A new model for the viscosity of miscible polymer blends is described. It combines a mixing rule for chain relaxation, based on the double reptation concept as adopted by Tsenoglou (1989), with a calculation of the concentration dependence of the monomeric friction factors, based on the self-concentration model of Lodge and McLeish (2000). The model is successful in anticipating the experimentally observed curvatures in plots of viscosity versus composition, and the predictions are in promising agreement with the data for several systems. The model introduces no freely adjustable parameters, and all the necessary parameters may be determined from measurements on pure components.

1.
Alegria
,
A.
,
J.
Colmenero
,
K. L.
Ngai
, and
C. M.
Roland
, “
Observation of the component dynamics in a miscible polymer blend by dielectric and mechanical spectroscopies
,”
Macromolecules
27
,
4486
4492
(
1994
).
2.
Aoki
,
Y.
, “
Viscoelastic properties of blends of poly(acrylonitrile-co-styrene) and poly[styrene-co-(N-phenylmaleimide)]
,”
Macromolecules
23
,
2309
2312
(
1990
).
3.
Aoki
,
Y.
, and
T.
Tanaka
, “
Viscoelastic properties of miscible poly(methylmethacrylate)/poly(styrene-co-acrylonitrile) blends in the molten state
,”
Macromolecules
32
,
8560
8565
(
1999
).
4.
Arrhenius
,
S.
, “
Über die innere Reibung verdünnter wässeriger Lösungen
,”
Z. Physik. Chem., Stoechiom. Verwandtschaftsl.
1
,
285
298
(
1887
).
5.
Balsara, N. P., “Thermodynamics of polymer blends,” Physical Properties of Polymers Handbook (AIP, Woodbury, NY, 1996), pp. 257–268.
6.
Berry
,
G. C.
, and
T. G.
Fox
, “
The viscosity of polymers and their concentrated solutions
,”
Fortschr. Hochpolym.-Forsch.
5
,
262
357
(
1968
).
7.
Chuang
,
H. K.
, and
C. D.
Han
, “
Rheological behavior of polymer blends
,”
J. Appl. Polym. Sci.
29
,
2205
2229
(
1984
).
8.
Chung
,
G. C.
,
J. A.
Kornfield
, and
S. D.
Smith
, “
Component dynamics miscible polymer blends: A two-dimensional deuteron NMR investigation
,”
Macromolecules
27
,
964
973
(
1994a
).
9.
Chung
,
G. C.
,
J. A.
Kornfield
, and
S. D.
Smith
, “
Compositional dependence of segmental dynamics in a miscible polymer blend
,”
Macromolecules
27
,
5729
5741
(
1994b
).
10.
Composto
,
R. J.
,
E. J.
Kramer
, and
D. M.
White
, “
Reptation in polymer blends
,”
Polymer
31
,
2320
2328
(
1990
).
11.
Composto
,
R. J.
,
E. J.
Kramer
, and
D. M.
White
, “
Matrix effects on diffusion in polymer blends
,”
Macromolecules
25
,
4167
4174
(
1992
).
12.
des Cloizeaux
,
J.
, “
Double reptation vs. simple reptation in polymer melts
,”
Europhys. Lett.
5
,
437
442
(
1988
).
13.
Doi, M., and S. F. Edwards, The Theory of Polymer Dynamics (Oxford University Press, Oxford, 1986).
14.
Ferry, J. D., Viscoelastic Properties of Polymers (J Wiley, New York, 1980).
15.
Fetters
,
L. J.
,
D. J.
Lohse
,
D.
Richter
,
T. A.
Witten
, and
A.
Zirkel
, “
Connection between polymer molecular weight, density, chain dimensions, and melt viscoelastic properties
,”
Macromolecules
27
,
4639
4647
(
1994
).
16.
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
).
17.
Gell
,
C. B.
,
R.
Krishnamoorti
,
E.
