Research ArticleNo Access

A Thermodynamic-Consistent Model for the Thermo-Chemo-Mechanical Couplings in Amorphous Shape-Memory Polymers

School of Civil Engineering and Architecture, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, P. R. China

and

Key Laboratory of Soft Machines and Smart, Devices of Zhejiang Province, Department of Engineering, Mechanics, Zhejiang University, Hangzhou 310027, P. R. China

E-mail Address: [email protected]

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S1758825121500228Cited by:19 (Source: Crossref)

Abstract

Chemically-responsive amorphous shape-memory polymers (SMPs) can transit from the temporary shape to the permanent shape in responsive to solvents. This effect has been reported in various polymer-solvent systems. However, limited attention has been paid to the constitutive modeling of this behavior. In this work, we develop a fully thermo-chemo-mechanical coupled thermodynamic framework for the chemically-responsive amorphous SMPs. The framework shows that the entropy, the chemical potential and the stress can be directly obtained if the Helmholtz free energy density is defined. Based on the entropy inequality, the evolution equation for the viscous strain, the temperature and the number of solvent molecules are also derived. We also provide an explicit form of Helmholtz free energy density as an example. In addition, based on the free volume concept, the dependence of viscosity and diffusivity on the temperature and solvent concentration is defined. The theoretical framework can potentially advance the fundamental understanding of chemically-responsive shape-memory effect. Meanwhile, it can also be used to describe other important physical processes such as the diffusion of solvents in glassy polymers.

Keywords:

