Deep neural networks for large deformation of photo-thermo-pH responsive cationic gels. (English) Zbl 1481.74042
Summary: In this work, a model is developed to analyze homogeneous and inhomogeneous large deformation of photo-thermo-pH responsive cationic gels. Constitutive equations are achieved by considering the equilibrium thermodynamics of swelling gels through variational method. Employing this model, coupling effects of light intensity, temperature and pH variations on large deformation of gels are analyzed. The simulation results are compared with available experimental data. Then deep neural networks are developed to approximate solutions to equilibrium equations of inhomogeneous swelling of spherical shell structure gels. The volume phase transition temperature of the gels and their dependence on light intensity are also demonstrated.
MSC:
| 74A20 | Theory of constitutive functions in solid mechanics |
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
Keywords:
deep neural networks; photo-thermo-pH responsive; cationic gels; spherical shell structure; inhomogeneous large deformationSoftware:
DeepXDEReferences:
| [1] | Ding, Z. W.; Toh, W.; Hu, J. Y.; Liu, Z. S.; Ng, T. Y., A simplified coupled thermo-mechanical model for the transient analysis of temperature-sensitive hydrogels, Mech. Mater., 97, 212-227 (2016) |
| [2] | Marcombe, R.; Cai, S.; Hong, W.; Zhao, X.; Lapusta, Y.; Suo, Z., A theory of constrained swelling of a pH-sensitive hydrogel, Soft Matter, 6, 784 (2010) |
| [3] | Li, H., Kinetics of smart hydrogels responding to electric field: A transient deformation analysis, Int. J. Solids Struct., 46, 1326-1333 (2009) · Zbl 1236.76077 |
| [4] | Zhao, R. K.; Kim, Y.; Chester, S. A.; Sharma, P.; Zhao, X. H., Mechanics of hard-magnetic soft materials, J. Mech. Phys. Solids, 124, 244-263 (2019) |
| [5] | Ahn, S.-K.; Kasi, R. M.; Kim, S.-C.; Sharma, N.; Zhou, Y., Stimuli-responsive polymer gels, Soft Matter, 4, 1151-1157 (2008) |
| [6] | Toh, W.; Ng, T. Y.; Hu, J. Y.; Liu, Z. S., Mechanics of inhomogeneous large deformation of photo-thermal sensitive hydrogels, Int. J. Solids Struct., 51, 4440-4451 (2014) |
| [7] | Hoffman, A. S., Hydrogels for biomedical applications, Adv. Drug Deliv. Rev., 54, 3-12 (2002) |
| [8] | Eddington, D. T.; Beebe, D. J., Flow control with hydrogels, Adv. Drug Deliv. Rev., 56, 199-210 (2004) |
| [9] | Mazaheri, H.; Baghani, M.; Naghdabadi, R.; Sohrabpour, S., Inhomogeneous swelling behavior of temperature sensitive PNIPAM hydrogels in micro-valves: analytical and numerical study, Smart Mater. Struct., 24, 9 (2015) |
| [10] | Randhawa, J. S.; Laflin, K. E.; Seelam, N.; Gracias, D. H., Microchemomechanical Systems, Adv. Funct. Mater., 21, 2395-2410 (2011) |
| [11] | Guo, W.; Li, M.; Zhou, J., Modeling programmable deformation of self-folding all-polymer structures with temperature-sensitive hydrogels, Smart Mater. Struct., 22 (2013) |
| [12] | Hong, W.; Zhao, X.; Zhou, J.; Suo, Z., A theory of coupled diffusion and large deformation in polymeric gels, J. Mech. Phys. Solids, 56, 1779-1793 (2008) · Zbl 1162.74313 |
| [13] | Yan, H.; Jin, B., Influence of microstructural parameters on mechanical behavior of polymer gels, Int. J. Solids Struct., 49, 436-444 (2012) |
| [14] | Yang, Q. S.; Ma, L. H.; Shang, J. J., The chemo-mechanical coupling behavior of hydrogels incorporating entanglements of polymer chains, Int. J. Solids Struct., 50, 2437-2448 (2013) |
| [15] | Ma, L. H.; Yang, Q. S.; Yang, C. H., Effects of the Junction Functionality and Chain Entanglements in Chemomechanical Behavior of Polyelectrolyte Gels, Adv. Condens. Matter Phys. 2015, 10 (2015) |
| [16] | Wu, Z.; Zhong, Z., Inhomogeneous Equilibrium Swelling of Core-Shell-Coating Gels, Soft Mater, 11, 215-220 (2013) |
| [17] | Cai, S. Q.; Suo, Z. G., Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels, J. Mech. Phys. Solids, 59, 2259-2278 (2011) · Zbl 1270.74163 |
| [18] | Ding, Z. W.; Liu, Z. S.; Hu, J. Y.; Swaddiwudhipong, S.; Yang, Z. Z., Inhomogeneous large deformation study of temperature-sensitive hydrogel, Int. J. Solids Struct., 50, 2610-2619 (2013) |
| [19] | Sershen, S. R.; Westcott, S. L.; Halas, N. J.; West, J. L., Temperature-sensitive polymer-nanoshell composites for photothermally modulated drug delivery, J. Biomed. Mater. Res, 51, 293-298 (2000), doi:10.1002/1097-4636(20000905)51:3<293::aid-jbm1>3.0.co;2-t |
