Polymer crystallization occurs in many plastic manufacturing processes, from injection molding to film blowing. Linear low-density polyethylene (LLDPE) is one of the most commonly processed polymers, wherein the type and extent of short-chain branching (SCB) may be varied to influence crystallization. In this work, we report simultaneous measurements of the rheology and Raman spectra, using a Rheo-Raman microscope, for two industrial-grade LLDPEs undergoing crystallization. These polymers are characterized by broad polydispersity, SCB, and the presence of polymer chain entanglements. The rheological behavior of these entangled LLDPE melts is modeled as a function of crystallinity using a slip-link model. The partially crystallized melt is represented by a blend of linear chains with either free or cross-linked ends, wherein the cross-links represent attachment to growing crystallites, and a modulus shift factor that increases with the degree of crystallinity. In contrast to our previous application of the slip-link model to isotactic polypropylene, in which the introduction of only bridging segments with cross-links at both ends was sufficient to describe the available data, for these LLDPEs, we find it necessary to introduce dangling segments, with cross-links at only one end. The model captures quantitatively the evolution of viscosity and elasticity with crystallization over the whole range of frequencies in the linear regime for the two LLDPE grades.

1.
Flory
,
P. J.
, “
Theory of crystallization in copolymers
,”
Trans. Faraday Soc.
51
,
848
857
(
1955
).
2.
Sanchez
,
I. C.
, and
R. K.
Eby
, “
Crystallization of random copolymers
,”
J. Res. Nat. Bur. Stand. Sect. A Phys. Chem.
77A
,
353
358
(
1973
).
3.
Doi
,
M.
, and
S. F.
Edwards
, “
Dynamics of concentrated polymer systems. Part I—Brownian motion in the equilibrium state
,”
J. Chem. Soc. Faraday Trans. 2 Mol. Chem. Phys.
74
,
1789
1801
(
1978
).
4.
Peters
,
G. W. M.
,
L.
Balzano
, and
R. J. A.
Steenbakkers
,
Flow-induced crystallization
, in
Handbook of Polymer Crystallization
(
Wiley
,
Hoboken, NJ
,
2013
), pp.
399
431
.
5.
Kumaraswamy
,
G.
, “
Crystallization of polymers from stressed melts
,”
J. Macromol. Sci. Polym. Rev.
45
,
375
397
(
2005
).
6.
Graham
,
R. S.
, “
Modelling flow-induced crystallisation in polymers
,”
Chem. Commun.
50
,
3531
3545
(
2014
).
7.
Janeschitz-Kriegl
,
H.
,
Crystallization Modalities in Polymer Melt Processing
(
Springer
,
Cham
,
2018
).
8.
Pirkle
,
J. J. C.
, and
R. D.
Braatz
, “
A thin-shell two-phase microstructural model for blown film extrusion
,”
J. Rheol.
54
,
471
505
(
2010
).
9.
Pirkle
,
J. J. C.
, and
R. D.
Braatz
, “
Dynamic modeling of blown-film extrusion
,”
Polym. Eng. Sci.
43
,
398
418
(
2003
).
10.
Housiadas
,
K. D.
,
G.
Klidis
, and
J.
Tsamopoulos
, “
Two- and three-dimensional instabilities in the film blowing process
,”
J. Nonnewton. Fluid Mech.
141
,
193
220
(
2007
).
11.
Andreev
,
M.
, and
G. C.
Rutledge
, “
A slip-link model for rheology of entangled polymer melts with crystallization
,”
J. Rheol.
64
,
213
222
(
2020
).
12.
Pantani
,
R.
,
V.
Speranza
, and
G.
Titomanlio
, “
Simultaneous morphological and rheological measurements on polypropylene: Effect of crystallinity on viscoelastic parameters
,”
J. Rheol.
59
,
377
390
(
2015
).
13.
Acierno
,
S.
, and
N.
Grizzuti
, “
Measurements of the rheological behavior of a crystallizing polymer by an ‘inverse quenching’ technique
,”
J. Rheol.
47
,
563
576
(
2003
).
