Abstract
The current study develops a 3D constitutive model for photo-thermal sensitive hydrogels based on free energy decomposition. The hydrogel under study is PNIPAM network with copper chlorophyllin nanoparticle agents attached to the network. The effect of light intensity is considered as a rise in temperature since chlorophyllin nanoparticle agents absorb light irradiation and convert it to heat. Moreover, it is necessary to consider the effect of dissociation of these agents on the hydrogel’s free energy function; therefore, a term is added to the free energy function. After introducing the model, some problems, including the free swelling and uniaxial loading problems, are studied, and the obtained results are compared with experimental data to validate the model. The results of the model are in good agreement with experiments, which confirms the validity of the model. Next, to develop a numerical tool to study problems with complicated boundary conditions, the model is implemented in ABAQUS by developing a user-defined UHYPER subroutine, and several practical problems are studied. For example, the deformation of a bilayer made of a sensitive hydrogel attached to a neutral elastomer and the behavior of a self-folding structure is investigated with respect to temperature and light intensity changes. Thereafter, the problem of coexistent phases in a rod due to the light irradiation is investigated. The obtained results confirm the performance of the presented model for use in complicated boundary value problems.
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References
Cai, S., Suo, Z.: Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels. J. Mech. Phys. Solids 59(11), 2259–2278 (2011)
Marcombe, R., Cai, S., Hong, W.: A theory of constrained swelling of a pH-sensitive hydrogel. Soft Matter 6, 784–793 (2010)
Wallmersperger, T., Kröplin, B., Gülch, R.W.: Coupled chemo-electro-mechanical formulation for ionic polymer gels––numerical and experimental investigations. Mech. Mater. 36(5–6), 411–420 (2004)
Hamzavi, N., Drozdov, A.D., Gu, Y., Birgersson, E.: Modeling equilibrium swelling of a dual pH-and temperature-responsive core/shell hydrogel. Int. J. Appl. Mech. 8(03), 1650039 (2016)
Hong, W., Zhao, X., Suo, Z.: Large deformation and electrochemistry of polyelectrolyte gels. J. Mech. Phys. Solids 58(4), 558–577 (2010)
Zheng, S., Liu, Z.: Constitutive model of salt concentration-sensitive hydrogel. Mech. Mater. 136, 103092 (2019)
Drozdov, A., Christiansen, J.D.: The effects of ph and ionic strength of swelling of cationic gels. Int. J. Appl. Mech. 8(05), 1650059 (2016)
Li, H.: Kinetics of smart hydrogels responding to electric field: a transient deformation analysis. Int. J. Solids Struct. 46(6), 1326–1333 (2009)
Suzuki, A.: Phase transition in gels of sub-millimeter size induced by interaction with stimuli. In: Responsive gels: volume transitions II, pp 199–240 (1993).
Yang, C., Wang, W., Yao, C., Xie, R., Ju, X.J., Liu, Z., Chu, L.Y.: Hydrogel walkers with electro-driven motility for cargo transport. Sci. Rep. 5, 13622 (2015). https://doi.org/10.1038/srep13622
Ionov, L.: Hydrogel-based actuators: possibilities and limitations. Mater. Today 17(10), 494–503 (2014)
Dong, L., Agarwal, A.K., Beebe, D.J., Jiang, H.: Adaptive liquid microlenses activated by stimuli-responsive hydrogels. Nature 442(7102), 551–554 (2006). https://doi.org/10.1038/nature05024
Beebe, D.J., Moore, J.S., Bauer, J.M., Yu, Q., Liu, R.H., Devadoss, C., Jo, B.-H.: Functional hydrogel structures for autonomous flow control inside microfluidic channels. Nature 404(6778), 588 (2000)
Mazaheri, H., Baghani, M., Naghdabadi, R., Sohrabpour, S.: Inhomogeneous swelling behavior of temperature sensitive PNIPAM hydrogels in micro-valves: analytical and numerical study. Smart Materials and Structures 24(4) (2015). Doi:https://doi.org/10.1088/0964-1726/24/4/045004
