We analyze the molecular mechanism of the chain stretching and orientation for the stress overshoot response of linear and comb polymers under shear using the nonequilibrium molecular dynamics simulation. Different from the strain overshoot behavior of linear polymers, the shear stress peak strain γmax of comb polymers vs the Rouse–Weissenberg number WiR=τRγ˙ displays three scaling law regions, in agreement with previous experimental results [F. Snijkers et al., ACS Macro Lett. 2, 601–604 (2013)]. In contrast to experiments, our simulations visually reveal the stretching and orientation dynamics of chain segments at the stress overshoot. According to the detailed information of stretching and orientation of the segment with different lengths, it is found that the size of a tension blob decreases with increasing WiR, and it follows a power-law with an exponent of −0.6 for a linear system. With respect to the comb systems, the size of a tension blob decreases accordingly with grafting density under the same shear rate. Unambiguous molecular pictures at the stress overshoot are also given at different shear rates for linear and comb polymers.

1.
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
).
2.
Kasehagen
,
L. J.
, and
C. W.
Macosko
, “
Nonlinear shear and extensional rheology of long-chain randomly branched polybutadiene
,”
J. Rheol.
42
,
1303
1327
(
1998
).
3.
McLeish
,
T. C. B.
, “
Tube theory of entangled polymer dynamics
,”
Adv. Phys.
51
,
1379
1527
(
2002
).
4.
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
).
5.
Fujimoto
,
T.
,
H.
Narukawa
, and
M.
Nagasawa
, “
Viscoelastic properties of comb-shaped polystyrenes
,”
Macromolecules
3
,
57
64
(
1970
).
6.
Liu
,
G.
,
H.
Ma
,
H.
Lee
,
H.
Xu
,
S.
Cheng
,
H.
Sun
,
T.
Chang
,
R. P.
Quirk
, and
S.-Q.
Wang
, “
Long-chain branched polymers to prolong homogeneous stretching and to resist melt breakup
,”
Polymer
54
,
6608
6616
(
2013
).
7.
Ramos
,
J.
, and
J.
Martínez-Salazar
, “
Computer modeling of the crystallization process of single-chain ethylene/1-hexene copolymers from dilute solutions
,”
J. Polym. Sci. B Polym. Phys.
49
,
421
430
(
2011
).
8.
Zhang
,
W.
, and
R. G.
Larson
, “
Direct all-atom molecular dynamics simulations of the effects of short chain branching on polyethylene oligomer crystal nucleation
,”
Macromolecules
51
,
4762
4769
(
2018
).
9.
Kumar
,
V.
,
C. R.
Locker
,
P. J.
in ’t Veld
, and
G. C.
Rutledge
, “
Effect of short chain branching on the interlamellar structure of semicrystalline polyethylene
,”
Macromolecules
50
,
1206
1214
(
2017
).
10.
Bailly
,
C.
,
V.
Stephenne
,
Z.
Muchtar
,
M.
Schappacher
, and
A.
Deffieux
, “
Linear viscoelastic behavior of densely grafted poly(chloroethyl vinyl ether)-g-polystyrene combs in the melt
,”
J. Rheol.
47
,
821
827
(
2003
).
11.
Read
,
D. J.
,
D.
Auhl
,
C.
Das
,
J.
den Doelder
,
M.
Kapnistos
,
I.
Vittorias
, and
T. C.
McLeish
, “
Linking models of polymerization and dynamics to predict branched polymer structure and flow
,”
Science
333
,
1871
1874
(
2011
).
12.
McLeish
,
T.
,
Structure and rheology of molten polymers from structure to flow behavior and back again
, in
Book Structure and Rheology of Molten Polymers: From Structure to Flow Behavior and Back Again
, edited by
J. M.
Dealy
,
D. J.
Read
, and
R. G.
Larson
(
Hanser
,
Cincinnati
,
2018
).
13.
Liu
,
G.
,
S.
Cheng
,
H.
Lee
,
H.
Ma
,
H.
Xu
,
T.
