of miscible blends of 1,4-polybutadiene and 1,2-polybutadiene (63% 1,2)
,”
Macromolecules
25
,
1096
1102
(
1992
).
44.
Rubinstein
,
M.
, and
R. H.
Colby
, “
Self-consistent theory of polydisperse entangled polymers: Linear viscoelasticity of binary blends
,”
J. Chem. Phys.
89
,
5291
5306
(
1988
).
45.
Sakaguchi
,
T.
,
N.
Taniguchi
,
O.
Urakawa
, and
K.
Adachi
, “
Calorimetric study of dynamical heterogeneity in blends of polyisoprene and poly(vinylethylene)
,”
Macromolecules
38
,
422
428
(
2005
).
46.
Struglinski
,
M. J.
, and
W. W.
Graessley
, “
Effects of polydispersity on the linear viscoelastic properties of entangled polymers. 1. Experimental observations for binary mixtures of linear polybutadiene
,”
Macromolecules
18
,
2630
2643
(
1985
).
47.
Thorpe
,
T. E.
, and
J. W.
Rodger
, “
The viscosity of mixtures of miscible liquids
,”
J. Chem. Soc.
71
,
374
(
1897
).
48.
Tsenoglou
,
C.
, “
Viscoelasticity of binary homopolymer blends
,”
Polym. Prepr. (Am. Chem. Soc. Div. Polym. Chem.)
28
,
185
186
(
1987
).
49.
Tsenoglou
,
C.
, “
Network architecture and modulus of miscible heteropolymer blends
,”
J. Polym. Sci., Part B: Polym. Phys.
26
,
2329
2339
(
1988
).
50.
Tsenoglou
,
C.
, “
Viscoelasticity and self-diffusion in miscible heteropolymer blends
,” New Trends Phys. Phys. Chem. Polym., [Proc. Int. Symp.],
375
383
(
1989
).
51.
Tuminello
,
W. H.
, “
Molecular weight and molecular weight distribution from dynamic measurements of polymer melts
,”
Polym. Eng. Sci.
26
,
1339
1347
(
1986
).
52.
Utracki
,
L. A.
, and
M. R.
Kamal
,
The rheology of polymer alloys and blends
, Polymer Blends Handbook (
Kluwer Academic Publishers
, Dordrecht, Netherlands,
2002
), Vol.
1
, pp.
449
546
.
53.
Viovy
,
J. L.
,
M.
Rubinstein
, and
R. H.
Colby
, “
Constraint release in polymer melts: tube reorganization versus tube dilation
,”
Macromolecules
24
,
3587
3596
(
1991
).
54.
Wang
,
S.
,
S.-Q.
Wang
,
A.
Halasa
, and
W. L.
Hsu
, “
Relaxation dynamics in mixtures of long and short chains: Tube dilation and impeded curvilinear diffusion
,”
Macromolecules
36
,
5355
5371
(
2003
).
55.
Watanabe
,
H.
, “
Viscoelasticity and dynamics of entangled polymers
,”
Prog. Polym. Sci.
24
,
1253
1403
(
2000
).
56.
Watanabe
,
H.
,
S.
Ishida
,
Y.
Matsumiya
, and
T.
Inoue
, “
Viscoelastic and dielectric behavior of entangled blends of linear polyisoprenes having widely separated molecular weights: Test of tube dilation picture
,”
Macromolecules
37
,
1937
1951
(
2004a
).
57.
Watanabe
,
H.
,
S.
Ishida
,
Y.
Matsumiya
, and
T.
Inoue
, “
Test of full and partial tube dilation pictures in entangled blends of linear polyisoprenes
,”
Macromolecules
37
,
6619
6631
(
2004b
).
58.
Watanabe
,
H.
, and
T.
Kotaka
, “
Viscoelastic properties and relaxation mechanisms of binary blends of narrow molecular weight distribution polystyrenes
,”
Macromolecules
17
,
2316
2325
(
1984
).
59.
Wisniewsky
,
C.
,
G.
Marin
, and
P.
Monge
, “
Viscoelastic behavior of compatible polymer blends. Polystryrene/tetramethylpolycarbonate
,”
Eur. Polym. J.
20
,
691
695
(
1984
).
60.
Wu
,
S.
, “
Entanglement between dissimilar chains in compatible polymer blends: poly(methyl methacrylate) and poly(vinylidene fluoride)
,”
J. Polym. Sci., Part B: Polym. Phys.
25
,
557
566
(
1987a
).
61.
Wu
,
S.
, “
Chain entanglement and melt viscosity of compatible polymer blends: Poly(methyl methacrylate) and poly(styrene-acrylonitrile)
,”
Polymer
28
,
1144
1148
(
1987b
).
62.
Wu
,
S.
, “
Entanglement, friction, and free volume between dissimilar chains in compatible polymer blends
,”
J. Polym. Sci., Part B: Polym. Phys.
25
,
2511
2529
(
1987c
).
63.
Yang
,
H. H.
,
C. D.
Han
, and
J. K.
Kim
, “
Rheology of miscible blends of poly(methyl methacrylate) with poly(styrene-co-acrylonitrile) and with poly(vinylidene fluoride)
,”
Polymer
35
,
1503
1511
(
1994
).
You do not currently have access to this content.