We report upon the characterization of the steady-state shear stresses and first normal stress differences as a function of shear rate using mechanical rheometry (both with a standard cone and plate and with a cone partitioned plate) and optical rheometry (with a flow-birefringence setup) of an entangled solution of asymmetric exact combs. The combs are polybutadienes (1,4-addition) consisting of an H-skeleton with an additional off-center branch on the backbone. We chose to investigate a solution in order to obtain reliable nonlinear shear data in overlapping dynamic regions with the two different techniques. The transient measurements obtained by cone partitioned plate indicated the appearance of overshoots in both the shear stress and the first normal stress difference during start-up shear flow. Interestingly, the overshoots in the start-up normal stress difference started to occur only at rates above the inverse stretch time of the backbone, when the stretch time of the backbone was estimated in analogy with linear chains including the effects of dynamic dilution of the branches but neglecting the effects of branch point friction, in excellent agreement with the situation for linear polymers. Flow-birefringence measurements were performed in a Couette geometry, and the extracted steady-state shear and first normal stress differences were found to agree well with the mechanical data, but were limited to relatively low rates below the inverse stretch time of the backbone. Finally, the steady-state properties were found to be in good agreement with model predictions based on a nonlinear multimode tube model developed for linear polymers when the branches are treated as solvent.

1.
McLeish
,
T. C. B.
, “
Tube theory of entangled polymer dynamics
,”
Adv. Phys.
51
,
1379
1527
(
2002
).
2.
Dealy
,
J. M.
, and
R. G.
Larson
,
Structure and Rheology of Molten Polymers
(
Hanser Publishers
,
Munich
,
2006
).
3.
Graessley
,
W. W.
,
Polymeric Liquids & Networks: Dynamics and Rheology
(
Taylor & Francis Group LLC
,
NY
,
2008
).
4.
Read
,
D. J.
,
D.
Auhl
,
C.
Das
,
J.
den Doelder
,
M.
Kapnistos
,
I.
Vittorias
, and
T. C. B.
McLeish
, “
Linking models of polymerization and dynamics to predict branched polymer structure and flow
,”
Science
333
,
1871
1874
(
2011
).
5.
Larson
,
R. G.
, “
Instabilities in viscoelastic flows
,”
Rheol. Acta
31
,
213
263
(
1992
).
6.
Wang
,
S. Q.
,
S.
Ravindranath
, and
P. E.
Boukany
, “
Homogeneous shear, wall slip, and shear banding of entangled polymeric liquids in simple-shear rheometry: A roadmap of nonlinear rheology
,”
Macromolecules
44
,
183
190
(
2011
).
7.
Li
,
Y. F.
,
M.
Hu
,
G. B.
McKenna
,
C. J.
Dimitriou
,
G. H.
McKinley
,
R. M.
Mick
,
D. C.
Venerus
, and
L. A.
Archer
, “
Flow field visualization of entangled polybutadiene solutions under nonlinear viscoelastic flow conditions
,”
J. Rheol.
57
,
1411
1428
(
2013
).
8.
Cromer
,
M.
,
M. C.
Villet
,
G. H.
Fredrickson
, and
L. G.
Leal
, “
Shear banding in polymer solutions
,”
Phys. Fluids
25
,
051703
(
2013
).
9.
Cromer
,
M.
,
G. H.
Fredrickson
, and
L. G.
Leal
, “
A study of shear banding in polymer solutions
,”
Phys. Fluids
26
,
063101
(
2014
).
10.
Boukany
,
P. E.
, and
S. Q.
Wang
, “
Exploring origins of interfacial yielding and wall slip in entangled linear melts during shear or after shear cessation
,”
Macromolecules
42
,
2222
2228
(
2009
).
11.
Likhtman
,
A. E.
, “
Whither tube theory: From believing to measuring
,”
J. Non-Newtonian Fluid Mech.
157
,
158
161
(
2009
).
12.
Hadjichristidis
,
N.
,
H.
Iatrou
,
S.
Pispas
, and
M.
Pitsikalis
, “
Anionic polymerization: High vacuum techniques
,”
J. Polym. Sci. Part A: Polym. Chem.
38
,
3211
3234
(
2000
).
13.
Hadjichristidis
,
N.
,
M.
Pitsikalis
,
S.
Pispas
, and
H.
Iatrou
, “
Polymers with complex architecture by living anionic polymerization
,”
Chem. Rev.
