We present a systematic experimental study of the shear rheology of metallosupramolecular assemblies based on entangled telechelic star polymers comprising one (single dynamic network) or two (double dynamics network) types of physical bonds with the aim to unravel the role of concentration and strength of these bonds on the nonlinear response. Model dynamic networks functionalized with terpyridine ligands were formed by adding different metal ions with increasing bonding strength, zinc, copper, and cobalt. The dynamics are driven by entanglement/disentanglement processes and a ligand exchange mechanism. Steady-state viscosities of single and double dynamics networks collapse onto a universal curve over a wide range of Weissenberg numbers based on terminal time (up to about 300 for single and 1000 for double), exhibiting stronger shear thinning (with an exponent of −0.76) compared to entangled neutral star polymers. Double dynamics networks consisting of two different metal ions (with different lifetimes) exhibit stronger mechanical coherence (rate-dependent fractional viscosity overshoot) and accumulate larger strain at steady-state flow compared to single-ion counterparts. The shear stress growth function signals exhibit weak, albeit unambiguous shear strain hardening, which becomes more pronounced for stronger associations. They also exhibit double overshoot, which reflects the interplay of association strength and chain deformation. Increasing the strength of associations leads to the failure of the Cox–Merz rule, which is more severe for single dynamic networks. The markedly different behavior of double dynamics networks is attributed to the fact that at sufficiently high ion content, the weaker bond acts as a sacrificial component, which provides local energy dissipation and enhances the overall deformability. This bears analogies with their linear viscoelastic response, which has revealed that the arm disentanglement (delayed due to the reversible bonds) effectively interpolates between the two single dynamic network components, depending on composition. Our results suggest ways to tailor the mechanical properties of this class of materials by judicious choice of the type and content of the ion.

1.
Brunsveld
,
L.
,
B. J. B.
Folmer
,
E. W.
Meijer
, and
R. P.
Sijbesma
, “
Supramolecular polymers
,”
Chem. Rev.
101
,
4071
4098
(
2001
).
2.
Williams
,
G. T.
,
C. J. E.
Haynes
,
M.
Fares
,
C.
Caltagirone
,
J. R.
Hiscock
, and
P. A.
Gale
, “
Advances in applied supramolecular technologies
,”
Chem. Soc. Rev.
50
,
2737
2763
(
2021
).
3.
Vereroudakis
,
E.
, and
D.
Vlassopoulos
, “
Tunable dynamic properties of hydrogen-bonded supramolecular assemblies in solution
,”
Prog. Polym. Sci.
112
,
101321
(
2021
).
4.
Lavrador
,
P.
,
M. R.
Esteves
,
V. M.
Gaspar
, and
J. F.
Mano
, “
Stimuli-responsive nanocomposite hydrogels for biomedical applications
,”
Adv. Funct. Mater.
31
,
2005941
(
2021
).
5.
He
,
Q.
,
Y.
Zhang
,
H.
Li
, and
Q.
Chen
, “
Rheological properties of ABA-type copolymers physically end-cross-linked by polyoxometalate
,”
Macromolecules
53
,
10927
10941
(
2020
).
6.
Yang
,
H.
,
S.
Wu
, and
Q.
Chen
, “
How to choose a secondary interaction to improve stretchability of associative polymers?
,”
Macromolecules
54
,
8112
8121
(
2021
).
7.
Suzuka
,
J.
,
M.
Tsuda
,
L.
Wang
,
S.
Kohsaka
,
K.
Kishida
,
S.
Semba
,
H.
Sugino
,
S.
Aburatani
,
M.
Frauenlob
,
T.
Kurokawa
,
S.
Kojima
,
T.
Ueno
,
Y.
Ohmiya
,
H.
Mano
,
K.
Yasuda
,
J. P.
Gong
, and
S.
Tanaka
, “
Rapid reprogramming of tumour cells into cancer stem cells on double-network hydrogels
,”
Nat. Biomed. Eng.
5
,
914
925
(
2021
).
8.
Heinzmann
,
C.
,
S.
Coulibaly
,
A.
Roulin
,
G. L.
Fiore
, and
C.
Weder
, “
Light-induced bonding and debonding with supramolecular adhesives
,”
ACS Appl. Mater. Interfaces
6
,
4713
4719
(
2014
).
9.
Bode
,
S.
,
L.
Zedler
,
F. H.
Schacher
,
B.