Chang
,
R. P.
Quirk
, and
S. Q.
Wang
, “
Strain hardening in startup shear of long-chain branched polymer solutions
,”
Phys. Rev. Lett.
111
,
068302
(
2013
).
14.
Xie
,
S.-J.
, and
K. S.
Schweizer
, “
Consequences of delayed chain retraction on the rheology and stretch dynamics of entangled polymer liquids under continuous nonlinear shear deformation
,”
Macromolecules
51
,
4185
4200
(
2018
).
15.
Wang
,
S.-Q.
,
Nonlinear Polymer Rheology: Macroscopic Phenomenology and Molecular Foundation
(
Wiley
,
New York
,
2018
).
16.
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
).
17.
Boukany
,
P. E.
,
S.-Q.
Wang
, and
X.
Wang
, “
Universal scaling behavior in startup shear of entangled linear polymer melts
,”
J. Rheol.
53
,
617
629
(
2009
).
18.
Nafar Sefiddashti
,
M. H.
,
B. J.
Edwards
, and
B.
Khomami
, “
Individual molecular dynamics of an entangled polyethylene melt undergoing steady shear flow steady-state and transient dynamics
,”
Polymers (Basel)
11,
476
(
2019
).
19.
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
).
20.
Lentzakis
,
H.
,
C.
Das
,
D.
Vlassopoulos
, and
D. J.
Read
, “
Pom-pom-like constitutive equations for comb polymers
,”
J. Rheol.
58
,
1855
1875
(
2014
).
21.
Milner
,
S.
, and
T.
McLeish
, “
Arm-length dependence of stress relaxation in star polymer melts
,”
Macromolecules
31
,
7479
7482
(
1998
).
22.
Boudara
,
V. A. H.
, and
D. J.
Read
, “
Stochastic and preaveraged nonlinear rheology models for entangled telechelic star polymers
,”
J. Rheol.
61
,
339
362
(
2017
).
23.
Huang
,
Q.
,
S.
Costanzo
,
C.
Das
, and
D.
Vlassopoulos
, “
Stress growth and relaxation of dendritically branched macromolecules in shear and uniaxial extension
,”
J. Rheol.
61
,
35
47
(
2017
).
24.
Wijesinghe
,
S.
,
D.
Perahia
, and
G. S.
Grest
, “
Polymer topology effects on dynamics of comb polymer melts
,”
Macromolecules
51
,
7621
7628
(
2018
).
25.
Shen
,
J.
,
X.
Lin
,
J.
Liu
, and
X.
Li
, “
Effects of cross-link density and distribution on static and dynamic properties of chemically cross-linked polymers
,”
Macromolecules
52
,
121
134
(
2018
).
26.
Luo
,
C.
,
M.
Kröger
, and
J.-U.
Sommer
, “
Entanglements and crystallization of concentrated polymer solutions: Molecular dynamics simulations
,”
Macromolecules
49
,
9017
9025
(
2016
).
27.
Luo
,
C.
,
M.
Kröger
, and
J.-U.
Sommer
, “
Molecular dynamics simulations of polymer crystallization under confinement: Entanglement effect
,”
Polymer
109
,
71
84
(
2017
).
28.
Olsson
,
P. A. T.
,
P. J.
in ’t Veld
,
E.
Andreasson
,
E.
Bergvall
,
E.
Persson Jutemar
,
V.
Petersson
,
G. C.
Rutledge
, and
M.
Kroon
, “
All-atomic and coarse-grained molecular dynamics investigation of deformation in semi-crystalline lamellar polyethylene
,”
Polymer
153
,
305
316
(
2018
).
29.
Jeong
,
S.
,
J. M.
Kim
,
S.
Cho
, and
C.
Baig
, “
Effect of short-chain branching on interfacial polymer structure and dynamics under shear flow
,”
Soft Matter
13
,
8644
8650
(
2017
).
30.
Holler
,
S.
,
A. J.
Moreno
,
M.
Zamponi
,
P.
Bačová
,
L.