101
,
3747
3792
(
2001
).
14.
Nikopoulou
,
A.
,
H.
Iatrou
,
D. J.
Lohse
, and
N.
Hadjichristidis
, “
Synthesis of exact comb polybutadienes with two and three branches
,”
J. Polym. Sci., Part A: Polym. Chem.
47
,
2597
2607
(
2009
).
15.
Snijkers
,
F.
,
E.
van Ruymbeke
,
P.
Kim
,
H.
Lee
,
A.
Nikopoulou
,
T.
Chang
,
N.
Hadjichristidis
,
J.
Pathak
, and
D.
Vlassopoulos
, “
Architectural dispersity in model branched polymers: Analysis and rheological consequences
,”
Macromolecules
44
,
8631
8643
(
2011
).
16.
van Ruymbeke
,
E.
,
H.
Lee
,
T.
Chang
,
A.
Nikopoulou
,
N.
Hadjichristidis
,
F.
Snijkers
, and
D.
Vlassopoulos
, “
Molecular rheology of branched polymers: Decoding and exploring the role of architectural dispersity through a synergy of anionic synthesis, interaction chromatography, rheometry and modeling
,”
Soft Matter
10
,
4762
4777
(
2014
).
17.
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
).
18.
Hassell
,
D. G.
,
D.
Auhl
,
T. C. B.
McLeish
, and
M. R.
Mackley
, “
The effect of viscoelasticity on stress fields with polyethylene melt flow for a cross-slot and contraction-expansion slit geometry
,”
Rheol. Acta
47
,
821
834
(
2008
).
19.
Oberhauser
,
J. P.
,
L. G.
Leal
, and
D. W.
Mead
, “
The response of entangled polymer solutions to step changes of shear rate: Signatures of segmental stretch?
,”
J. Polym. Sci. B Polym. Phys.
36
,
265
280
(
1998
).
20.
Wang
,
Y.
, and
S. Q.
Wang
, “
Exploring stress overshoot phenomenon upon startup deformation of entangled linear polymeric liquids
,”
J. Rheol.
53
,
1389
1401
(
2009
).
21.
Boukany
,
P. E.
, and
S. Q.
Wang
, “
Shear banding or not in entangled DNA solutions
,”
Macromolecules
43
,
6950
6952
(
2010
).
22.
Cheng
,
S. W.
, and
S. Q.
Wang
, “
Is shear banding a metastable property of well-entangled polymer solutions?
,”
J. Rheol.
56
,
1413
1428
(
2012
).
23.
Wang
,
S. Q.
,
Y.
Wang
,
S.
Cheng
,
X.
Li
,
X.
Zhu
, and
H.
Sun
, “
New experiments for improved theoretical description of nonlinear rheology of entangled polymers
,”
Macromolecules
46
,
3147
3159
(
2013
).
24.
Wang
,
Y.
, and
S. Q.
Wang
, “
From elastic deformation to terminal flow of a monodisperse entangled melt in uniaxial extension
,”
J. Rheol.
52
,
1275
1290
(
2008
).
25.
Graham
,
R. S.
,
A. E.
Likhtman
,
T. C. B.
McLeish
, and
S. T.
Milner
, “
Microscopic theory of linear, entangled polymer chains under rapid deformation including chain stretch and convective constraint release
,”
J. Rheol.
47
,
1171
1200
(
2003
).
26.
Auhl
,
D.
,
J.
Rodrigez
,
A. E.
Likhtmann
,
P.
Chambon
, and
C.
Fernyhough
, “
Linear and nonlinear shear flow behavior of monodisperse polyisoprene melts with a large range of molecular weights
,”
J. Rheol.
52
,
801
835
(
2008
).
27.
Huang
,
C. C.
,
R. G.
Winkler
,
G.
Sutmann
, and
G.
Gompper
, “
Semidilute polymer solutions at equilibrium and under shear flow
,”
Macromolecules
43
,
10107
10116
(
2010
).
28.
Cao
,
J.
, and
A. E.
Likhtman
, “
Shear banding in molecular dynamics of polymer melts
,”
Phys. Rev. Lett.
108
,
028302
(
2012
).
29.
Masubuchi
,
Y.
, and
H.
Watanabe
, “
Origin of stress overshoot under start-up shear in primitive chain network simulation
,”
ACS Macro Lett.
3
,
1183
1186
(
2014
).
30.