Dietzek
,
M.
Schmitt
,
J.
Popp
,
M. D.
Hager
, and
U. S.
Schubert
, “
Self-healing polymer coatings based on crosslinked metallosupramolecular copolymers
,”
Adv. Mater.
25
,
1634
1638
(
2013
).
10.
Rao
,
Y.-L.
,
A.
Chortos
,
R.
Pfattner
,
F.
Lissel
,
Y.-C.
Chiu
,
V.
Feig
,
J.
Xu
,
T.
Kurosawa
,
X.
Gu
,
C.
Wang
,
M.
He
,
J. W.
Chung
, and
Z.
Bao
, “
Stretchable self-healing polymeric dielectrics cross-linked through metal-ligand coordination
,”
J. Am. Chem. Soc.
138
,
6020
6027
(
2016
).
11.
Tomkovic
,
T.
, and
S. G.
Hatzikiriakos
, “
Nonlinear rheology of poly(ethylene-co-methacrylic acid) ionomers
,”
J. Rheol.
62
,
1319
1329
(
2018
).
12.
Chen
,
Q.
,
G. J.
Tudryn
, and
R. H.
Colby
, “
Ionomer dynamics and the sticky rouse model
,”
J. Rheol.
57
,
1441
1462
(
2013
).
13.
Rubinstein
,
M.
, and
A. N.
Semenov
, “
Dynamics of entangled solutions of associating polymers
,”
Macromolecules
34
,
1058
1068
(
2001
).
14.
Schaefer
,
C.
,
P. R.
Laity
,
C.
Holland
, and
T. C. B.
McLeish
, “
Silk protein solution: A natural example of sticky reptation
,”
Macromolecules
53
,
2669
2676
(
2020
).
15.
Bedrov
,
D.
,
G. D.
Smith
, and
J. F.
Douglas
, “
Influence of self-assembly on dynamical and viscoelastic properties of telechelic polymer solutions
,”
Europhys. Lett.
59
,
384
390
(
2002
).
16.
van Ruymbeke
,
E.
,
D.
Vlassopoulos
,
M.
Mierzwa
,
T.
Pakula
,
D.
Charalabidis
,
M.
Pitsikalis
, and
N.
Hadjichristidis
, “
Rheology and structure of entangled telechelic linear and star polyisoprene melts
,”
Macromolecules
43
,
4401
4411
(
2010
).
17.
Metri
,
V.
,
A.
Louhichi
,
J.
Yan
,
G. P.
Baeza
,
K.
Matyjaszewski
,
D.
Vlassopoulos
, and
W. J.
Briels
, “
Physical networks from multifunctional telechelic star polymers: A rheological study by experiments and simulations
,”
Macromolecules
51
,
2872
2886
(
2018
).
18.
Zuliki
,
M.
,
S.,
Zhang
,
T.
Tomkovic
, and
S. G.
Hatzikiriakos
, “
Capillary flow of sodium and zinc ionomers
,”
Phys. Fluids
32
,
023106
(
2020
).
19.
Zuliki
,
M.
,
S.
Zhang
,
K.
Nyamajaro
,
T.
Tomkovic
, and
S. G.
Hatzikiriakos
, “
Rheology of sodium and zinc ionomers: Effects of neutralization and valency
,”
Phys. Fluids
32
,
023104
(
2020
).
20.
Shabbir
,
A.
,
Q.
Huang
,
G. P.
Baeza
,
D.
Vlassopoulos
,
Q.
Chen
,
R. H.
Colby
,
N. J.
Alvarez
, and
O.
Hassager
, “
Nonlinear shear and uniaxial extensional rheology of polyether-ester-sulfonate copolymer ionomer melts
,”
J. Rheol.
61
,
1279
1289
(
2017
).
21.
Shabbir
,
A.
,
Q.
Huang
,
Q.
Chen
,
R. H.
Colby
,
N. J.
Alvarez
, and
O.
Hassager
, “
Brittle fracture in associative polymers: The case of ionomer melts
,”
Soft Matter
12
,
7606
7612
(
2016
).
22.
Zhuge
,
F.
,
L. G. D.
Hawke
,
C.-A.
Fustin
,
J.-F.
Gohy
, and
E.
van Ruymbeke
, “
Decoding the linear viscoelastic properties of model telechelic metallo-supramolecular polymers
,”
J. Rheol.
61
,
1245
1262
(
2017
).
