The core-shell composite droplets with well-designed functionality and morphology are widely used in polymer blends. Although great progress has been achieved in modeling the rheology of viscoelastic binary emulsions, no such model has been proposed to predict the rheology of ternary blends containing core-shell droplets. In this work, a ternary core-shell emulsion (CSE) model was developed to predict the linear viscoelasticity of ternary core-shell blends. The components’ contribution to the stress was evaluated from the velocity gradient in three domains. The evolutions of core-shell interface and shell-matrix interface were solved under small amplitude oscillatory shear, leading to the stress contribution from the two interfaces. Two impact polypropylene copolymers (IPCs), as a typical polymer containing core-shell droplets, were selected to validate the new model. Three components, including homopolypropylene matrix, ethylene–propylene block copolymer (core domain), and ethylene–propylene random copolymer (shell domain), were separated using a good solvent at different temperatures, and their rheology behavior was investigated. The new CSE model can accurately describe the components’ contribution to the linear rheology of IPCs, while the interfacial contribution of the CSE model is lower than the experimental data due to the agglomerated nature of core-shell droplets in IPCs. Because the components’ contribution dominates at high frequency, this work can be used to approximate the nonlinear steady-shear viscosity and first normal stress difference of core-shell ternary blends at high shear rates using the Cox–Merz rule and Laun's rule, respectively. Thus, the CSE model can guide the design of core-shell morphology with desired rheological properties.

1.
Liu
,
H. L.
,
D. Y.
Bai
,
S. L.
Du
,
X.
Li
,
H. W.
Bai
, and
Q.
Fu
, “
Stereocomplex crystallization induced significant improvement in transparency and stiffness-toughness performance of core-shell rubber nanoparticles toughened poly(L-lactide) blends
,”
Macromol. Mater. Eng.
306
,
2100021
(
2021
).
2.
Wang
,
X.
,
Y.
Gao
,
J.
Jin
, and
W.
Jiang
, “
A strategy to develop homo-polypropylene composites with high impact and high rigidity
,”
Macromolecules
57
,
4576
4583
(
2024
).
3.
Mazidi
,
M. M.
,
M. K.
Razavi Aghjeh
, and
A.
Pegoretti
, “
Toughened ternary and quaternary polymer alloys of core-shell morphology; correlations among processing, microstructure, micromechanics, and macroscopic mechanical performance in reactive systems
,”
Polymer
282
,
126186
(
2023
).
4.
Kakhk
,
S. H. H.
,
J. K.
Rad
,
H.
Abedini
, and
A. R.
Mahdavian
, “
Thermomechanical study on toughened PVC with an impact modifier based on the acrylonitrile-styrene-acrylate core-shell particles
,”
Polymer
290
,
126545
(
2024
).
5.
Alizadeh
,
F.
,
S.
Habibi
,
M. K.
Razavi Aghjeh
,
M.
Salami-Kalajahi
,
M.
Mehrabi-Mazidi
,
H. A.
Khonakdar
, and
H.
Ruckdaschel
, “
Design and synthesis of polystyrene-occluded reactive core–shell particles of natural rubber to balance stiffness and toughness in poly(lactic acid)
,”
ACS Appl. Polym. Mater.
6
,
5316
5330
(
2024
).
6.
Mousavi
,
S. R.
,
S.
Estaji
,
M.
Raouf Javidi
,
A.
Paydayesh
,
H. A.
Khonakdar
,
M.
Arjmand
,
E.
Rostami
, and
S. H.
Jafari
, “
Toughening of epoxy resin systems using core–shell rubber particles: A literature review
,”
J. Mater. Sci.
56
,
18345
18367
(
2021
).
7.
Kishi
,
H.
,
S.
Matsuda
,
J.
Imade
,
Y.
Shimoda
,
T.
Nakagawa
, and
Y.
Furukawa
, “
The effects of the toughening mechanism and the molecular weights between cross-links on the fatigue resistance of epoxy polymer blends
,”
Polymer
223
,
123712
(
2021
).