Andreev
,
M.
,
H. L.
Feng
,
L.
Yang
, and
J. D.
Schieber
, “
Universality and speedup in equilibrium and nonlinear rheology predictions of the fixed slip-link model
,”
J. Rheol.
58
,
723
736
(
2014
).
31.
de Oliveira
,
I. S. S.
,
B. W.
Fitzgerald
,
W. K.
den Otter
, and
W. J.
Briels
, “
Mesoscale modeling of shear-thinning polymer solutions
,”
J. Chem. Phys.
140
,
104903
(
2014
).
32.
Snijkers
,
F.
,
R.
Pasquino
,
P. D.
Olmsted
, and
D.
Vlassopoulos
, “
Perspectives on the viscoelasticity and flow behavior of entangled linear and branched polymers
,”
J. Phys.: Condens. Matter
27
,
473002
(
2015
).
33.
Snijkers
,
F.
,
D.
Vlassopoulos
,
H.
Lee
,
J.
Yang
,
T.
Chang
,
P.
Driva
, and
N.
Hadjichristidis
, “
Start-up and relaxation of well-characterized comb polymers in simple shear
,”
J. Rheol.
57
,
1079
1100
(
2013
).
34.
Kirkwood
,
K. M.
,
L. G.
Leal
,
D.
Vlassopoulos
,
P.
Driva
, and
N.
Hadjichristidis
, “
Stress relaxation of comb polymers with short branches
,”
Macromolecules
42
,
9592
9608
(
2009
).
35.
Schwarzl
,
F. R.
, “
The numerical calculation of storage and loss compliance from creep data for linear viscoelastic materials
,”
Rheol. Acta
8
,
6
17
(
1969
).
36.
Meissner
,
J.
,
R. W.
Garbella
, and
J.
Hostettler
, “
Measuring normal stress differences in polymer melt shear flow
,”
J. Rheol.
33
,
843
864
(
1989
).
37.
Schweizer
,
T.
, “
Measurement of the first and second normal stress differences in a polystyrene melt with a cone and partitioned plate tool
,”
Rheol. Acta
41
,
337
344
(
2002
).
38.
Schweizer
,
T.
, “
Comparing cone partitioned plate and cone standard plate shear rheometry of a polystyrene melt
,”
J. Rheol.
47
,
1071
1085
(
2003
).
39.
Schweizer
,
T.
,
J.
van Meerveld
, and
H. C.
Öttinger
, “
Nonlinear shear rheology of polystyrene melt with narrow molecular weight distribution—Experiment and theory
,”
J. Rheol.
48
,
1345
1363
(
2004
).
40.
Snijkers
,
F.
, and
D.
Vlassopoulos
, “
Cone partitioned-plate geometry for the ARES rheometer with temperature control
,”
J. Rheol.
55
,
1167
1186
(
2011
).
41.
Schweizer
,
T.
, and
A.
Bardow
, “
The role of instrument compliance in normal force measurements of polymer melts
,”
Rheol. Acta
45
,
393
402
(
2006
).
42.
Hansen
,
M. G.
, and
F.
Nazem
, “
Transient normal force transducer response in a modified Weissenberg rheogoniometer
,”
Trans. Soc. Rheol.
19
,
21
36
(
1975
).
43.
Macosko
,
C. W.
,
Rheology: Principles, Measurements, and Applications
(
Wiley-VCH
,
NY
,
1994
).
44.
Mark
,
J. E.
,
Physical Properties of Polymers Handbook
, 2nd ed. (
Springer
,
NY
,
2007
).
45.
Frattini
,
P. L.
, and
G. G.
Fuller
, “
A note on phase-modulated flow birefringence: A promising rheo-optical method
,”
J. Rheol.
28
,
61
70
(
1984
).
46.
Johnson
,
S. J.
,
P. L.
Frattini
, and
G. G.
Fuller
, “
Simultaneous dichroism and birefringence measurements of dilute colloidal suspensions in transient shear flow
,”
J. Colloid Interface Sci.
104
,
440
455
(
1985
).
47.
Cohen
,
Y.
, and
A. B.
Metzner
, “
Apparent slip flow of polymer solutions
,”
J. Rheol.
29
,
67
102
(
1985
).
48.
Brunn
,
P.
,
M.
Müller
, and
S.
Bschorer
, “
Slip of complex fluids in viscometry
,”
Rheol. Acta
35
,
242
251
(
1996
).