23.
Li
,
Y.
,
C.
Pyromali
,
F.
Zhuge
,
C.-A.
Fustin
,
J.-F.
Gohy
,
D.
Vlassopoulos
, and
E.
Van Ruymbeke
, “
Dynamics of entangled metallo-supramolecular polymer networks combining stickers with different lifetimes
,”
J. Rheol.
66
, 1203–1220 (
2021
).
24.
Ahmadi
,
M.
,
L. G. D.
Hawke
,
H.
Goldansaz
, and
E.
van Ruymbeke
, “
Dynamics of entangled linear supramolecular chains with sticky side groups: Influence of hindered fluctuations
,”
Macromolecules
48
,
7300
7310
(
2015
).
25.
Pellens
,
L.
,
R.
Gamez Corrales
, and
J.
Mewis
, “
General nonlinear rheological behavior of associative polymers
,”
J. Rheol.
48
,
379
393
(
2004
).
26.
Caram
,
Y.
,
F.
Bautista
,
J. E.
Puig
, and
O.
Manero
, “
On the rheological modeling of associative polymers
,”
Rheol. Acta
46
,
45
57
(
2006
).
27.
Suzuki
,
S.
,
T.
Uneyama
, and
H.
Watanabe
, “
Concentration dependence of nonlinear rheological properties of hydrophobically modified ethoxylated urethane aqueous solutions
,”
Macromolecules
46
,
3497
3504
(
2013
).
28.
English
,
R. J.
,
S. R.
Raghavan
,
R. D.
Jenkins
, and
S. A.
Khan
, “
Associative polymers bearing n-alkyl hydrophobes: Rheological evidence for microgel-like behavior
,”
J. Rheol.
43
,
1175
1194
(
1999
).
29.
Mewis
,
J.
,
B.
Kaffashi
,
J.
Vermant
, and
R. J.
Butera
, “
Determining relaxation modes in flowing associative polymers using superposition flows
,”
Macromolecules
34
,
1376
1383
(
2001
).
30.
Annable
,
T.
,
R.
Buscall
,
R.
Ettelaie
, and
D.
Whittlestone
, “
The rheology of solutions of associating polymers: Comparison of experimental behavior with transient network theory
,”
J. Rheol.
37
,
695
726
(
1993
).
31.
Xu
,
D.
, and
S. L.
Craig
, “
Multiple dynamic processes contribute to the complex steady shear behavior of cross-linked supramolecular networks of semidilute entangled polymer solutions
,”
J. Phys. Chem. Lett.
1
,
1683
1686
(
2010
).
32.
Witten
,
T. A.
, and
M. H.
Cohen
, “
Crosslinking in shear-thickening ionomers
,”
Macromolecules
18
,
1915
1918
(
1985
).
33.
Suzuki
,
S.
,
T.
Uneyama
,
T.
Inoue
, and
H.
Watanabe
, “
Nonlinear rheology of telechelic associative polymer networks: Shear thickening and thinning behavior of hydrophobically modified ethoxylated urethane (HEUR) in aqueous solution
,”
Macromolecules
45
,
888
898
(
2012
).
34.
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
).
35.
Park
,
G. W.
, and
G.
Ianniruberto
, “
A new stochastic simulation for the rheology of telechelic associating polymers
,”
J. Rheol.
61
,
1293
1305
(
2017
).
36.
Inoue
,
T.
,
Y.
Inoue
, and
H.
Watanabe
, “
Nonlinear rheology of CTAB/NaSal aqueous solutions: finite extensibility of a network of wormlike micelles
,”
Langmuir
21
,
1201
1208
(
2005
).
37.
Koga
,
T.
,
F.
Tanaka
,
I.
Kaneda
, and
F. M.
Winnik
, “
Stress buildup under start-up shear flows in self-assembled transient networks of telechelic associating polymers
,”
Langmuir
25
,
8626
8638
(
2009
).
38.
Séréro
,
Y.
,
V.
Jacobsen
,
J.-F.
Berret
, and
R.
May
, “
Evidence of nonlinear chain stretching in the rheology of transient networks
,”
Macromolecules
33
,
1841
1847
(
2000
).
39.
Amin
,
D.
, and
Z.
Wang
, “
Nonlinear rheology and dynamics of supramolecular polymer networks formed by associative telechelic chains under shear and extensional flows
,”
J. Rheol.
64
,
581
600
(
2020
).