8.
Galli
,
P.
, and
G.
Vecellio
, “
Technology: Driving force behind innovation and growth of polyolefins
,”
Prog. Polym. Sci.
26
,
1287
1336
(
2001
).
9.
Santos
,
R. A. M.
,
L.
Gorbatikh
, and
Y.
Swolfs
, “
Commercial self-reinforced composites: A comparative study
,”
Composites, Part B
223
,
109108
(
2021
).
10.
Tordjeman
,
P.
,
C.
Robert
,
G.
Marin
, and
P.
Gerard
, “
The effect of α, β crystalline structure on the mechanical properties of polypropylene
,”
Eur. Phys. J. E
4
,
459
465
(
2001
).
11.
Shirvanimoghaddam
,
K.
,
K. V.
Balaji
,
R.
Yadav
,
O.
Zabihi
,
M.
Ahmadi
,
P.
Adetunji
, and
M.
Naebe
, “
Balancing the toughness and strength in polypropylene composites
,”
Composites, Part B
223
,
109121
(
2021
).
12.
Fasihi
,
M.
, and
H.
Mansouri
, “
Effect of rubber interparticle distance distribution on toughening behavior of thermoplastic polyolefin elastomer toughened polypropylene
,”
J. Appl. Polym. Sci.
133
,
44068
(
2016
).
13.
Fanegas
,
N.
,
M. A.
Gómez
,
I.
Jiménez
,
C.
Marco
,
J. M.
Garcia-Martínez
, and
G.
Ellis
, “
Optimizing the balance between impact strength and stiffness in polypropylene/elastomer blends by incorporation of a nucleating agent
,”
Polym. Eng. Sci.
48
,
80
87
(
2008
).
14.
Li
,
F.
,
N.
Zhang
,
Y.
Gao
,
N.
Yan
,
J.
Jin
,
Z.
Su
, and
W.
Jiang
, “
In situ formation of core-shell rubber particles in polypropylene matrix by melt blending and its effects on the toughness and stiffness of the composites
,”
Polym. Eng. Sci.
62
,
4090
4099
(
2022
).
15.
Zhang
,
J. Q.
,
Y. J.
Zhang
,
C. Y.
Zhang
, and
Q.
Chen
, “
Structural and rheological properties of PP/EPR/PE alloys
,”
Chin. J. Polym. Sci.
41
,
240
249
(
2023
).
16.
Tian
,
Z.
,
L. F.
Feng
,
Z. Q.
Fan
, and
G. H.
Hu
, “
Ethylene-propylene segmented copolymer as an in situ compatibilizer for impact polypropylene copolymer: An assessment of rheology and morphology
,”
Ind. Eng. Chem. Res.
53
,
11345
11354
(
2014
).
17.
Zhou
,
Y.
,
H.
Niu
,
L.
Kong
,
Y.
Zhao
,
J. Y.
Dong
, and
D.
Wang
, “
Probing into the pristine basic morphology of high impact polypropylene particles
,”
Polymer
50
,
4690
4695
(
2009
).
18.
Tian
,
Y.
,
S.
Song
,
J.
Feng
, and
J.
Yi
, “
Phase morphology evolution upon melt annealing treatment and corresponding mechanical performance of impact-resistant polypropylene copolymer
,”
Mater. Chem. Phys.
133
,
893
900
(
2012
).
19.
Cecchin
,
G.
,
G.
Morini
, and
A.
Pelliconi
, “
Polypropene product innovation by reactor granule technology
,”
Macromol. Symp.
173
,
195
210
(
2001
).
20.
Cai
,
H.
,
X.
Luo
,
D.
Ma
,
J.
Wang
, and
H.
Tan
, “
Structure and properties of impact copolymer polypropylene. I. Chain structure
,”
J. Appl. Polym. Sci.
71
,
93
101
(
1999
).
21.
Pastor-Garcia
,
M. T.
,
I.