49.
Kirkwood
,
K. M.
, “
Stress relaxation of comb polymers
,” Ph.D. dissertation,
University of California
, Santa Barbara,
2009
.
50.
Fuller
,
G. G.
,
Optical Rheometry of Complex Fluids
(
Oxford University
,
NY
,
1995
).
51.
Janeschitz-Kriegl
,
H.
, “
Flow birefringence of elastico-viscous polymer systems
,”
Adv. Polym. Sci.
6
,
170
318
(
1969
).
52.
Oberhauser
,
J. P.
,
K.
Pham
, and
L. G.
Leal
, “
Rheo-optical studies of the response of entangled polymer solutions to step changes in shear rate
,”
J. Rheol.
48
,
1229
1249
(
2004
).
53.
Tezel
,
A. M.
,
L. G.
Leal
, and
T. C. B.
McLeish
, “
Rheo-optical evidence of CCR in an entangled four-arm star
,”
Macromolecules
38
,
1451
1455
(
2005
).
54.
Tezel
,
A. K.
,
J. P.
Oberhauser
,
S.
Richard
,
R. S.
Graham
,
K.
Jagannathan
,
T. C. B.
McLeish
, and
L. G.
Leal
, “
The nonlinear response of entangled star polymers to startup of shear flow
,”
J. Rheol.
53
,
1193
1214
(
2009
).
55.
Ianniruberto
,
G.
, and
G.
Marrucci
, “
Stress tensor and stress-optical law in entangled polymers
,”
J. Non-Newtonian Fluid Mech.
79
,
225
234
(
1998
).
56.
Marrucci
,
G.
, and
G.
Ianniruberto
, “
Flow-induced orientation and stretch in entangled polymers
,”
Phil. Trans. R. Soc. London A
361
,
677
688
(
2003
).
57.
Das
,
C.
,
N. J.
Inkson
,
D. J.
Read
,
M. A.
Kelmanson
, and
T. C. B.
McLeish
, “
Computational linear rheology of general branch-on-branch polymers
,”
J. Rheol.
50
,
207
234
(
2006
).
58.
McLeish
,
T. C. B.
, “
Hierarchical relaxation in tube models of branched polymers
,”
Europhys. Lett.
6
,
511
516
(
1988
).
59.
McLeish
,
T. C. B.
,
J.
Allgaier
,
D. K.
Bick
,
G.
Bishko
,
P.
Biswas
,
R.
Blackwell
,
B.
Blottiere
,
N.
Clarke
,
B.
Gibbs
,
D. J.
Groves
,
A.
Hakiki
,
R. K.
Heenan
,
J. M.
Johnson
,
R.
Kant
,
D. J.
Read
, and
R. N.
Young
, “
Dynamics of entangled H-polymers: Theory, rheology, and neutron-scattering
,”
Macromolecules
32
,
6734
6758
(
1999
).
60.
Daniels
,
D. R.
,
T. C. B.
McLeish
,
B. J.
Crosby
,
R. N.
Young
, and
C. M.
Fernyhough
, “
Molecular rheology of comb polymer melts. 1. Linear viscoelastic response
,”
Macromolecules
34
,
7025
7033
(
2001
).
61.
Kapnistos
,
M.
,
D.
Vlassopoulos
,
J.
Roovers
, and
L. G.
Leal
, “
Linear rheology of architecturally complex macromolecules: Comb polymers with linear backbones
,”
Macromolecules
38
,
7852
7862
(
2005
).
62.
van Ruymbeke
,
E.
,
M.
Kapnistos
,
M.
Lang
,
D.
Vlassopoulos
,
T. Z.
Huang
, and
D. M.
Knauss
, “
Linear melt rheology of pom-pom polystyrenes with unentangled branches
,”
Macromolecules
40
,
1713
1719
(
2007
).
63.
Snijkers
,
F.
,
D.
Vlassopoulos
,
G.
Ianniruberto
,
G.
Marrucci
,
H.
Lee
,
J.
Yang
, and
T.
Chang
, “
Double stress overshoot in start-up of simple shear flow of entangled comb polymers
,”
ACS Macro Lett.
2
,
601
604
(
2013
).
64.
Somma
,
E.
,
O.
Valentino
,
G.
Titomanlio
, and
G.
Ianniruberto
, “
Parallel superposition in entangled polydisperse polymer melts: Experiments and theory
,”
J. Rheol.
51
,
987
1005
(
2007
).
