We develop a method for efficient prediction of linear and nonlinear rheology of polydisperse polymers by judicious selection of a small number of representative polymer molecules from the large ensemble of chains comprising the molecular weight and branching distribution. Specifically, we use a numerical inversion of the double reptation model to select five or six representative molecular species to optimally fit the linear rheology of commercial polymers and then use the regressed parameters to compute the nonlinear rheology via the Rolie-double-poly (RDP) model. The method is tested for several model systems, namely, two polydisperse linear polystyrene (PS) samples described in Shivokhin et al. [Polym. Eng. Sci. 56, 1012–1020 (2016)] and Münstedt [J. Rheol. 24, 847–867 (1980)], a commercial linear low density polyethylene (LLDPE), and a low density polyethylene (LDPE) whose rheological properties are measured in the current study. For the linear polymers including the PS samples and the LLDPE, the predictions of the “representative” RDP model of the start-up extensional rheology are comparable to those of the “full” RDP model based on all the species drawn from the gas permeation chromatography characterization. The method then successfully predicts the linear rheology of blends of LLDPE and LDPE using the same representative molecules found by fitting each of the pure polymers. Further fitting the extensional rheology of the LDPE requires using the “priorities” qi and stretch relaxation times τs,i of the representative molecules as adjustable parameters, whose values are then held fixed when predicting the extensional rheology of blends of the LDPE with the LLDPE roughly as successfully as does branch-on-branch model. The reduction in the number of representative polymer species offers new opportunities for faster simulations of flowing polymers, as well as for the prediction of segmental orientation to be used in the modeling of flow-induced crystallization.

