Tough hydrogels can be synthesized by incorporating self-healing physical crosslinks in a chemically crosslinked gel network. Due to the breaking and reattachment of these physical crosslinks, these gels exhibit a rate-dependent behavior that can be different from a classical linear viscoelastic solid. In this work, we develop a theory to describe the linear mechanical response of a dual-crosslink gel in a parallel-plate torsional rheometer. Our theory is based on a newly developed finite strain constitutive model. We show that some of the parameters in the constitutive model can be determined by carrying oscillatory torsional experiments. For consistency, we also show that the torsion data in an oscillatory test can be predicted using our theory with parameters obtained from tension tests. Our theory provides a basis for interpreting and understanding the test data of these gels obtained from rheometry.
References
1.
Bird
, R. B.
, R. C.
Armstrong
, and O.
Hassager
, Dynamics of Polymeric Liquids: Fluid Mechanics
, 2nd ed. (Wiley
, New York
, 1987
), Vol. 1.2.
Bower
, A. F.
, Applied Mechanics of Solids
(CRC, Taylor and Francis Group
, London, 2010
).3.
Calvert
, P.
, “Hydrogels for soft machines
,” Adv. Mater.
21
(7
), 743
–756
(2009
).5.
Ferry
, J. D.
, Viscoelastic Properties of Polymers
(John Wiley & Sons
, New York, 1980
).6.
Gong
, J. P.
, “Why are double network hydrogels so tough?
,” Soft Matter
6
(12
), 2583
–2590
(2010
).7.
Gong
, J. P.
, Y.
Katsuyama
, T.
Kurokawa
, and Y.
Osada
, “Double-network hydrogels with extremely high mechanical strength
,” Adv. Mater.
15
(14
), 1155
–1158
(2003
).8.
9.
Green
, M. S.
, and A. V.
Tobolsky
, “A new approach to the theory of relaxing polymeric media
,” J. Chem. Phys.
14
(2
), 80
–92
(1946
).10.
Henderson
, K. J.
, T. C.
Zhou
, K. J.
Otim
, and K. R.
Shull
, “Ionically cross-linked triblock copolymer hydrogels with high strength
,” Macromolecules
43
(14
), 6193
–6201
(2010
).11.
Holten-Andersen
, N.
, M. J.
Harrington
, H.
Birkedal
, B. P.
Lee
, P.
Messersmith
, K. Y. C.
Lee
, and J. H.
Waite
, “pH-induced metal-ligand cross-links inspired by mussel yield self-healing polymer networks with near-covalent elastic moduli
,” Proc. Natl. Acad. Sci. U.S.A.
108
(7
), 2651
–2655
(2011
).12.
Indei
, T.
, and J.
Takimoto
, “Linear viscoelastic properties of transient networks formed by associating polymers with multiple stickers
,” J. Chem. Phys.
133
, 194902
(2010
).13.
Janmey
, P. A.
, M. E.
McCormick
, S.
Rammensee
, J. L.
Leight
, P. C.
Georges
, and F. C.
MacKintosh
, “Negative normal stress in semiflexible biopolymer gels
,” Nat. Mater.
6
, 48
–51
(2007
).14.
Keita
, G.
, A.
Richard
, R.
Audebert
, E.
Pezron
, and L.
Leibler
, “The poly(vinyl alcohol)-borate system: Influence of polyelectrolyte effects on phase diagrams
,” Polymer
36
(3
), 49
–54
(1995
).15.
Koike
, A.
, N.
Nemoto
, T.
Inoue
, and K.
Osaki
, “Dynamic light scattering and dynamic viscoelasticity of Poly(vinyl alcohol) in aqueous borax solutions. 1. Concentration effect
,” Macromolecules
28
(7
), 2339
–2344
(1995
).16.
Kurokawa
, H.
, M.
Shibayama
, T.
Ishimaru
, and S.
Namura
, “Phase behaviour and sol-gel transition of poly(vinyl alcohol)-borate complex in aqueous solution
,” Polymer
33
(10
), 2182
–2188
(1992
).17.
Lee
, K. Y.
, and D. J.
Mooney
, “Hydrogels for tissue engineering
,” Chem. Rev.
101
(7
), 1869
–1879
(2001
).18.
Leibler
, L.
, M.
Rubinstein
, and R. H.
Colby
, “Dynamics of reversible networks
,” Macromolecules
24
(16
), 4701
–4707
(1991
).19.
Leibler
, L.
, P.
Erwoan
, and P. A.
Pincus
, “Viscosity behaviour of polymer solutions in the presence of complexing ions
,” Polymer
29
(6
), 1105
–1109
(1988
).20.
Li
, J.
, Z.
Suo
, and J. J.
Vlassak
, “Stiff, strong, and tough hydrogels with good chemical stability
,” J. Mater. Chem. B
2
(39
), 6708
–6713
(2014
).21.
Li
, L.
, B.
Yan
, J.
Yang
, L.
Chen
, and H.
Zeng
, “Novel mussel-inspired injectable self-healing hydrogel with anti-biofouling property
,” Adv. Mater.
27
(7
), 1294
–1299
(2015
).22.
Lin
, W. C.
, W.
Fan
, A.
Marcellan
, D.
Hourdet
, and C.