Geryak, R., Tsukruk, V.V.: Reconfigurable and actuating structures from soft materials. Soft Matter 10(9), 1246–1263 (2014). https://doi.org/10.1039/c3sm51768c
Banerjee, H., Suhail, M., Ren, H.: Hydrogel actuators and sensors for biomedical soft robots: brief overview with impending challenges. Biomimetics (Basel) 3(3) (2018). doi:https://doi.org/10.3390/biomimetics3030015
Peppas, N.A., Hilt, J.Z., Khademhosseini, A., Langer, R.: Hydrogels in biology and medicine: from molecular principles to bionanotechnology. Adv. Mater. 18(11), 1345–1360 (2006). https://doi.org/10.1002/adma.200501612
Chan, G., Mooney, D.J.: New materials for tissue engineering: towards greater control over the biological response. Trends Biotechnol. 26(7), 382–392 (2008). https://doi.org/10.1016/j.tibtech.2008.03.011
Sershen, S., Westcott, S., Halas, N., West, J.: Temperature-sensitive polymer–nanoshell composites for photothermally modulated drug delivery. J. Biomed. Mater. Res. 51(3), 293–298 (2000)
Lo, C.-W., Zhu, D., Jiang, H.: An infrared-light responsive graphene-oxide incorporated poly (N-isopropylacrylamide) hydrogel nanocomposite. Soft Matter 7(12), 5604–5609 (2011)
Satoh, T., Sumaru, K., Takagi, T., Kanamori, T.: Fast-reversible light-driven hydrogels consisting of spirobenzopyran-functionalized poly (N-isopropylacrylamide). Soft Matter 7(18), 8030–8034 (2011)
Szilágyi, A., Sumaru, K., Sugiura, S., Takagi, T., Shinbo, T., Zrínyi, M., Kanamori, T.: Rewritable microrelief formation on photoresponsive hydrogel layers. Chem. Mater. 19(11), 2730–2732 (2007)
Yoon, J., Bian, P., Kim, J., McCarthy, T.J., Hayward, R.C.: Local switching of chemical patterns through light-triggered unfolding of creased hydrogel surfaces. Angew. Chem. Int. Ed. 51(29), 7146–7149 (2012)
Gorelikov, I., Field, L.M., Kumacheva, E.: Hybrid microgels photoresponsive in the near-infrared spectral range. J. Am. Chem. Soc. 126(49), 15938–15939 (2004)
Suzuki, A., Tanaka, T.: Phase transition in polymer gels induced by visible light. Nature 346(6282), 345–347 (1990)
Dehghany, M., Zhang, H., Naghdabadi, R., Hu, Y.: A thermodynamically-consistent large deformation theory coupling photo-chemical reaction and electrochemistry for light-responsive gels. J. Mech. Phys. Solids 116, 239–266 (2018). https://doi.org/10.1016/j.jmps.2018.03.018
Gibbs, J.W.: The scientific papers of J. Willard Gibbs, vol. 1. Longmans, Green and Company, (1906)
Biot, M.A.: General theory of three-dimensional consolidation. J. Appl. Phys. 12(2), 155–164 (1941)
Tanaka, T., Fillmore, D.J.: Kinetics of swelling of gels. J. Chem. Phys. 70(3), 1214–1218 (1979)
Hong, W., Zhao, X., Zhou, J., Suo, Z.: A theory of coupled diffusion and large deformation in polymeric gels. J. Mech. Phys. Solids 56(5), 1779–1793 (2008)
Flory, P.J., Rehner, J., Jr.: Statistical mechanics of cross-linked polymer networks I. Rubberlike elasticity. J. Chem. Phys. 11(11), 512–520 (1943)
Flory, P.J.: Thermodynamics of high polymer solutions. J. Chem. Phys. 10(1), 51–61 (1942)
Huggins, M.L.: Solutions of long chain compounds. J. Chem. Phys. 9(5), 440–440 (1941)
Chester, S.A., Anand, L.: A coupled theory of fluid permeation and large deformations for elastomeric materials. J. Mech. Phys. Solids 58(11), 1879–1906 (2010)
Duda, F.P., Souza, A.C., Fried, E.: A theory for species migration in a finitely strained solid with application to polymer network swelling. J. Mech. Phys. Solids 58(4), 515–529 (2010)
Liu, Z., Toh, W., Ng, T.Y.: Advances in mechanics of soft materials: a review of large deformation behavior of hydrogels. Int. J. Appl. Mech. 7(05), 1530001 (2015)
Chester, S.A., Anand, L.: A thermo-mechanically coupled theory for fluid permeation in elastomeric materials: application to thermally responsive gels. J. Mech. Phys. Solids 59(10), 1978–2006 (2011)
Mazaheri, H., Baghani, M., Naghdabadi, R.: Inhomogeneous and homogeneous swelling behavior of temperature-sensitive poly-(N-isopropylacrylamide) hydrogels. J. Intell. Mater. Syst. Struct. 27(3), 324–336 (2015). https://doi.org/10.1177/1045389x15571381