14.
Coppola
,
S.
,
S.
Acierno
,
N.
Grizzuti
, and
D.
Vlassopoulos
, “
Viscoelastic behavior of semicrystalline thermoplastic polymers during the early stages of crystallization
,”
Macromolecules
39
,
1507
1514
(
2006
).
15.
Pogodina
,
N. V.
, and
H. H.
Winter
, “
Polypropylene crystallization as a physical gelation process
,”
Macromolecules
31
,
8164
8172
(
1998
).
16.
Pogodina
,
N. V.
,
V. P.
Lavrenko
,
S.
Srinivas
, and
H. H.
Winter
, “
Rheology and structure of IPP near gel point: Quiescent and shear-induced crystallization
,”
Polymer
42
,
9031
9043
(
2001
).
17.
Pogodina
,
N. V.
,
S. K.
Siddiquee
,
J. W.
Van Egmond
, and
H. H.
Winter
, “
Correlation of rheology and light scattering in isotactic polypropylene during early stages of crystallization
,”
Macromolecules
32
,
1167
1174
(
1999
).
18.
Roozemond
,
P. C.
,
V.
Janssens
,
P.
van Puyvelde
, and
G. W. M.
Peters
, “
Suspension-like hardening behavior of HDPE and time-hardening superposition
,”
Rheol. Acta
51
,
97
109
(
2012
).
19.
Steenbakkers
,
R. J. A.
, and
G. W. M.
Peters
, “
Suspension-based rheological modeling of crystallizing polymer melts
,”
Rheol. Acta
47
,
643
665
(
2008
).
20.
Christensen
,
R. M.
, and
K. H.
Lo
, “
Solutions for effective shear properties in three phase sphere and cylinder models
,”
J. Mech. Phys. Solids
27
,
315
330
(
1979
).
21.
Kotula
,
A. P.
, and
K. B.
Migler
, “
Evaluating models for polycaprolactone crystallization via simultaneous rheology and Raman spectroscopy
,”
J. Rheol.
62
,
343
356
(
2018
).
22.
Boutahar
,
K.
,
C.
Carrot
, and
J.
Guillet
, “
Crystallization of polyolefins from rheological measurements—Relation between the transformed fraction and the dynamic moduli
,”
Macromolecules
31
,
1921
1929
(
1998
).
23.
Roozemond
,
P. C.
,
M.
van Drongelen
,
L.
Verbelen
,
P.
Van Puyvelde
, and
G. W. M.
Peters
, “
Flow-induced crystallization studied in the RheoDSC device: Quantifying the importance of edge effects
,”
Rheol. Acta
54
,
1
8
(
2015
).
24.
Plog
,
J. P.
,
M.
Meyer
,
F.
De Vito
,
F.
Soergel
, and
A.
Kotula
, “
Rheo-Raman microscope: Tracking molecular structures as a function of deformation and temperature
,”
AIP Conf. Proc.
1736
,
020072
(
2016
).
25.
Kotula
,
A. P.
,
M. W.
Meyer
,
F.
De Vito
,
J.
Plog
,
A. R.
Hight Walker
, and
K. B.
Migler
, “
The Rheo-Raman microscope: Simultaneous chemical, conformational, mechanical, and microstructural measures of soft materials
,”
Rev. Sci. Instrum.
87
,
105105
(
2016
).
26.
Kotula
,
A.
, “
A frequency-dependent effective medium model for the rheology of crystallizing polymers
,”
J. Rheol.
64
,
505
515
(
2020
).
27.
Roy
,
D.
,
D. J.
Audus
, and
K. B.
Migler
, “
Rheology of crystallizing polymers: The role of spherulitic superstructures, gap height, and nucleation densities
,”
J. Rheol.
63
,
851
862
(
2019
).
28.
Schieber
,
J. D.
,
J.
Neergaard
, and
S.
Gupta
, “
A full-chain, temporary network model with sliplinks, chain-length fluctuations, chain connectivity and chain stretching
,”
J. Rheol.
47
,
213
233
(
2003
).
29.