Creton
, “Large strain and fracture properties of poly(dimethylacrylamide)/silica hybrid hydrogels
,” Macromolecules
43
(5
), 2554
–2563
(2010
).23.
Long
, R.
, K.
Mayumi
, C.
Creton
, T.
Narita
, and C. Y.
Hui
, “Time dependent behavior of a dual cross-link self-healing gel: Theory and experiments
,” Macromolecules
47
(20
), 7243
–7250
(2014
).24.
Mayumi
, K.
, A.
Marcellan
, G.
Ducouret
, C.
Creton
, and T.
Narita
, “Stress-strain relationship of highly stretchable dual cross-link gels: Separability of strain and time effect
,” ACS Macro Lett.
2
(12
), 1065
–1068
(2013
).25.
Meyvis
, T. K. L.
, S. C.
De Smedt
, J.
Demeester
, and W. E.
Hennink
, “Rheological monitoring of long-term degrading polymer hydrogels
,” J. Rheol.
43
(4
), 933
–950
(1999
).26.
Mihai
, L. A.
, and A.
Goriely
, “Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials
,” Proc. R. Soc. London, Ser. A
467
, 3633
–3646
(2011
).27.
Munster
, S.
, L. M.
Jawerth
, B. A.
Leslie
, J. I.
Weitz
, B.
Fabry
, and D. A.
Weitz
, “Strain history dependence of the nonlinear stress response of fibrin and collagen networks
,” Proc. Natl. Acad. Sci. U.S.A.
110
(30
), 12197
–12202
(2013
).28.
Narita
, T.
, K.
Mayumi
, G.
Ducouret
, and P.
Hebraud
, “Viscoelastic properties of Poly(vinyl alcohol) hydrogels having permanent and transient cross-links studied by microrheology, classical rheometry, and dynamic light scattering
,” Macromolecules
46
(10
), 4174
–4183
(2013
).29.
Nemoto
, N.
, A.
Koike
, and K.
Osaki
, “Dynamic light scattering and dynamic viscoelasticity of Poly(vinyl alcohol) in aqueous borax solutions. 2. Polymer concentration and molecular weight effects
,” Macromolecules
29
(5
), 1445
–1451
(1996
).30.
Peak
, C.
, J.
Wilker
, and G.
Schmidt
, “A review on tough and sticky hydrogels
,” Colloid Polym. Sci.
291
(9
), 2031
–2047
(2013
).31.
Peppas
, N.
, and J. J.
, Sahlin
, “Hydrogels as mucoadhesive and bioadhesive materials: A review
,” Biomaterials
17
(16
), 1553
–1561
(1996
).32.
Pritchard
, R. H.
, Y. Y. S.
Huang
, and E. M.
Terentjev
, “Mechanics of biological networks: Form the cell cytoskeleton to connective tissue
,” Soft Matter
10
, 1864
–1884
(2014
).33.
Rivlin
, R. S.
, “Large elastic deformations of isotropic materials. VII. Experiments on the deformation of rubber
,” Philos. Trans. R. Soc. London, Ser. A
243
(865
), 251
–288
(1951
).34.
Rubinstein
, M.
, and A. N.
Semenov
, “Dynamics of entangled solutions of associating polymers
,” Macromolecules
34
(4
), 1058
–1068
(2001
).35.
36.
Savins
, J. G.
, “Shear thickening phenomena in poly(vinyl)alcohol-borate complexes
,” Rheol. Acta
7
(1
), 87
–93
(1968
).37.
Shibayama
, M.
, T.
Takeuchi
, and S.
Nomura
, “Swelling/shrinking and dynamic light scattering studies on chemically cross-linked poly(vinyl alcohol) gels in the presence of borate ions
,” Macromolecules
27
(9
), 5350
–5358
(1994
).38.
Storm
, C.
, J. J.
Pastore
, F. C.
MacKintosh
, T. C.
Lubensky
, and P. A.
Janmey
, “Nonlinear elasticity in biological gels
,” Nature
435
, 191
–194
(2005
).39.
Sun
, J. Y.
, X.
Zhao
, W. R.
Illeperuma
, O.
Chaudhuri
, K. H.
Oh
, D. J.
Mooney
, J. J.
Vlassak
, and Z.
Suo
, “Highly stretchable and tough hydrogels
,” Nature
489
, 133
–136
(2012
).40.
Sun
, T. L.
, T.
Kurokawa
, S.
Kuroda
, A. B.
Ihsan
, I.
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
).41.
Tanaka
, F.
, and S. F.
Edwards
, “Viscoelastic properties of physically cross-linked networks. Transient network theory
,” Macromolecules
25
(5
), 1516
–1523
(1992
).42.
Webber
, R. E.
, C.
Creton
, H. R.
Brown
, and J. P.
Gong
, “Large strain hysteresis and Mullin's effect of tough double-network hydrogels
,” Macromolecules
40
(8
), 2919
–2927
(2007
).43.
Wolff
, L.
, and K.
Kroy
, “Minimal model for the inelastic mechanics of biopolymer networks and cells
,” Phys. Rev. E
86
(4
), 040901
(2012
).44.
Zhao
, X.
, “Multi-scale multi-mechanism design of tough hydrogels: building dissipation into stretchy networks
,” Soft Matter
10
(5
), 672
–687
(2014
).© 2015 The Society of Rheology.
2015
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