Polydispersity is inevitable in industrially produced polymers. Established theories of polymer dynamics and rheology, however, were mostly built on monodisperse linear polymers. Dynamics of polydisperse polymers is yet to be fully explored—specifically how chains of different lengths affect the dynamics of one another in a mixture. This study explored the dynamics of bidisperse polymer melts using molecular dynamics and a bead–spring chain model. Binary mixtures between a moderately entangled long-chain species and an unentangled or marginally entangled short-chain species were investigated. We found that adding short chains can significantly accelerate the dynamics of the long chains by substantially lessening their extent of entanglement. Meanwhile, although introducing long chains also hinders the motion of the short chains, it does not qualitatively alter the nature of their dynamics—unentangled short chains still follow classical Rouse dynamics even in a matrix containing entangled chains. Detailed Rouse mode analysis was used to reveal the effects of entanglement at chain segments of different scales. Stress relaxation following a step shear strain was also studied, and semi-empirical mixing rules that predict the linear viscoelasticity of polydisperse polymers based on that of monodisperse systems were evaluated with simulation results.

1.
J. M.
Dealy
,
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 and Co KG
,
2018
).
2.
P. E.
Rouse
, Jr.
, “
A theory of the linear viscoelastic properties of dilute solutions of coiling polymers
,”
J. Chem. Phys.
21
,
1272
1280
(
1953
).
3.
R. B.
Bird
,
C. F.
Curtis
,
R. C.
Armstrong
, and
O.
Hassager
,
Dynamics of Polymeric Liquids
, 2nd ed. (
Wiley
,
New York
,
1987
), Vol.
2
.
4.
M.
Doi
and
S. F.
Edwards
,
The Theory of Polymer Dynamics
(
Oxford University Press
,
1988
), Vol.
73
.
5.
S. F.
Edwards
, “
Statistical mechanics with topological constraints. I
,”
Proc. Phys. Soc. (1958–1967)
91
,
513
(
1967
).
6.
P.-G.
de Gennes
, “
Reptation of a polymer chain in the presence of fixed obstacles
,”
J. Chem. Phys.
55
,
572
579
(
1971
).
7.
E.
Van Ruymbeke
,
R.
Keunings
,
V.
Stéphenne
,
A.
Hagenaars
, and
C.
Bailly
, “
Evaluation of reptation models for predicting the linear viscoelastic properties of entangled linear polymers
,”
Macromolecules
35
,
2689
2699
(
2002
).
8.
M.
Doi
,
W.
Graessley
,
E.
Helfand
, and
D.
Pearson
, “
Dynamics of polymers in polydisperse melts
,”
Macromolecules
20
,
1900
1906
(
1987
).
9.
J.
Des Cloizeaux
, “
Relaxation of entangled and partially entangled polymers in melts: Time-dependent reptation
,”
Macromolecules
25
,
835
841
(
1992
).
10.
S.
Barsky
, “
Molecular dynamics study of diffusion in bidisperse polymer melts
,”
J. Chem. Phys.
112
,
3450
3456
(
2000
).
11.
A.
Kopf
,
B.
Dünweg
, and
W.
Paul
, “
Dynamics of polymer ‘isotope’ mixtures: Molecular dynamics simulation and Rouse model analysis
,”
J. Chem. Phys.
107
,
6945
6955
(
1997
).
12.
J. T.
Kalathi
,
S. K.
Kumar
,
M.
Rubinstein
, and
G. S.
Grest
, “
Rouse mode analysis of chain relaxation in homopolymer melts
,”
Macromolecules
47
,
6925
6931
(
2014
).
13.
J. S.
Shaffer
, “
Effects of chain topology on polymer dynamics: Configurational relaxation in polymer melts
,”
J. Chem. Phys.
103
,
761
772
(
1995
).
14.
J.
Baschnagel
,
W.
Paul
,
V.
Tries
, and
K.
Binder
, “
Statics and dynamics of bidisperse polymer melts: A Monte Carlo study of the bond-fluctuation model
,”
Macromolecules
31
,
3856
3867
(
1998
).
15.
H.
Lin
,
W. L.
Mattice
, and
E. D.
Von Meerwall
, “
Chain dynamics of bidisperse polyethylene melts: A Monte Carlo study on a high-coordination lattice
,”
Macromolecules
40
,
959
966
(
2007
).
16.
M.
Rubinstein
,
R. H.
Colby
 et al,
Polymer Physics
(
Oxford University Press
,
New York
,
2003
), Vol.
23
.
17.
K.
Kremer
and
G. S.
Grest
, “
Dynamics of entangled linear polymer melts: A molecular-dynamics simulation
,”
J. Chem. Phys.
92
,
5057
5086
(
1990
).
18.
M.
Kröger
,
W.
Loose
, and
S.