Kim
,
W. W.
Graessley
, and
L. J.
Fetters
, “
Viscoelasticity and diffusion in miscible blends of saturated hydrocarbon polymers
,”
Rheol. Acta
36
,
217
228
(
1997
).
18.
Gisser
,
D. J.
, and
M. D.
Ediger
, “
Modification of solvent rotational dynamics by the addition of small molecules or polymers
,”
J. Phys. Chem.
97
,
10818
10823
(
1993
).
19.
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
).
20.
Han
,
C. D.
, and
J. K.
Kim
, “
Molecular theory for the viscoelasticity of compatible polymer mixtures. 1. A tube model approach
,”
Macromolecules
22
,
1914
1921
(
1989a
).
21.
Han
,
C. D.
, and
J. K.
Kim
, “
Molecular theory for the viscoelasticity of compatible polymer mixtures. 2. Tube model with reptation and constraint release contributions
,”
Macromolecules
22
,
4292
4302
(
1989b
).
22.
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
).
23.
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
(
2003
).
24.
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
).
25.
Hoffmann
,
M.
, “
Rheological behavior and molecular structure of polymers and their solutions. Interdependence of quantitative relations
,”
Makromol. Chem.
153
,
99
124
(
1972
).
26.
Hoffmann
,
S.
,
L.
Willner
,
D.
Richter
,
A.
Arbe
,
J.
Colmenero
, and
B.
Farago
, “
Origin of dynamic heterogeneities in miscible polymer blends: A quasielastic neutron scattering study
,”
Phys. Rev. Lett.
85
,
772
775
(
2000
).
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.
Kim
,
E.
,
E. J.
Kramer
, and
J. O.
Osby
, “
Tracer diffusion in the blends of polystyrene and tetramethylbisphenol A polycarbonate
,”
Macromolecules
28
,
1979
1989
(
1995
).
30.
Kumar
,
S. K.
,
R. H.
Colby
,
S. H.
Anastasiadis
, and
G.
Fytas
, “
Concentration fluctuation induced dynamic heterogeneities in polymer blends
,”
J. Chem. Phys.
105
,
3777
3788
(
1996
).
31.
Lau
,
S. F.
,
J.
Pathak
, and
B.
Wunderlich
, “
Study of phase separation in blends of polystyrene and poly(α-methylstyrene) in the glass transition region using quantitative thermal analysis
,”
Macromolecules
15
,
1278
1283
(
1982
).
32.
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
).
33.
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
).
34.
Lodge
,
T. P.
, and
T. C. B.
McLeish
, “
Self-concentrations and effective glass transition temperatures in polymer blends
,”
Macromolecules
33
,
5278
5284
(
2000
).
35.
Lutz
,
T. R.
,
Y.
He
,
M. D.
Ediger
,
H.
Cao
,
G.
Lin
, and
A. A.
Jones
, “
Rapid poly(ethylene oxide) segmental dynamics in blends with poly(methyl methacrylate)
,”
Macromolecules
36
,
1724
1730
(
2003
).
36.
McAllister
,
R. A.
, “
The viscosity of liquid mixtures
,”
AIChE J.
6
,
427
431
(
1960
).
37.
McLeish
,
T. C. B.
, “
Tube theory of entangled polymer dynamics
,”
Adv. Phys.
51
,
1379
1527
(
2002
).
38.
Miller
,
J. B.
,
K. J.
McGrath
,
C. M.
Roland
,
C. A.
Trask
, and
A. N.
Garroway
, “
Nuclear magnetic resonance study of polyisoprene/poly(vinylethylene) miscible blends
,”
Macromolecules
23
,
4543
4547
(
1990
).
39.
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
).
40.
Min
,
B.
,
X.
Qiu
,
M. D.
Ediger
,
M.
Pitsikalis
, and
N.
Hadjichristidis
, “
Component dynamics in polyisoprene/polyvinylethylene blends well above Tg,
Macromolecules
34
,
4466
4475
(
2001
).