References

Adam, G. and Gibbs, J. H. [1965] “ On the temperature dependence of cooperative relaxation properties in the glass-forming liquids,” The Journal of Chemical Physics 43, 139–146. Crossref, Web of Science, Google Scholar
Adkins, C. J. and Adkins, C. J. [1983] Equilibrium Thermodynamics (Cambridge University Press, Cambridge). Crossref, Google Scholar
Arruda, E. M. and Boyce, M. C. [1993] “ A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials,” Journal of the Mechanics and Physics of Solids 41, 389–412. Crossref, Web of Science, Google Scholar
Boyce, M. C., Parks, D. M. and Argon, A. S. [1988] “ Large inelastic deformation of glassy polymers. Part I: Rate dependent constitutive model,” Mechanics of Materials 7, 15–33. Crossref, Web of Science, Google Scholar
Boyle, A., Weems, A., Hasan, S., Nash, L., Monroe, M. and Maitland, D. [2016] “ Solvent stimulated actuation of polyurethane-based shape memory polymer foams using dimethyl sulfoxide and ethanol,” Smart Materials and Structures 25(7), 075014. Crossref, Web of Science, Google Scholar
Buckley, C., Dooling, P., Harding, J. and Ruiz, C. [2004] “ Deformation of thermosetting resins at impact rates of strain. Part 2: Constitutive model with rejuvenation,” Journal of the Mechanics and Physics of Solids 52(10), 2355–2377. Crossref, Web of Science, Google Scholar
Cai, S. and Suo, Z. [2011] “ Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels,” Journal of the Mechanics and Physics of Solids 59(11), 2259–2278. Crossref, Web of Science, Google Scholar
Chen, S., Mei, Z., Ren, H., Zhuo, H., Liu, J. and Ge, Z. [2016] “ Pyridine type zwitterionic polyurethane with both multi-shape memory effect and moisture-sensitive shape memory effect for smart biomedical application,” Polymer Chemistry 7(37), 5773–5782. Crossref, Web of Science, Google Scholar
Chester, S. A. [2012] “ A constitutive model for coupled fluid permeation and large viscoelastic deformation in polymeric gels,” Soft Matter 8(31), 8223–8233. Crossref, Web of Science, Google Scholar
Chester, S. A. and Anand, L. [2010] “ A coupled theory of fluid permeation and large deformations for elastomeric materials,” Journal of the Mechanics and Physics of Solids 58(11), 1879–1906. Crossref, Web of Science, Google Scholar
Chester, S. A. and Anand, L. [2011] “ A thermo-mechanically coupled theory for fluid permeation in elastomeric materials: application to thermally responsive gels,” Journal of the Mechanics and Physics of Solids 59(10), 1978–2006. Crossref, Web of Science, Google Scholar
Choi, J., Ortega, A. M., Xiao, R., Yakacki, C. M. and Nguyen, T. D. [2012] “ Effect of physical aging on the shape-memory behavior of amorphous networks,” Polymer 53(12), 2453–2464. Crossref, Web of Science, Google Scholar
Dai, L., Tian, C. and Xiao, R. [2020] “ Modeling the thermo-mechanical behavior and constrained recovery performance of cold-programmed amorphous shape-memory polymers,” International Journal of Plasticity 127, 102654. Crossref, Web of Science, Google Scholar
Dimarzio, E. A. and Gibbs, J. H. [1963] “Molecular interpretation of glass temperature depression by plasticizers,” Journal of Polymer Science Part A: General Papers 1(4), 1417–1428. Google Scholar
Doolittle, A. K. [1951] “ Studies in newtonian flow. II. The dependence of the viscosity of liquids on free-space,” Journal of Applied Physics 22(12), 1471–1475. Crossref, Web of Science, Google Scholar
Du, H. and Zhang, J. [2010] “ Solvent induced shape recovery of shape memory polymer based on chemically cross-linked poly (vinyl alcohol),” Soft Matter 6(14), 3370–3376. Crossref, Web of Science, Google Scholar
Duan, Z., Zhang, J., An, Y. and Jiang, H. [2013] “ Simulation of the transient behavior of gels based on an analogy between diffusion and heat transfer,” Journal of Applied Mechanics 80(4), 041017. Crossref, Web of Science, Google Scholar
Dupaix, R. B. and Boyce, M. C. [2007] “ Constitutive modeling of the finite strain behavior of amorphous polymers in and above the glass transition,” Mechanics of Materials 39, 39–52. Crossref, Web of Science, Google Scholar
Ferry, J. D. [1980] Viscoelastic Properties of Polymers (John Wiley and Sons, New York, NY). Google Scholar
