Abstract
We fabricated the doubly crosslinked gel, with internal stress by stretching the gel during the gelation reaction using tetra-PEG gels, which are formed by the AB type crosslink-coupling of two mutually reactive tetra-arm polyethylene glycol (PEG). In a doubly crosslinked gel, two networks having different reference states coexist with and balance each other, resulting in enhanced Young’s modulus and residual strain. We investigated these properties by tuning the time for the imposition of the stretching of the gels and the stretching ratio. The residual strain increased with increase in the time for the imposition of stretching and the stretching ratio. On the other hand, the Young’s modulus had a maximum value at a certain time for the imposition of the stretching of the gels and increased with increasing stretching ratio. These results were well explained by the balance between the strain energies of the first and second networks under the framework of the classical two-network theory, where the total strain energy is described as a simple sum of the energies of the first and second networks.
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References
Hikmet RAM, Lub J, Broer DJ. Anisotropic networks formed by photopolymerization of liquid-crystalline molecules. Adv Mater. 1991;3:392–4.
Kumpfer JR, Wie JJ, Swanson JP, Beyer FL, Mackay ME, Rowan SJ. Influence of metal ion and polymer core on the melt rheology of metallosupramolecular films. Macromolecules. 2012;45:473–80.
de Haan LT, Schenning APHJ, Broer DJ. Programmed morphing of liquid crystal networks. Polymer. 2014;55:5885–96.
Pei Z, Yang Y, Chen Q, Terentjev EM, Wei Y, Ji Y. Mouldable liquid-crystalline elastomer actuators with exchangeable covalent bonds. Nat Mater. 2013;13:36.
Xia Y, Yang P, Sun Y, Wu Y, Mayers B, Gates B, Yin Y, Kim F, Yan H. One-dimensional nanostructures: synthesis, characterization, and applications. Adv Mater. 2003;15:353–89.
Ruoff RS, Lorents DC. Mechanical and thermal properties of carbon nanotubes. Carbon. 1995;33:925–30.
Tobolsky AV, Takahashi Y, Naganuma S. Effect of additional crosslinking of continuous chemical stress relaxation of cis-polybutadiene. Polym J. 1972;3:60–&.
Andrews RD, Tobolsky AV, Hanson EE. The theory of permanent set at elevated temperatures in natural and synthetic rubber vulcanizates. J Appl Phys. 1946;17:352–61.
Berry JP, Scanlan J, Watson WF. Cross-link formation in stretched rubber networks. T Faraday Soc. 1956;52:1137–51.
Kaang S, Nah C. Fatigue crack growth of double-networked natural rubber. Polymer. 1998;39:2209–14.
Meng Y, Yang J-C, Lewis CL, Jiang J, Anthamatten M. Photoinscription of chain anisotropy into polymer networks. Macromolecules. 2016;49:9100–7.
Mott PH, Roland CM. Mechanical and optical behavior of double network rubbers. Macromolecules. 2000;33:4132–7.
Singh NK, Lesser AJ. A physical and mechanical study of prestressed competitive double network thermoplastic elastomers. Macromolecules. 2011;44:1480–90.
Wang J, Hamed GR, Umetsu K, Roland CM. The Payne effect in double network elastomers. Rubber Chem Technol. 2005;78:76–83.
Flory PJ. Elasticity of polymer networks cross-linked in states of strain. T Faraday Soc. 1960;56:722–43.
Fricker HS. The effects on rubber elasticity of the addition and scission of cross-links under strain. Proc R Soc Lond Ser A. 1973;335:267–87.
Shibayama M, Takata S, Norisuye T. Static inhomogeneities and dynamic fluctuations of temperature sensitive polymer gels. Phys A. 1998;249:245–52.
Allen G, Kirkham MJ, Padget J, Price C. Thermodynamics of rubber elasticity at constant volume. Trans Faraday Soc. 1971;67:1278–92.
Candau S, Peters A, Herz J. Experimental-evidence for trapped chain entanglements—their influence on macroscopic behavior of networks. Polymer. 1981;22:1504–10.
Flory, PJ. Principles of polymer chemistry. (Cornell University Press, Ithaca, 1953).
Wall FT. Statistical thermodynamics of rubber II. J Chem Phys. 1942;10:485–8.
Kawamura T, Urayama K, Kohjiya S. Multiaxial deformations of end-linked poly(dimethylsiloxane) networks 5. Revisit to Mooney-Rivlin approach to strain energy density function. Nihon Reoroji Gakkaishi. 2003;31:213–7.
Kawamura T, Urayama K, Kohjiya S. Multiaxial deformations of end-linked poly (dimethylsiloxane) networks. III. Effect of entanglement density on strain-energy density function. J Polym Sci Pol Phys. 2002;40:2780–90.
Kawamura T, Urayama K, Kohjiya S. Structure and mechanical properties of bimodal pdms networks in the swollen state. J Soc Mater Sci Jpn. 1998;47:113–6.