Suarez
,
M. T.
Exposito
,
B.
Coto
, and
R. A.
Garcia-Munoz
, “
Engineered PP impact copolymers in a single reactor as efficient method for determining their structure and properties
,”
Eur. Polym. J.
157
,
110642
(
2021
).
22.
Qian
,
L.
,
Y.
Wang
,
Y.
Lu
, and
Y.
Men
, “
Crystallization behavior of impact copolymer polypropylene revealed by fast scanning chip calorimetry analysis
,”
Polymer
239
,
124441
(
2022
).
23.
Chen
,
F.
,
B.
Qiu
,
Y.
Shangguan
,
Y.
Song
, and
Q.
Zheng
, “
Correlation between impact properties and phase structure in impact polypropylene copolymer
,”
Mater. Des.
69
,
56
63
(
2015
).
24.
Li
,
C.
,
Z.
Wang
,
W.
Liu
,
X.
Ji
, and
Z.
Su
, “
Copolymer distribution in core–shell rubber particles in high-impact polypropylene investigated by atomic force microscopy–infrared
,”
Macromolecules
53
,
2686
2693
(
2020
).
25.
Gahleitner
,
M.
,
C.
Tranninger
, and
P.
Doshev
, “
Heterophasic copolymers of polypropylene: Development, design principles, and future challenges
,”
J. Appl. Polym. Sci.
130
,
3028
3037
(
2013
).
26.
Palierne
,
J. F.
, “
Linear rheology of viscoelastic emulsions with interfacial-tension
,”
Rheol. Acta
29
,
204
214
(
1990
).
27.
Bousmina
,
M.
, “
Effect of interfacial tension on linear viscoelastic behavior of immiscible polymer blends
,”
Rheol. Acta
38
,
251
254
(
1999
).
28.
Yu
,
W.
, and
C.
Zhou
, “
A simple constitutive equation for immiscible blends
,”
J. Rheol.
51
,
179
194
(
2007
).
29.
Javidi
,
Z.
,
M.
Mohamadi
, and
H.
Nazockdast
, “
A comparative study on capability of emulsion models for predicting the viscoelastic behavior of ternary polymer blends with core-shell morphology
,”
Rheol. Acta
59
,
73
82
(
2020
).
30.
Choi
,
S. J.
, and
W. R.
Schowalter
, “
Rheological properties of non-dilute suspensions of deformable particles
,”
Phys. Fluids
18
,
420
427
(
1975
).
31.
Zhao
,
X.
,
B.
Li
,
S.
Liu
,
L.
Peng
,
X.
Huang
, and
W.
Yu
, “
Modeling linear and nonlinear rheology of industrial incompatible polymer blends
,”
J. Rheol.
68
,
187
204
(
2024
).
32.
Lamb
,
H.
,
Hydrodynamics
, 6th ed. (
Dover
,
New York
,
1945
).
33.
Frankel
,
N. A.
, and
A.
Acrivos
, “
Constitutive equation for a dilute emulsion
,”
J. Fluid Mech.
44
,
65
78
(
1970
).
34.
Yu
,
W.
,
M.
Bousmina
,
M.
Grmela
, and
C.
Zhou
, “
Modeling of oscillatory shear flow of emulsions under small and large deformation fields
,”
J. Rheol.
46
,
1401
1418
(
2002
).
35.
Yu
,
W.
,
C.
Zhou
, and
M.
Bousmina
, “
Theory of morphology evolution in mixtures of viscoelastic immiscible components
,”
J. Rheol.
49
,
215
236
(
2005
).
36.
Palierne
,
J. F.
, “
Linear rheology of viscoelastic emulsions with interfacial tension
,”
Rheol. Acta
29
,
204
214
(
1990
).
37.
Zhang
,
C.
,
Y.
Shangguan
,
R.
Chen
,
Y.
Wu
,
F.
Chen
,
Q.
Zheng
, and
G.