Hess
, “
Rheology and structural changes of polymer melts via nonequilibrium molecular dynamics
,”
J. Rheol.
37
,
1057
1079
(
1993
).
19.
J.
Padding
and
W. J.
Briels
, “
Time and length scales of polymer melts studied by coarse-grained molecular dynamics simulations
,”
J. Chem. Phys.
117
,
925
943
(
2002
).
20.
A. E.
Likhtman
,
S. K.
Sukumaran
, and
J.
Ramirez
, “
Linear viscoelasticity from molecular dynamics simulation of entangled polymers
,”
Macromolecules
40
,
6748
6757
(
2007
).
21.
J.
Cao
and
A. E.
Likhtman
, “
Time-dependent orientation coupling in equilibrium polymer melts
,”
Phys. Rev. Lett.
104
,
207801
(
2010
).
22.
R.
Picu
and
A.
Rakshit
, “
Coarse grained model of diffusion in entangled bidisperse polymer melts
,”
J. Chem. Phys.
127
,
144909
(
2007
).
23.
B. L.
Peters
,
K. M.
Salerno
,
T.
Ge
,
D.
Perahia
, and
G. S.
Grest
, “
Effect of chain length dispersity on the mobility of entangled polymers
,”
Phys. Rev. Lett.
121
,
057802
(
2018
).
24.
B. L.
Peters
,
K. M.
Salerno
,
T.
Ge
,
D.
Perahia
, and
G. S.
Grest
, “
Viscoelastic response of dispersed entangled polymer melts
,”
Macromolecules
53
,
8400
8405
(
2020
).
25.
C.
Baig
,
P. S.
Stephanou
,
G.
Tsolou
,
V. G.
Mavrantzas
, and
M.
Kröger
, “
Understanding dynamics in binary mixtures of entangled cis-1,4-polybutadiene melts at the level of primitive path segments by mapping atomistic simulation data onto the tube model
,”
Macromolecules
43
,
8239
8250
(
2010
).
26.
Z.
Wang
and
R. G.
Larson
, “
Constraint release in entangled binary blends of linear polymers: A molecular dynamics study
,”
Macromolecules
41
,
4945
4960
(
2008
).
27.
S.
Shanbhag
and
Z.
Wang
, “
Molecular simulation of tracer diffusion and self-diffusion in entangled polymers
,”
Macromolecules
53
,
4649
4658
(
2020
).
28.
S.
Shanbhag
, “
Unusual dynamics of ring probes in linear matrices
,”
J. Polym. Sci., Part B: Polym. Phys.
55
,
169
177
(
2017
).
29.
G. S.
Grest
, “
Communication: Polymer entanglement dynamics: Role of attractive interactions
,”
J. Chem. Phys.
145
,
141101
(
2016
).
30.
A.
Makke
,
M.
Perez
,
J.
Rottler
,
O.
Lame
, and
J.-L.
Barrat
, “
Predictors of cavitation in glassy polymers under tensile strain: A coarse-grained molecular dynamics investigation
,”
Macromol. Theory Simul.
20
,
826
836
(
2011
).
31.
S.
Zhang
and
L.
Xi
, “
Effects of precursor topology on polymer networks simulated with molecular dynamics
,”
Polymer
116
,
143
152
(
2017
).
32.
L.
Xi
, “
Molecular simulation for predicting the rheological properties of polymer melts
,”
Mol. Simul.
45
,
1242
1264
(
2019
).
33.
S.
Plimpton
, “
Fast parallel algorithms for short-range molecular dynamics
,”
J. Comput. Phys.
117
,
1
19
(
1995
).
34.
Y. R.
Sliozberg
and
J. W.
Andzelm
, “
Fast protocol for equilibration of entangled and branched polymer chains
,”
Chem. Phys. Lett.
523
,
139
143
(
2012
).
35.
R.
Auhl
,
R.
Everaers
,
G. S.
Grest
,
K.
Kremer
, and
S. J.
Plimpton
, “
Equilibration of long chain polymer melts in computer simulations
,”
J. Chem. Phys.
119
,
12718
12728
(
2003
).
36.
K.
Kremer
and
G. S.
Grest
, “
Simulations for structural and dynamic properties of dense polymer systems
,”
J. Chem. Soc., Faraday Trans.
88
,
1707
1717
(
1992
).
37.
H. P.
Hsu
and
K.
Kremer
, “
Static and dynamic properties of large polymer melts in equilibrium
,”
J. Chem. Phys.
144
,
154907
(
2016
).
38.
W. H.
Press
,
S. A.
Teukolsky
,
B. P.
Flannery
, and
W. T.
Vetterling
,
Numerical Recipes in Fortran 77: Volume 1
, Volume 1 of Fortran Numerical Recipes: The Art of Scientific Computing (
Cambridge University Press
,
1992
).
39.
V.
Calandrini
,
E.