40.
Yan
,
T.
,
K.
Schröter
,
F.
Herbst
,
W. H.
Binder
, and
T.
Thurn-Albrecht
, “
Unveiling the molecular mechanism of self-healing in a telechelic, supramolecular polymer network
,”
Sci. Rep.
6
,
32356
(
2016
).
41.
Yan
,
T.
,
K.
Schröter
,
F.
Herbst
,
W. H.
Binder
, and
T.
Thurn-Albrecht
, “
What controls the structure and the linear and nonlinear rheological properties of dense, dynamic supramolecular polymer networks?
,”
Macromolecules
50
,
2973
2985
(
2017
).
42.
Zhang
,
Q.
,
X.
Zhu
,
C.-H.
Li
,
Y.
Cai
,
X.
Jia
, and
Z.
Bao
, “
Disassociation and reformation under strain in polymer with dynamic metal-ligand coordination cross-linking
,”
Macromolecules
52
,
660
668
(
2019
).
43.
Skrzeszewska
,
P. J.
,
J.
Sprakel
,
F. A.
de Wolf
,
R.
Fokkink
,
M. A.
Cohen Stuart
, and
J.
van der Gucht
, “
Fracture and self-healing in a well-defined self-assembled polymer network
,”
Macromolecules
43
,
3542
3548
(
2010
).
44.
Ghahramani
,
N.
,
K. A.
Iyer
,
A. K.
Doufas
, and
S. G.
Hatzikiriakos
, “
Rheology of thermoplastic vulcanizates (TPVs)
,”
J. Rheol.
64
,
1325
1341
(
2020
).
45.
Vereroudakis
,
E.
,
M.
Bantawa
,
R. P. M.
Lafleur
,
D.
Parisi
,
N. M.
Matsumoto
,
J. W.
Peeters
,
E.
Del Gado
,
E. W.
Meijer
, and
D.
Vlassopoulos
, “
Competitive supramolecular associations mediate the viscoelasticity of binary hydrogels
,”
ACS Cent. Sci.
6
,
1401
1411
(
2020
).
46.
Sun
,
T. L.
,
T.
Kurokawa
,
S.
Kuroda
,
A. B.
Ihsan
,
T.
Akasaki
,
K.
Sato
,
M. A.
Haque
,
T.
Nakajima
, and
J. P.
Gong
, “
Physical hydrogels composed of polyampholytes demonstrate high toughness and viscoelasticity
,”
Nat. Mater.
12
,
932
937
(
2013
).
47.
Filippidi
,
E.
,
T. R.
Cristiani
,
C. D.
Eisenbach
,
J. H.
Waite
,
J. N.
Israelachvili
,
B. K.
Ahn
, and
M. T.
Valentine
, “
Toughening elastomers using mussel-inspired iron-catechol complexes
,”
Science
358
,
502
505
(
2017
).
48.
Aldana
,
A. A.
,
S.
Houben
,
L.
Moroni
,
M. B.
Baker
, and
L. M.
Pitet
, “
Trends in double networks as bioprintable and injectable hydrogel scaffolds for tissue regeneration
,”
ACS Biomater. Sci. Eng.
7
,
4077
4101
(
2021
).
49.
King
,
D. R.
,
T.
Okumura
,
R.
Takahashi
,
T.
Kurokawa
, and
J. P.
Gong
, “
Macroscale double networks: Design criteria for optimizing strength and toughness
,”
ACS Appl. Mater. Interfaces
11
,
35343
35353
(
2019
).
50.
Chen
,
Q.
,
H.
Chen
,
L.
Zhu
, and
J.
Zheng
, “
Fundamentals of double network hydrogels
,”
J. Mater. Chem. B
3
,
3654
3676
(
2015
).
51.
Gong
,
J. P.
,
Y.
Katsuyama
,
T.
Kurokawa
, and
Y.
Osada
, “
Double-network hydrogels with extremely high mechanical strength
,”
Adv. Mater.
15
,
1155
1158
(
2003
).
52.
Gong
,
J. P.
, “
Why are double network hydrogels so tough?
,”
Soft Matter
6
,
2583
2590
(
2010
).
53.
Ducrot
,
E.
,
Y.
Chen
,
M.
Bulters
,
R. P.
Sijbesma
, and
C.
Creton
, “
Toughening elastomers with sacrificial bonds and watching them break
,”
Science
344
,
186
189
(
2014
).