1.
Shivokhin
,
M. E.
,
L.
Urbanczyk
,
J.
Michel
, and
C.
Bailly
, “
The influence of molecular weight distribution of industrial polystyrene on its melt extensional and ultimate properties
,”
Polym. Eng. Sci.
56
,
1012
1020
(
2016
).
2.
Münstedt
,
H.
, “
Dependence of the elongational behavior of polystyrene melts on molecular weight and molecular weight distribution
,”
J. Rheol.
24
,
847
867
(
1980
).
3.
Larson
,
R. G.
, “
Combinatorial rheology of branched polymer melts
,”
Macromolecules
34
,
4556
4571
(
2001
).
4.
Wang
,
Z.
,
X.
Chen
, and
R. G.
Larson
, “
Comparing tube models for predicting the linear rheology of branched polymer melts
,”
J. Rheol.
54
,
223
260
(
2010
).
5.
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
).
6.
Ahmadi
,
M.
,
C.
Bailly
,
R.
Keunings
,
M.
Nekoomanesh
,
H.
Arabi
, and
E.
van Ruymbeke
, “
Time marching algorithm for predicting the linear rheology of monodisperse comb polymer melts
,”
Macromolecules
44
,
647
659
(
2011
).
7.
Osswald
,
T.
, and
J. P.
Hernández-Ortiz
,
Polymer Processing: Modeling and Simulation
(
Hanser
,
Munich, Cincinnati
,
2006
).
8.
Read
,
D. J.
,
C.
McIlroy
,
C.
Das
,
O. G.
Harlen
, and
R. S.
Graham
, “
PolySTRAND model of flow-induced nucleation in polymers
,”
Phys. Rev. Lett.
124
,
147802
(
2020
).
9.
Michler
,
G. H.
, and
F. J.
Baltá-Calleja
,
Mechanical Properties of Polymers Based on Nanostructure and Morphology
(
Taylor & Francis
,
London
,
2005
).
10.
Das
,
C.
,
D. J.
Read
,
D.
Auhl
,
M.
Kapnistos
,
J.
den Doelder
,
I.
Vittorias
, and
T. C. B.
McLeish
, “
Numerical prediction of nonlinear rheology of branched polymer melts
,”
J. Rheol.
58
,
737
757
(
2014
).
11.
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
).
12.
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
).
13.
Boudara
,
V. A. H.
,
J. D.
Peterson
,
L. G.
Leal
, and
D. J.
Read
, “
Nonlinear rheology of polydisperse blends of entangled linear polymers: Rolie-double-poly models
,”
J. Rheol.
63
,
71
91
(
2018
).
14.
Auhl
,
D.
,
P.
Chambon
,
T. C. B.
McLeish
, and
D. J.
Read
, “
Elongational flow of blends of long and short polymers: Effective stretch relaxation time
,”
Phys. Rev. Lett.
103
,
136001
(
2009
).
15.
Zhang
,
W.
,
E. D.
Gomez
, and
S. T.
Milner
, “
Predicting nematic phases of semiflexible polymers
,”
Macromolecules
48
,
1454
1462
(
2015
).
16.
Yi
,
P.
,
C. R.
Locker
, and
G. C.
Rutledge
, “
Molecular dynamics simulation of homogeneous crystal nucleation in polyethylene
,”
Macromolecules
46
,
4723
4733
(
2013
).
17.
Pathaweeisariyakul
,
T.
,
K.
Narkchamnan
,
B.
Thitisuk
, and
W.
Yau
, “
Methods of long chain branching detection in PE by triple-detector gel permeation chromatography
,”
J. Appl. Polym. Sci.
132
,
42222
(
2015
).
18.
Yau
,
W.
,
R.
Brown
,
P.
Tyler
,
T.
Huang
,
R.
Cong
,
C.
Klinker
, and
L.
Hazlitt
, “
A ‘systematic approach’ to TD-GPC data processing with band broadening correction
,”
Macromol. Symp.
330
,
53
62
(
2013
).
19.
Hodder
,
P.
, and
A.
Franck
, “
A new tool for measuring extensional viscosity
,”
Ann. Trans. Nord. Rheol. Soc.
13
,
227
232
(
2005
).
20.
Boudara
,
V. A. H.
,
D. J.
Read
, and
J.
Ramírez
, “
Reptate rheology software: Toolkit for the analysis of theories and experiments
,”
J. Rheol.
64
,
709
722
(
2020
).
21.
Patnode
,
W.
, and
W. J.
Scheiber
, “
The density, thermal expansion, vapor pressure, and refractive index of styrene, and the density and thermal expansion of polystyrene
,”
J. Am. Chem. Soc.
61
,
3449
3451
(
1939
).
22.
Larson
,
R. G.
,
T.
Sridhar
,
L. G.
Leal
,
G. H.
McKinley
,
A. E.
Likhtman
, and
T. C. B.
McLeish
, “
Definitions of entanglement spacing and time constants in the tube model
,”
J. Rheol.
47
,
809
818
(
2003
).
23.
Park
,
S. J.
, and
R. G.
Larson
, “
Modeling the linear viscoelastic properties of metallocene-catalyzed high density polyethylenes with long-chain branching
,”
J. Rheol.
49
,
523
536
(
2005
).
24.
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
).
25.
Mark
,
J. E.
,
Physical Properties of Polymers Handbook
(
Springer
,
New York
,
2006
).
26.
Fetters
,
L. J.
,
D. J.
Lohse
,
C. A.
García-Franco
,
P.
Brant
, and
D.
Richter
, “
Prediction of melt state poly(α-olefin) rheological properties: The unsuspected role of the average molecular weight per backbone bond
,”
Macromolecules
35
,
10096
10101
(
2002
).
27.
Chen
,
X.
,
F. J.
Stadler
,
H.
Münstedt
, and
R. G.
Larson
, “
Method for obtaining tube model parameters for commercial ethene/α-olefin copolymers
,”
J. Rheol.
54
,
393
406
(
2010
).
28.
Vega
,
J. F.
,
S.
Rastogi
,
G. W. M.
Peters
, and
H. E. H.
Meijer
, “
Rheology and reptation of linear polymers. Ultrahigh molecular weight chain dynamics in the melt
,”
J. Rheol.
48
,
663
678
(
2004
).
29.
Pattamaprom
,
C.
, and
R. G.
Larson
, “
Predicting the linear viscoelastic properties of monodisperse and polydisperse polystyrenes and polyethylenes
,”
Rheol. Acta
40
,
516
532
(
2001
).
30.
Raju
,
V. R.
,
G. G.
Smith
,
G.
Marin
,
J. R.
Knox
, and
W. W.
Graessley
, “
Properties of amorphous and crystallizable hydrocarbon polymers. I. Melt rheology of fractions of linear polyethylene
,”
J. Polym. Sci. Polym. Phys. Ed.
17
,
1183
1195
(
1979
).
31.
Dealy
,
J. M.
,
D. J.
Read
, and
R. G.
Larson
,
Structure and Rheology of Molten Polymers
, 2nd ed. (
Hanser
,
Cincinnati
,
2018
).
32.
Likhtman
,
A. E.
, and
T. C. B.
McLeish
, “
Quantitative theory for linear dynamics of linear entangled polymers
,”
Macromolecules
35
,
6332
6343
(
2002
).
33.
Inkson
,
N. J.
,
T. C. B.
McLeish
,
O. G.
Harlen
, and
D. J.
Groves
, “
Predicting low density polyethylene melt rheology in elongational and shear flows with ‘pom-pom’ constitutive equations
,”
J. Rheol.
43
,
873
896
(
1999
).
34.
Zhang
,
W.
, and
R. G.
Larson
, “
A metastable nematic precursor accelerates polyethylene oligomer crystallization as determined by atomistic simulations and self-consistent field theory
,”
J. Chem. Phys.
150
,
244903
(
2019
).
35.
Read
,
D. J.
,
M. E.
Shivokhin
, and
A. E.
Likhtman
, “
Contour length fluctuations and constraint release in entangled polymers: Slip-spring simulations and their implications for binary blend rheology
,”
J. Rheol.
62
,
1017
1036
(
2018
).
36.
See supplementary material at https://doi.org/10.1122/8.0000125 for the correlation on the density of PE and temperature to obtain the density of the PE samples for simulation at 150°C; blending verification for LLDPE and LDPE blends; more characterizations other than those in the main text for LDPE and LLDPE; the effect of neglect of Rouse modes in nonlinear BoB simulations of the start-up of the extensional flow; and the extensional viscosity obtained when taking the representative ensemble from fits to the experimental data is compared to that obtained by fitting to the linear rheology predictions of BoB for LLDPE.

Supplementary Material

You do not currently have access to this content.