41.
Ngai
,
K. L.
,
R. W.
Rendell
,
A. K.
Rajagopal
, and
S.
Teitler
, “
Three coupled relations for relaxations in complex systems
,”
Ann. N.Y. Acad. Sci.
484
,
150
184
(
1986
).
42.
Patel
,
S. S.
, and
K. M.
Takahashi
, “
Polymer dynamics in dilute and semidilute solutions
,”
Macromolecules
25
,
4382
4391
(
1992
).
43.
Pathak
,
J. A.
,
R. H.
Colby
,
G.
Floudas
, and
R.
Jerome
, “
Dynamics in miscible blends of polystyrene and poly(vinyl methyl ether)
,”
Macromolecules
32
,
2553
2561
(
1999
).
44.
Powell
,
R. E.
,
W. E.
Roseveare
, and
H.
Eyring
, “
Diffusion, thermal conductivity and viscous flow of liquids
,”
J. Ind. Eng. Chem.
33
,
430
435
(
1941
).
45.
Prest
, Jr.,
W. M.
, “
Viscoelastic properties of blends of entangled polymers
,”
J. Polym. Sci., Polym. Phys. Ed.
8
,
1897
1908
(
1970
).
46.
Roland
,
C. M.
, and
K. L.
Ngai
, “
Dynamical heterogeneity in a miscible polymer blend
,”
Macromolecules
24
,
2261
2265
(
1991
).
47.
Roland
,
C. M.
, and
K. L.
Ngai
, “
Segmental relaxation in miscible polymer blends
,”
J. Rheol.
36
,
1691
1706
(
1992
).
48.
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
(
1992a
).
49.
Roovers
,
J.
, and
P. M.
Toporowski
, “
Microheterogeneity in miscible blends of 1,2-polybutadiene and 1,4-polyisoprene
,”
Macromolecules
25
,
3454
3461
(
1992b
).
50.
Salaniwal
,
S.
,
R.
Kant
,
R. H.
Colby
, and
S. K.
Kumar
, “
Computer simulations of local concentration variations in miscible polymer blends
,”
Macromolecules
35
,
9211
9218
(
2002
).
51.
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
).
52.
Tomlin
,
D. W.
, and
C. M.
Roland
, “
Negative excess enthalpy in a van der Waals polymer mixture
,”
Macromolecules
25
,
2994
2996
(
1992
).
53.
Tsenoglou, C., “Viscoelasticity and self-diffusion in miscible heteropolymer blends,” New Trends Phys. Phys. Chem. Polym., [Proc. Int. Symp.] , 375–383 (1989).
54.
Tsenoglou
,
C.
, “
Molecular weight polydispersity effects on the viscoelasticity of entangled linear polymers
,”
Macromolecules
24
,
1762
1767
(
1991
).
55.
Wasserman
,
S. H.
, and
W. W.
Graessley
, “
Effects of polydispersity on linear viscoelasticity in entangled polymer melts
,”
J. Rheol.
36
,
543
572
(
1992
).
56.
Wisniewsky
,
C.
,
G.
Marin
, and
P.
Monge
, “
Viscoelastic behavior of compatible polymer blends. Polystyrene/tetramethylpolycarbonate
,”
Eur. Polym. J.
20
,
691
695
(
1984
).
57.
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
).
58.
Wu
,
S.
, “
Chain entanglement and melt viscosity of compatible polymer blends: Poly(methyl methacrylate) and poly(styrene-acrylonitrile)
,”
Polymer
28
,
1144
1148
(
1987b
).
59.
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
).
60.
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
).
61.
Zawada
,
J. A.
,
G. G.
Fuller
,
R. H.
Colby
,
L. J.
Fetters
, and
J.
Roovers
, “
Component dynamics in miscible blends of 1,4-polyisoprene and 1,2-polybutadiene
,”
Macromolecules
27
,
6861
6870
(
1994
).
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