54.
Li
,
Y.
,
L.
Yang
,
Y.
Zeng
,
Y.
Wu
,
Y.
Wei
, and
L.
Tao
, “
Self-Healing hydrogel with a double dynamic network comprising imine and borate ester linkages
,”
Chem. Mater.
31
,
5576
5583
(
2019
).
55.
Li
,
S.
,
N.
Chen
,
X.
Li
,
Y.
Li
,
Z.
Xie
,
Z.
Ma
,
J.
Zhao
,
X.
Hou
, and
X.
Yuan
, “
Bioinspired double-dynamic-bond crosslinked bioadhesive enables post-wound closure care
,”
Adv. Funct. Mater.
30
,
2000130
(
2020
).
56.
Zhuge
,
F.
,
J.
Brassinne
,
C.-A.
Fustin
,
E.
van Ruymbeke
, and
J.-F.
Gohy
, “
Synthesis and rheology of bulk metallo-supramolecular polymers from telechelic entangled precursors
,”
Macromolecules
50
,
5165
5175
(
2017
).
57.
Winter
,
A.
, and
U. S.
Schubert
, “
Synthesis and characterization of metallo-supramolecular polymers
,”
Chem. Soc. Rev.
45
,
5311
5357
(
2016
).
58.
Snijkers
,
F.
, and
D.
Vlassopoulos
, “
Cone-partitioned-plate geometry for the ARES rheometer with temperature control
,”
J. Rheol.
55
,
1167
1186
(
2011
).
59.
Costanzo
,
S.
,
Q.
Huang
,
G.
Ianniruberto
,
G.
Marrucci
,
O.
Hassager
, and
D.
Vlassopoulos
, “
Shear and extensional rheology of polystyrene melts and solutions with the same number of entanglements
,”
Macromolecules
49
,
3925
3935
(
2016
).
60.
Costanzo
,
S.
,
G.
Ianniruberto
,
G.
Marrucci
, and
D.
Vlassopoulos
, “
Measuring and assessing first and second normal stress differences of polymeric fluids with a modular cone-partitioned plate geometry
,”
Rheol. Acta
57
,
363
376
(
2018
).
61.
F.
Zhuge
,
Synthesis and dynamics of metallo-supramolecular polymeric assemblies
,
Ph.D. thesis
,
Université Catholique de Louvain
,
2018
.
62.
Snijkers
,
F.
,
K.
Ratkanthwar
,
D.
Vlassopoulos
, and
N.
Hadjichristidis
, “
Viscoelasticity, nonlinear shear start-up, and relaxation of entangled star polymers
,”
Macromolecules
46
,
5702
5713
(
2013
).
63.
Petekidis
,
G.
,
D.
Vlassopoulos
, and
P. N.
Pusey
, “
Yielding and flow of sheared colloidal glasses
,”
J. Phys.: Condens. Matter
16
,
S3955
S3963
(
2004
).
64.
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
).
65.
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
).
66.
Osaki
,
K.
,
T.
Inoue
, and
T.
Isomura
, “
Stress overshoot of polymer solutions at high rates of shear; polystyrene with bimodal molecular weight distribution
,”
J. Polym. Sci., Part B: Polym. Phys.
38
,
2043
2050
(
2000
).
67.
Osaki
,
K.
,
T.
Inoue
, and
T.
Isomura
, “
Stress overshoot of polymer solutions at high rates of shear
,”
J. Polym. Sci., Part B: Polym. Phys.
38
,
1917
1925
(
2000
).
68.
Schneider
,
S.
,
G.
Brehm
,
C.-J.
Prenzel
,
W.
Jäger
,
M. I.
Silva
,
H. D.
Burrows
, and
S. T.
Formosinho
, “
Vibrational spectra, normal coordinate analysis and excited-state lifetimes for a series of polypyridylruthenium(II) complexes
,”
J. Raman Spectrosc.
27
,
163
175
(
1996
).
69.
B. G. G.
Lohmeijer
,
Playing LEGO with macromolecules : Connecting polymer chains using terpyridine metal complexes
,
Ph.D. thesis
,
Technische Universiteit Eindhoven
,
2004
.
70.
See supplementary material at https://www.scitation.org/doi/suppl/10.1122/8.0000429 for metal-ligand binding constant, rheometry, differential scanning calorimetry, and data analysis of single and double dynamics networks.
You do not currently have access to this content.