Khaliullin
,
R. N.
, and
J. D.
Schieber
, “
Self-consistent modeling of constraint release in a single-chain mean-field slip-link model
,”
Macromolecules
42
,
7504
7517
(
2009
).
30.
Andreev
,
M.
,
H.
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.
Andreev
,
M.
, and
J. D.
Schieber
, “
Accessible and quantitative entangled polymer rheology predictions, suitable for complex flow calculations
,”
Macromolecules
48
,
1606
1613
(
2015
).
32.
Katzarova
,
M.
,
M.
Andreev
,
Y.
Sliozberg
,
R. A.
Mrozek
,
J. L.
Lenhart
,
J. W.
Andzelm
, and
J. D.
Schieber
, “
Rheological predictions of network systems swollen with entangled solvent
,”
AIChE J.
60
,
1372
1380
(
2014
).
33.
Jensen
,
M. K.
,
R.
Khaliullin
, and
J. D.
Schieber
, “
Self-consistent modeling of entangled network strands and linear dangling structures in a single-strand mean-field slip-link model
,”
Rheol. Acta
51
,
21
35
(
2012
).
34.
Moore
,
J. C.
, “
Gel permeation chromatography. I. A new method for molecular weight distribution of high polymers
,”
J. Polym. Sci. Part A Gen. Pap.
2
,
835
843
(
1964
).
35.
Monrabal
,
B.
,
J.
Sancho-Tello
,
N.
Mayo
, and
L.
Romero
, “
Crystallization elution fractionation. A new separation process for polyolefin resins
,”
Macromol. Symp.
257
,
71
79
(
2007
).
36.
Hollis
,
C.
,
A.
Parrott
,
R.
Cong
, and
M.
Cheatham
, Chromatography of polymers with reduced co-crystallization, WO2017040127 (2017).
37.
Geri
,
M.
,
B.
Keshavarz
,
T.
Divoux
,
C.
Clasen
,
D. J.
Curtis
, and
G. H.
McKinley
, “
Time-resolved mechanical spectroscopy of soft materials via optimally windowed chirps
,”
Phys. Rev. X
8
,
041042
(
2018
).
38.
Migler
,
K. B.
,
A. P.
Kotula
, and
A. R.
Hight Walker
, “
Trans-rich structures in early stage crystallization of polyethylene
,”
Macromolecules
48
,
4555
4561
(
2015
).
39.
Strobl
,
G. R.
, and
W.
Hagedorn
, “
Raman spectroscopic method for determining the crystallinity of polyethylene
,”
AIP Conf. Proc.
16
,
1181
1193
(
1978
).
40.
Schieber
,
J. D.
, and
M.
Andreev
, “
Entangled polymer dynamics in equilibrium and flow modeled through slip links
,”
Annu. Rev. Chem. Biomol. Eng.
5
,
367
381
(
2014
).
41.
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
).
42.
Taletskiy
,
K.
,
T. A.
Tervoort
, and
J. D.
Schieber
, “
Predictions of the linear rheology of polydisperse, entangled linear polymer melts by using the discrete slip-link model
,”
J. Rheol.
62
,
1331
1338
(
2018
).
43.
Shivokhin
,
M. E.
,
T.
Narita
,
L.
Talini
,
A.
Habicht
,
S.
Seiffert
,
T.
Indei
, and
J. D.
Schieber
, “
Interplay of entanglement and association effects on the dynamics of semidilute solutions of multisticker polymer chains
,”
J. Rheol.
61
,
1231
1241
(
2017
).
44.
See supplementary material at https://doi.org/10.1122/8.0000110 for Raman spectra and peak deconvolution of LLDPE B during crystallization at 116 °C; full sets of slip-link model fits to the dynamic modulus G during crystallization for LLDPE A and LLDPE B; G and G crossover frequency during the crystallization of LLDPE A and LLDPE B; details of dangling chain constraint dynamics implementation; and strain sweeps of LLDPE A and LLDPE B in the melt and semicrystalline states.

Supplementary Material

You do not currently have access to this content.