Afroze, F., Nies, E., Berghmans, H.: Phase transitions in the system poly (N-isopropylacrylamide)/water and swelling behaviour of the corresponding networks. J. Mol. Struct. 554(1), 55–68 (2000)
De, S.K., Aluru, N.R.: A chemo-electro-mechanical mathematical model for simulation of pH sensitive hydrogels. Mech. Mater. 36(5–6), 395–410 (2004)
Mazaheri, H., Baghani, M., Naghdabadi, R., Sohrabpour, S.: Coupling behavior of the pH/temperature sensitive hydrogels for the inhomogeneous and homogeneous swelling. Smart Mater. Struct. 25(8), 085034 (2016)
Yu, Y., Landis, C.M., Huang, R.: Salt-induced swelling and volume phase transition of polyelectrolyte gels. J. Appl. Mech. 84(5), 051005 (2017)
Huang, R., Zheng, S., Liu, Z., Ng, T.Y.: Recent advances of the constitutive models of smart materials-hydrogels and shape memory polymers. Int. J. Appl. Mech. 12, 2050014 (2020)
Kuksenok, O., Balazs, A.C.: Modeling the photoinduced reconfiguration and directed motion of polymer gels. Adv. Func. Mater. 23(36), 4601–4610 (2013)
Toh, W., Ng, T.Y., Hu, J., Liu, Z.: Mechanics of inhomogeneous large deformation of photo-thermal sensitive hydrogels. Int. J. Solids Struct. 51(25–26), 4440–4451 (2014). https://doi.org/10.1016/j.ijsolstr.2014.09.014
Drozdov, A.D., Declaville Christiansen, J.: Modeling the effects of pH and ionic strength on swelling of polyelectrolyte gels. J. Chem. Phys. 142(11):114904 (2015). https://doi.org/10.1063/1.4914924
Mazaheri, H.: Study of swelling behavior of temperature sensitive hydrogels considering inextensibility of network. Sci. Iranica 26(2), 887–896 (2019)
Flory, P.J., Rehner, J., Jr.: Statistical mechanics of cross-linked polymer networks II Swelling. J. Chem. Phys. 11(11), 521–526 (1943)
Huggins, M.L.: Some properties of solutions of long-chain compounds. J. Phys. Chem. 46(1), 151–158 (1942)
Drozdov, A.D., Declaville Christiansen, J.: (2015) Swelling of p H-sensitive hydrogels. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 91(2): 022305. Doi:https://doi.org/10.1103/PhysRevE.91.022305
Hong, W., Liu, Z., Suo, Z.: Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load. Int. J. Solids Struct. 46(17), 3282–3289 (2009)
Ding, Z., Toh, W., Hu, J., Liu, Z., Ng, T.Y.: A simplified coupled thermo-mechanical model for the transient analysis of temperature-sensitive hydrogels. Mech. Mater. 97, 212–227 (2016)
Cheng, Y., Ren, K., Yang, D., Wei, J.: Bilayer-type fluorescence hydrogels with intelligent response serve as temperature/pH driven soft actuators. Sens. Actuators B Chem. 255, 3117–3126 (2018). https://doi.org/10.1016/j.snb.2017.09.137
Le, X., Lu, W., Zhang, J., Chen, T.: Recent Progress in Biomimetic Anisotropic Hydrogel Actuators. Adv Sci (Weinh) 6(5), 1801584 (2019). https://doi.org/10.1002/advs.201801584
Abdolahi, J., Baghani, M., Arbabi, N., Mazaheri, H.: Analytical and numerical analysis of swelling-induced large bending of thermally-activated hydrogel bilayers. Int. J. Solids Struct. 99, 1–11 (2016). https://doi.org/10.1016/j.ijsolstr.2016.08.017
Arbabi, N., Baghani, M., Abdolahi, J., Mazaheri, H., Mashhadi, M.M.: Finite bending of bilayer pH-responsive hydrogels: A novel analytic method and finite element analysis. Compos. B Eng. 110, 116–123 (2017)
Fernandes, R., Gracias, D.H.: Self-folding polymeric containers for encapsulation and delivery of drugs. Adv. Drug Deliv. Rev. 64(14), 1579–1589 (2012)
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The corresponding author is grateful for the research support of the Iran's National Elites Foundation (INEF).
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Mazaheri, H., Namdar, A.H. & Ghasemkhani, A. A model for inhomogeneous large deformation of photo-thermal sensitive hydrogels. Acta Mech 232, 2955–2972 (2021). https://doi.org/10.1007/s00707-021-02991-w
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DOI: https://doi.org/10.1007/s00707-021-02991-w