65.
van Ruymbeke
,
E.
,
S.
Coppola
,
L.
Balacca
,
S.
Righi
, and
D.
Vlassopoulos
, “
Decoding the viscoelastic response of polydisperse star/linear polymer blends
,”
J. Rheol.
54
,
507
538
(
2010
).
66.
Doi
,
M.
, “
Explanation for the 3.4-power law for viscosity of polymeric liquids on the basis of the tube model
,”
J. Polym. Sci. Polym. Phys. Ed.
21
,
667
684
(
1983
).
67.
Ianniruberto
,
G.
, and
G.
Marrucci
, “
A multi-mode CCR model for entangled polymers with chain stretch
,”
J. Non-Newtonian Fluid Mech.
102
,
383
395
(
2002
).
68.
Ferry
,
J. D.
,
Viscoelastic Properties of Polymers
, 3rd ed. (
Wiley-VCH
,
NY
,
1980
).
69.
Zoller
,
P.
, and
D.
Walsh
,
Standard Pressure-Volume-Temperature Data for Polymers
(
Technomic Publishing Co.
,
NY
,
1995
).
70.
Watanabe
,
H.
, “
Viscoelasticity and dynamics of entangled polymers
,”
Prog. Polym. Sci.
24
,
1253
1403
(
1999
).
71.
van Ruymbeke
,
E.
,
Y.
Masubuchi
, and
H.
Watanabe
, “
Effective value of the dynamic dilution exponent in bidisperse linear polymers: From 1 to 4/3
,”
Macromolecules
45
,
2085
2098
(
2012
).
72.
Colby
,
R. H.
,
L. J.
Fetters
,
W. G.
Funk
, and
W. W.
Graessley
, “
Effects of concentration and thermodynamic interaction on the viscoelastic properties of polymer solutions
,”
Macromolecules
24
,
3873
3882
(
1991
).
73.
Lentzakis
,
H.
,
D.
Vlassopoulos
,
D. J.
Read
,
H.
Lee
,
T.
Chang
,
P.
Driva
, and
N.
Hadjichristidis
, “
Uniaxial extensional rheology of well-characterized comb polymers
,”
J. Rheol.
57
,
605
625
(
2013
).
74.
Likhtman
,
A. E.
, and
T. C. B.
McLeish
, “
Quantitative theory for linear dynamics of linear entangled polymers
,”
Macromolecules
35
,
6332
6343
(
2002
).
75.
Larson
,
R. G.
,
Q.
Zhou
,
S.
Shanbhag
, and
S. J.
Park
, “
Advances in modeling of polymer melt rheology
,”
AIChE J.
53
,
542
548
(
2007
).
76.
Masubuchi
,
Y.
,
Y.
Matsumiya
,
H.
Watanabe
,
G.
Marrucci
, and
G.
Ianniruberto
, “
Primitive chain network simulations for pom-pom polymers in uniaxial elongational flows
,”
Macromolecules
47
,
3511
3519
(
2014
).
77.
Menezes
,
E. V.
, and
W. W.
Graessley
, “
Nonlinear rheological behavior of polymer systems for several shear-flow histories
,”
J. Polym. Sci. Polym. Phys. Ed.
20
,
1817
1833
(
1982
).
78.
Pearson
,
D.
,
E.
Herbolzheimer
,
N.
Grizzuti
, and
G.
Marrucci
, “
Transient behavior of entangled polymers at high shear rates
,”
J. Polym. Sci. B
29
,
1589
1597
(
1991
).
79.
Cox
,
W. P.
, and
E. H.
Merz
, “
Correlation of dynamic and steady flow viscosities
,”
J. Polym. Sci.
28
,
619
622
(
1958
).
80.
Snijkers
,
F.
, and
D.
Vlassopoulos
, “
Appraisal of the Cox-Merz rule for well-characterized entangled linear and branched polymers
,”
Rheol. Acta
53
,
935
946
(
2014
).
81.
Ianniruberto
,
G.
, and
G.
Marrucci
, “
Convective constraint release (CCR) revisited
,”
J. Rheol.
58
,
89
102
(
2014
).
82.
Ianniruberto
,
G.
, “
Quantitative appraisal of a new CCR model for entangled linear polymers
,”
J. Rheol.
59
,
211
235
(
2015
).
You do not currently have access to this content.