Garshasbi, M. and Malek Bagomghaleh, S. [2020] “ An iterative approach to solve a nonlinear moving boundary problem describing the solvent diffusion within glassy polymers,” Mathematical Methods in the Applied Sciences 43(6), 3754–3772. Crossref, Web of Science, Google Scholar
Ge, Q., Sakhaei, A. H., Lee, H., Dunn, C. K., Fang, N. X. and Dunn, M. L. [2016] “ Multimaterial 4D printing with tailorable shape memory polymers,” Scientific Reports 6, 31110. Crossref, Web of Science, Google Scholar
Gu, J., Zhao, S., Zhang, X., Cai, Z. and Sun, H. [2020] “ A hygro-thermo-mechanical constitutive model for hygrothermally activated shape memory polymers under finite deformations,” Mechanics of Materials 150, 103594. Crossref, Web of Science, Google Scholar
Guo, Y., Lv, Z., Huo, Y., Sun, L., Chen, S., Liu, Z., He, C., Bi, X., Fan, X. and You, Z. [2019] “ A biodegradable functional water-responsive shape memory polymer for biomedical applications,” Journal of Materials Chemistry B 7(1), 123–132. Crossref, Web of Science, Google Scholar
Gurtin, M. E., Eliot, F. and Lallit, A. [2010] The Mechanics and Thermodynamics of Continua (Cambridge University Press, Cambridge). Crossref, Google Scholar
Hasan, O. and Boyce, M. [1995] “ A constitutive model for the nonlinear viscoelastic viscoplastic behavior of glassy polymers,” Polymer Engineering & Science 35(4), 331–344. Crossref, Web of Science, Google Scholar
He, D. and Hu, Y. [2020] “ Nonlinear visco-poroelasticity of gels with different rheological parts,” Journal of Applied Mechanics 87(7), 071010. Crossref, Web of Science, Google Scholar
Holzapfel, G. A. [2000] Nonlinear Solid Mechanics: A Continuum Approach for Engineers (John Wiley and Sons, Chichester). Google Scholar
Hong, W., Zhao, X., Zhou, J. and Suo, Z. [2008] “ A theory of coupled diffusion and large deformation in polymeric gels,” Journal of the Mechanics and Physics of Solids 56(5), 1779–1793. Crossref, Web of Science, Google Scholar
Huang, R., Zheng, S., Liu, Z. and Ng, T. Y. [2020] “ Recent advances of the constitutive models of smart materials-hydrogels and shape memory polymers,” International Journal of Applied Mechanics 12(2), 2050014. Link, Web of Science, Google Scholar
Lei, J., Li, Z., Xu, S. and Liu, Z. [2021] “ Recent advances of hydrogel network models for studies on mechanical behaviors,” Acta Mechanica Sinica 37. https://doi.org/10.1007/s10409–021–01058–2. Crossref, Web of Science, Google Scholar
Li, J., Kan, Q., Chen, K., Liang, Z. and Kang, G. [2019] “ In situ observation on rate-dependent strain localization of thermo-induced shape memory polyurethane,” Polymers 11(6), 982. Crossref, Web of Science, Google Scholar
Liu, C., Lu, H., Li, G., Hui, D. and Fu, Y.-Q. [2019] “ A “cross-relaxation effects” model for dynamic exchange of water in amorphous polymer with thermochemical shape memory effect,” Journal of Physics D: Applied Physics 52(34), 345305. Crossref, Web of Science, Google Scholar
Liu, Z., Toh, W. and Ng, T. Y. [2015] “ Advances in mechanics of soft materials: A review of large deformation behavior of hydrogels,” International Journal of Applied Mechanics 7(5), 1530001. Link, Web of Science, Google Scholar
Lu, H., Lu, C., Huang, W. M. and Leng, J. [2016] “ Quantitative separation of the influence of copper (ii) chloride mass migration on the chemo-responsive shape memory effect in polyurethane shape memory polymer,” Smart Materials and Structures 25(10), 105003. Crossref, Web of Science, Google Scholar
Luo, C., Lei, Z., Mao, Y., Shi, X., Zhang, W. and Yu, K. [2018] “ Chemomechanics in the moisture-induced malleability of polyimine-based covalent adaptable networks,” Macromolecules 51(23), 9825–9838. Crossref, Web of Science, Google Scholar
Mao, Y., Chen, F., Hou, S., Qi, H. J. and Yu, K. [2019] “ A viscoelastic model for hydrothermally activated malleable covalent network polymer and its application in shape memory analysis,” Journal of the Mechanics and Physics of Solids 127, 239–265. Crossref, Web of Science, Google Scholar
Nguyen, T., Qi, H. J., Castro, F. and Long, K. N. [2008] “ A thermoviscoelastic model for amorphous shape memory polymers: Incorporating structural and stress relaxation,” Journal of the Mechanics and Physics of Solids 56, 2792–2814. Crossref, Web of Science, Google Scholar