Kawamura T, Urayama K, Kohjiya S. Multiaxial deformations of end-linked poly(dimethylsiloxane) networks. 1. Phenomenological approach to strain energy density function. Macromolecules. 2001;34:8252–60.
Urayama K, Kawamura T, Kohjiya S. Multiaxial deformations of end-linked poly(dimethylsiloxane) networks. 2. Experimental tests of molecular entanglement models of rubber elasticity. Macromolecules. 2001;34:8261–9.
Urayama K, Kawamura T, Kohjiya S. Structure-mechanical property correlations of model siloxane elastomers with controlled network topology. Polymer. 2009;50:347–56.
Urayama K, Kawamura T, Kohjiya S. Multiaxial deformations of end-linked poly(dimethylsiloxane) networks. 4. Further assessment of the slip-link model for chain-entanglement effect on rubber elasticity. J Chem Phys. 2003;118:5658–64.
Rubinstein M, Panyukov S. Elasticity of polymer networks. Macromolecules. 2002;35:6670–86.
Everaers R. Constrained fluctuation theories of rubber elasticity: general results and an exactly solvable model. Eur Phys J B. 1998;4:341–50.
Rottach DR, Curro JG, Grest GS, Thompson AP. Effect of strain history on stress and permanent set in cross-linking networks: aA molecular dynamics study. Macromolecules. 2004;37:5468–73.
Rottach DR, Curro JG, Budzien J, Grest GS, Svaneborg C, Everaers R. Molecular dynamics simulations of polymer networks undergoing sequential cross-linking and scission reactions. Macromolecules. 2007;40:131–9.
Sakai T, Matsunaga T, Yamamoto Y, Ito C, Yoshida R, Suzuki S, Sasaki N, Shibayama M, Chung UI. Design and fabrication of a high-strength hydrogel with ideally homogeneous network structure from tetrahedron-like macromonomers. Macromolecules. 2008;41:5379–84.
Sakai T. Gelation mechanism and mechanical properties of Tetra-PEG gel. React Funct Polym. 2013;73:898–903.
Sakai T. Experimental verification of homogeneity in polymer gels. Polym J. 2014;46:517–23.
Matsunaga T, Sakai T, Akagi Y, Chung U, Shibayama M. Structure characterization of tetra-PEG gel by small-angle neutron scattering. Macromolecules. 2009;42:1344–51.
Akagi Y, Katashima T, Katsumoto Y, Fujii K, Matsunaga T, Chung U, Shibayama M, Sakai T. Examination of the theories of rubber elasticity using an ideal polymer network. Macromolecules. 2011;44:5817–21.
Akagi Y, Gong JP, Chung U-I, Sakai T. Transition between phantom and affine network model observed in polymer gels with controlled network structure. Macromolecules. 2013;46:1035–40.
Nishi K, Fujii K, Chijiishi M, Katsumoto Y, Chung U, Sakai T, Shibayama M. Kinetic study for AB-type coupling reaction of tetra-arm polymers. Macromolecules. 2012;45:1031–6.
Lange F, Schwenke K, Kurakazu M, Akagi Y, Chung UI, Lane M, Sommer JU, Sakai T, Saalwachter K. Connectivity and structural defects in model hydrogels: a combined proton NMR and Monte Carlo simulation Study.Macromolecules. 2011;44:9666–74.
Katashima T, Urayama K, Chung U-I, Sakai T. Probing the cross-effect of strains in non-linear elasticity of nearly regular polymer networks by pure shear deformation. J Chem Phys. 2015;142:174908.
Akagi Y, Katashima T, Sakurai H, Chung U-I, Sakai T. Ultimate elongation of polymer gels with controlled network structure. RSC Adv. 2013;3:13251–8.
Flory PJ, Rehner J. Statistical mechanics of cross-linked polymer networks I Rubberlike elasticity. J Chem Phys. 1943;11:512–20.
Akagi Y, Matsunaga T, Shibayama M, Chung U, Sakai T. Evaluation of topological defects in Tetra-PEG gels. Macromolecules. 2010;43:488–93.
Acknowledgements
This work was supported by the Japan Society for the Promotion of Science (JSPS) through the Grants-in-Aid for the Graduate Program for Leaders in Life Innovation (GPLLI), the International Core Research Center for Nanobio, the Core-to-Core Program A. Advanced Research Networks, the Grants-in-Aid for Young Scientists (A) Grant Number 23700555 (to TS), and Scientific Research (S) Grant Number 16746899 (to UC). This work was also supported by the Japan Science and Technology Agency (JST) through the Center of Innovation program (to UC) and the PREST (to TS).
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Katashima, T., Chung, Ui. & Sakai, T. Mechanical properties of doubly crosslinked gels. Polym J 51, 851–859 (2019). https://doi.org/10.1038/s41428-019-0203-6
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DOI: https://doi.org/10.1038/s41428-019-0203-6
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