Hu
, “
Morphology, microstructure and compatibility of impact polypropylene copolymer
,”
Polymer
51
,
4969
4977
(
2010
).
38.
Liu
,
W.
,
J.
Zhang
,
M.
Hong
,
P.
Li
,
Y.
Xue
,
Q.
Chen
, and
X.
Ji
, “
Chain microstructure of two highly impact polypropylene resins with good balance between stiffness and toughness
,”
Polymer
188
,
122146
(
2020
).
39.
Fernández
,
A.
,
M. T.
Expósito
,
B.
Peña
,
R.
Berger
,
J.
Shu
,
R.
Graf
,
H. W.
Spiess
, and
R. A.
García-Muñoz
, “
Molecular structure and local dynamic in impact polypropylene copolymers studied by preparative TREF, solid state NMR spectroscopy, and SFM microscopy
,”
Polymer
61
,
87
98
(
2015
).
40.
Chen
,
Y.
,
Y.
Chen
,
W.
Chen
, and
D.
Yang
, “
Evolution of phase morphology of high impact polypropylene particles upon thermal treatment
,”
Eur. Polym. J.
43
,
2999
3008
(
2007
).
41.
Liu
,
W.
,
M.
Hong
,
Y.
Xue
,
L.
Shi
,
P.
Li
,
R.
Li
,
M.
Zhang
,
Y.
An
,
Y.
Gao
, and
X.
Ji
, “
Comparison of chain microstructure between two propylene−ethylene copolymer resins with bimodal melting temperature distribution
,”
Polymer
211
,
123118
(
2020
).
42.
de Goede
,
E.
,
P.
Mallon
, and
H.
Pasch
, “
Fractionation and analysis of an impact poly(propylene) copolymer by TREF and SEC-FTIR
,”
Macromol. Mater. Eng.
295
,
366
373
(
2010
).
43.
Tang
,
F.
,
P.
Bao
,
A.
Roy
,
Y.
Wang
, and
Z.
Su
, “
In-situ spectroscopic and thermal analyses of phase domains in high-impact polypropylene
,”
Polymer
142
,
155
163
(
2018
).
44.
Kruczala
,
K.
,
B.
Varghese
,
J. G.
Bokria
, and
S.
Schlick
, “
Thermal aging of heterophasic propylene−ethylene copolymers: Morphological aspects based on ESR, FTIR, and DSC
,”
Macromolecules
36
,
1899
1908
(
2003
).
45.
Lu
,
L.
,
H.
Fan
,
B. G.
Li
, and
S.
Zhu
, “
Polypropylene and ethylene−propylene copolymer reactor alloys prepared by metallocene/Ziegler−Natta hybrid catalyst
,”
Ind. Eng. Chem. Res.
48
,
8349
8355
(
2009
).
46.
Lu
,
X. Y.
,
J. J.
Yi
,
S. T.
Chen
,
F. H.
Zu
, and
R. B.
Li
, “
Characterization of impact polypropylene copolymers by solvent fractionation
,”
Chin. J. Polym. Sci.
30
,
122
129
(
2012
).
47.
Larson
,
R. G.
,
The Structure and Rheology of Complex Fluids
(
Oxford University
,
New York
,
1999
).
48.
Han
,
C. D.
,
Rheology and Processing of Polymeric Materials
(
Oxford University
,
New York
,
2007
).
49.
Hyun
,
K.
,
M.
Wilhelm
,
C. O.
Klein
,
K.
Cho
,
J. G.
Nam
,
K. H.
Ahn
,
S.
Lee
,
R. H.
Ewoldt
, and
G. H.
McKinley
, “
A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS)
,”
Prog. Polym. Sci.
36
,
1697
1753
(
2011
).
50.
Sun
,
D.
,
P.
He
,
Y.
Wang
,
X.
Shi
, and
W.
Yu
, “
Abnormal crystallization behavior of high impact polypropylene under shear
,”
Polymer
136
,
17
26
(
2018
).
You do not currently have access to this content.