Ramdas, M. R., Kumar, K. S. and Nair, C. R. [2016] “ Heat and solvent responsive polytriazole: shape recovery properties in different solvents,” RSC Advances 6(59), 53602–53613. Crossref, Web of Science, Google Scholar
Ramesh, N., Davis, P., Zielinski, J., Danner, R. and Duda, J. [2011] “ Application of free-volume theory to self diffusion of solvents in polymers below the glass transition temperature: A review,” Journal of Polymer Science Part B: Polymer Physics 49(23), 1629–1644. Crossref, Web of Science, Google Scholar
Reese, S. and Govindjee, S. [1997] “ Theoretical and numerical aspects in the thermo-viscoelastic material behaviour of rubber-like polymers,” Mechanics of Time-Dependent Materials 1(4), 357–396. Crossref, Google Scholar
Vijalapura, P. K. and Govindjee, S. [2003] “ Numerical simulation of coupled-stress case ii diffusion in one dimension,” Journal of Polymer Science Part B: Polymer Physics 41(18), 2091–2108. Crossref, Web of Science, Google Scholar
Wang, D., Li, L., Zhang, B., Zhang, Y.-F., Wu, M. S., Gu, G. and Ge, Q. [2020] “ Effect of temperature on the programmable helical deformation of a reconfigurable anisotropic soft actuator,” International Journal of Solids and Structures 199, 169–180. Crossref, Web of Science, Google Scholar
Wang, X., Lu, H., Wu, N., Hui, D., Chen, M. and Fu, Y.-Q. [2019] “ Cooperative principle in multiple glass transitions and strain relaxations of thermochemically responsive shape memory polymer,” Smart Materials and Structures 28(8), 085011. Crossref, Web of Science, Google Scholar
Xiao, R., Choi, J., Lakhera, N., Yakacki, C., Frick, C. and Nguyen, T. [2013] “ Modeling the glass transition of amorphous networks for shape-memory behavior,” Journal of the Mechanics and Physics of Solids 61(7), 1612–1635. Crossref, Web of Science, Google Scholar
Xiao, R. and Huang, W. M. [2020] “ Heating/solvent responsive shape-memory polymers for implant biomedical devices in minimally invasive surgery: Current status and challenge,” Macromolecular Bioscience 20(8), 2000108. Crossref, Web of Science, Google Scholar
Xiao, R. and Nguyen, T. D. [2013] “ Modeling the solvent-induced shape-memory behavior of glassy polymers,” Soft Matter 9(39), 9455–9464. Crossref, Web of Science, Google Scholar
Xiao, R. and Nguyen, T. D. [2015] “ An effective temperature theory for the nonequilibrium behavior of amorphous polymers,” Journal of the Mechanics and Physics of Solids 82, 62–81. Crossref, Web of Science, Google Scholar
Xiao, R. and Tian, C. [2019] “ A constitutive model for strain hardening behavior of predeformed amorphous polymers: Incorporating dissipative dynamics of molecular orientation,” Journal of the Mechanics and Physics of Solids 125, 472–487. Crossref, Web of Science, Google Scholar
Xiao, R., Zhang, C., Gou, X. and Huang, W. M. [2017] “ Tunable shape-memory behaviors in amorphous polymers through bound solvent,” Materials Letters 209, 131–133. Crossref, Web of Science, Google Scholar
Xu, S. and Liu, Z. [2019] “ A nonequilibrium thermodynamics approach to the transient properties of hydrogels,” Journal of the Mechanics and Physics of Solids 127, 94–110. Crossref, Web of Science, Google Scholar
Xu, S. and Liu, Z. [2020] “ Coupled theory for transient responses of conductive hydrogels with multi-stimuli,” Journal of the Mechanics and Physics of Solids 143, 104055. Crossref, Web of Science, Google Scholar
Yang, B., Huang, W., Li, C. and Li, L. [2006] “ Effects of moisture on the thermomechanical properties of a polyurethane shape memory polymer,” Polymer 47(4), 1348–1356. Crossref, Web of Science, Google Scholar
Yu, C., Kang, G. and Chen, K. [2017a] “ A hygro-thermo-mechanical coupled cyclic constitutive model for polymers with considering glass transition,” International Journal of Plasticity 89, 29–65. Crossref, Web of Science, Google Scholar
Yu, Y., Landis, C. M. and Huang, R. [2017b] “ Salt-induced swelling and volume phase transition of polyelectrolyte gels,” Journal of Applied Mechanics 84(5), 051005. Crossref, Web of Science, Google Scholar