Pellegrini
,
P.
Calligari
,
K.
Hinsen
, and
G. R.
Kneller
, “
nmoldyn-interfacing spectroscopic experiments, molecular dynamics simulations and models for time correlation functions
,”
École Thém. Soc. Française Neutron.
12
,
201
232
(
2011
).
40.
J. L.
Viovy
,
M.
Rubinstein
, and
R. H.
Colby
, “
Constraint release in polymer melts: Tube reorganization versus tube dilation
,”
Macromolecules
24
,
3587
3596
(
1991
).
41.
S.
Wang
,
E. D.
von Meerwall
,
S.-Q.
Wang
,
A.
Halasa
,
W.-L.
Hsu
,
J.
Zhou
, and
R.
Quirk
, “
Diffusion and rheology of binary polymer mixtures
,”
Macromolecules
37
,
1641
1651
(
2004
).
42.
P. H.
Verdier
, “
Monte Carlo studies of lattice-model polymer chains. I. Correlation functions in the statistical-bead model
,”
J. Chem. Phys.
45
,
2118
2121
(
1966
).
43.
M.
Vladkov
and
J.-L.
Barrat
, “
Linear and nonlinear viscoelasticity of a model unentangled polymer melt: Molecular dynamics and rouse modes analysis
,”
Macromol. Theory Simul.
15
,
252
262
(
2006
).
44.
J. T.
Kalathi
,
S. K.
Kumar
,
M.
Rubinstein
, and
G. S.
Grest
, “
Rouse mode analysis of chain relaxation in polymer nanocomposites
,”
Soft Matter
11
,
4123
4132
(
2015
).
45.
J.
Padding
and
W. J.
Briels
, “
Uncrossability constraints in mesoscopic polymer melt simulations: Non-rouse behavior of C120H242
,”
J. Chem. Phys.
115
,
2846
2859
(
2001
).
46.
Y.
Li
,
M.
Kröger
, and
W. K.
Liu
, “
Nanoparticle effect on the dynamics of polymer chains and their entanglement network
,”
Phys. Rev. Lett.
109
,
118001
(
2012
).
47.
L.
Xi
,
M.
Shah
, and
B. L.
Trout
, “
Hopping of water in a glassy polymer studied via transition path sampling and likelihood maximization
,”
J. Phys. Chem. B
117
,
3634
3647
(
2013
).
48.
H. P.
Hsu
and
K.
Kremer
, “
Detailed analysis of Rouse mode and dynamic scattering function of highly entangled polymer melts in equilibrium
,”
Eur. Phys. J.: Spec. Top.
226
,
693
703
(
2017
).
49.
P. J.
Daivis
and
D. J.
Evans
, “
Comparison of constant pressure and constant volume nonequilibrium simulations of sheared model decane
,”
J. Chem. Phys.
100
,
541
547
(
1994
).
50.
J.
Ramírez
,
S. K.
Sukumaran
,
B.
Vorselaars
, and
A. E.
Likhtman
, “
Efficient on the fly calculation of time correlation functions in computer simulations
,”
J. Chem. Phys.
133
,
154103
(
2010
).
51.
R.
Anderssen
and
D.
Mead
, “
Theoretical derivation of molecular weight scaling for rheological parameters
,”
J. Non-Newtonian Fluid Mech.
76
,
299
306
(
1998
).
52.
D.
Maier
,
A.
Eckstein
,
C.
Friedrich
, and
J.
Honerkamp
, “
Evaluation of models combining rheological data with the molecular weight distribution
,”
J. Rheol.
42
,
1153
1173
(
1998
).
53.
W. H.
Tuminello
, “
Determining molecular weight distributions from the rheological properties of polymer melts
,” in
Proceedings of the 71st Society of Rheology Meeting
,
Madison, Wisconsin
(
1999
).
54.
G.
Marrucci
, “
Relaxation by reptation and tube enlargement: A model for polydisperse polymers
,”
J. Polym. Sci.: Polym. Phys. Ed.
23
,
159
177
(
1985
).
55.
W.
Thimm
,
C.
Friedrich
,
M.
Marth
, and
J.
Honerkamp
, “
On the rouse spectrum and the determination of the molecular weight distribution from rheological data
,”
J. Rheol.
44
,
429
438
(
2000
).
56.
W. H.
Tuminello
, “
Molecular weight and molecular weight distribution from dynamic measurements of polymer melts
,”
Polym. Eng. Sci.
26
,
1339
1347
(
1986
).
57.
C.
Tsenoglou
, “
Molecular weight polydispersity effects on the viscoelasticity of entangled linear polymers
,”
Macromolecules
24
,
1762
1767
(
1991
).
58.
J.
Des Cloizeaux
, “
Relaxation of entangled polymers in melts
,”
Macromolecules
23
,
3992
4006
(
1990
).
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