Willner
,
H.
Iatrou
,
P.
Falus
, and
D.
Richter
, “
The role of the functionality in the branch point motion in symmetric star polymers: A combined study by simulations and neutron spin echo spectroscopy
,”
Macromolecules
51
,
242
253
(
2017
).
31.
Bačová
,
P.
,
L. G. D.
Hawke
,
D. J.
Read
, and
A. J.
Moreno
, “
Dynamics of branched polymers: A combined study by molecular dynamics simulations and tube theory
,”
Macromolecules
46
,
4633
4650
(
2013
).
32.
Kremer
,
K.
, and
G. S.
Grest
, “
Dynamics of entangled linear polymer melts:  A molecular-dynamics simulation
,”
J. Chem. Phys.
92
,
5057
5086
(
1990
).
33.
Theodorou
,
D. N.
,
T. D.
Boone
,
L. R.
Dodd
, and
K. F.
Mansfield
, “
Stress tensor in model polymer systems with periodic boundaries
,”
Macromol. Theory Simul.
2
,
191
238
(
1993
).
34.
Kröger
,
M.
, “
Shortest multiple disconnected path for the analysis of entanglements in two- and three-dimensional polymeric systems
,”
Comput. Phys. Commun.
168
,
209
232
(
2005
).
35.
Wang
,
Z.
,
A. E.
Likhtman
, and
R. G.
Larson
, “
Segmental dynamics in entangled linear polymer melts
,”
Macromolecules
45
,
3557
3570
(
2012
).
36.
Xu
,
W.-S.
,
J.-M. Y.
Carrillo
,
C. N.
Lam
,
B. G.
Sumpter
, and
Y.
Wang
, “
Molecular dynamics investigation of the relaxation mechanism of entangled polymers after a large step deformation
,”
ACS Macro Lett.
7
,
190
195
(
2018
).
37.
Hsu
,
H. P.
, and
K.
Kremer
, “
Static and dynamic properties of large polymer melts in equilibrium
,”
J. Chem. Phys.
144
,
154907
(
2016
).
38.
Dealy
,
J. M.
,
D. J.
Read
, and
R. G.
Larson
,
Structure and Rheology of Molten Polymers: From Structure to Flow Behavior and Back Again
(
Carl Hanser Verlag GmbH Co KG
, Cincinnati,
2018
).
39.
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
).
40.
Abbasi
,
M.
,
L.
Faust
,
K.
Riazi
, and
M.
Wilhelm
, “
Linear and extensional rheology of model branched polystyrenes: From loosely grafted combs to bottlebrushes
,”
Macromolecules
50
,
5964
5977
(
2017
).
41.
Doi
,
M.
, and
S. F.
Edwards
,
The Theory of Polymer Dynamics
(Oxford University, Oxford
1986
).
42.
Xie
,
S. J.
, and
K. S.
Schweizer
, “
Entangled chain polymer liquids under continuous shear deformation: consequences of a microscopically anharmonic confining tube
,”
Soft Matter
14
,
7052
7063
(
2018
).
43.
Yan
,
Z.-C.
,
S.
Costanzo
,
Y.
Jeong
,
T.
Chang
, and
D.
Vlassopoulos
, “
Linear and nonlinear shear rheology of a marginally entangled ring polymer
,”
Macromolecules
49
,
1444
1453
(
2016
).
44.
Leduc
,
P.
,
C.
Haber
,
G.
Bao
, and
D.
Wirtz
, “
Dynamics of individual flexible polymers in a shear flow
,”
Nature
399
,
564
566
(
1999
).
45.
Schweizer
,
K. S.
, and
S.-J.
Xie
, “
Physics of the stress overshoot and chain stretch dynamics of entangled polymer liquids under continuous startup nonlinear shear
,”
ACS Macro Lett.
7
,
218
222
(
2018
).
46.
Rubinstein
,
M.
, and
R. H.
Colby
,
Polymer Physics
(
Oxford University
,
New York
,
2003
), Vol. 23.
You do not currently have access to this content.