| [20] | Liu, J.; Nie, J.; Zhao, Y.; He, Y., Preparation and properties of different photoresponsive hydrogels modulated with UV and visible light irradiation, J. Photoch. Photobio. A, 211, 20-25 (2010) |
| [21] | Mudiyanselage, T. K.; Neckers, D. C., Photochromic superabsorbent polymers, Soft Matter, 4, 768-774 (2008) |
| [22] | Drozdov, A. D., Swelling of pH-responsive cationic gels: Constitutive modeling and structure-property relations, Int. J. Solids Struct., 64, 65, 176-190 (2015) |
| [23] | Yan, H. X.; Jin, B.; Gao, S. H.; Chen, L. W., Equilibrium swelling and electrochemistry of polyampholytic pH-sensitive hydrogel, Int. J. Solids Struct., 51, 4149-4156 (2014) |
| [24] | Yan, H. X.; Jin, B., Equilibrium swelling of a polyampholytic pH-sensitive hydrogel, Eur. Phys. J. E, 36, 7 (2013) |
| [25] | Yan, H.; Jin, B., Influence of environmental solution pH and microstructural parameters on mechanical behavior of amphoteric pH-sensitive hydrogels, Eur. Phys. J. E, 35, 36 (2012) |
| [26] | Li, H.; Ng, T. Y.; Yew, Y. K.; Lam, K. Y., Modeling and simulation of the swelling behavior of pH-stimulus-responsive hydrogels, Biomacromolecules, 6, 109-120 (2005) |
| [27] | Luo, R. M.; Li, H.; Birgersson, E.; Lam, K. Y., Modeling of electric-stimulus-responsive hydrogels immersed in different bathing solutions, J. Biomed. Mater. Res. Part A, 85A, 248-257 (2008) |
| [28] | Liu, Z. S.; Toh, W.; Ng, T. Y., Advances in Mechanics of Soft Materials: A Review of Large Deformation Behavior of Hydrogels, Int. J. Appl. Mech., 7, 35 (2015) |
| [29] | (Siegel, R. A.; Dušek, K., Responsive Gels: Volume Transitions I (1993), Springer Berlin Heidelberg: Springer Berlin Heidelberg Berlin, Heidelberg), 233-267, Editor |
| [30] | (Irie, M.; Dušek, K., Responsive Gels: Volume Transitions II (1993), Springer Berlin Heidelberg: Springer Berlin Heidelberg Berlin, Heidelberg), 49-65, Editor |
| [31] | (Okano, T.; Dušek, K., Responsive Gels: Volume Transitions II (1993), Springer Berlin Heidelberg: Springer Berlin Heidelberg Berlin, Heidelberg), 179-197, Editor |
| [32] | Dehghany, M.; Zhang, H. H.; Naghdabadi, R.; Hu, Y. H., A thermodynamically-consistent large deformation theory coupling photochemical reaction and electrochemistry for light-responsive gels, J. Mech. Phys. Solids, 116, 239-266 (2018) |
| [33] | 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, 13 (2016) |
| [34] | Yan, H.-X.; Hong, H.-L.; Zheng, L.-H.; Su, H.-D., Analysis of The Coupling Behavior of a Thin Layer of a Temperature-pH Dual Sensitive Hydrogel for an Inhomogeneous Large Deformation, J. Korean Phys. Soc., 73, 965-972 (2018) |
| [35] | Yan, H. X.; Su, H. D.; Zhong, Z., Modeling of the Photo-Thermal-pH Triple-Responsive Hydrogels Considering the Coupled Effect of Photothermal Conversion and Electrochemistry, J. Appl. Mech.-Trans. ASME, 87, 9 (2020) |
| [36] | Hong, W.; Liu, Z.; Suo, Z., Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load, Int. J. Solids Struct., 46, 3282-3289 (2009) · Zbl 1167.74333 |
| [37] | Toh, W.; Ng, T. Y.; Liu, Z. S.; Hu, J. Y., Deformation kinetics of pH-sensitive hydrogels, Polym. Int., 63, 1578-1583 (2014) |
| [38] | Yi, C. Z.; Zhang, X. W.; Yan, H. X.; Jin, B., Finite Element Simulation and the Application of Amphoteric pH-sensitive Hydrogel, Int. J. Appl. Mech., 9, 25 (2017) |
| [39] | 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) |
| [40] | Chester, S. A.; Di Leo, C. V.; Anand, L., A finite element implementation of a coupled diffusion-deformation theory for elastomeric gels, Int. J. Solids Struct., 52, 1-18 (2015) |
| [41] | Su, H.; Yan, H.; Jin, B., Finite element method for coupled diffusion-deformation theory in polymeric gel based on slip-link model, Appl. Math. Mech. -Engl. Ed., 39, 581-596 (2018) · Zbl 1390.74055 |
| [42] | Lucantonio, A.; Nardinocchi, P.; Teresi, L., Transient analysis of swelling-induced large deformations in polymer gels, J. Mech. Phys. Solids, 61, 205-218 (2013) |
| [43] | Birgersson, E.; Lib, H.; Wua, S., Transient analysis of temperature-sensitive neutral hydrogels, J. Mech. Phys. Solids, 56, 444-466 (2008) · Zbl 1171.74320 |
| [44] | Han, J.; Jentzen, A.; Weinan, E., Solving high-dimensional partial differential Eq.s using deep learning, Proc. Natl. Acad. Sci. U. S. A., 115, 8505-8510 (2018) · Zbl 1416.35137 |
| [45] | Berg, J.; Nystrom, K., A unified deep artificial neural network approach to partial differential Eq.s in complex geometries, Neurocomputing, 317, 28-41 (2018) |
| [46] | Liu, Z. Y.; Yang, Y. T.; Cai, Q. D., Neural network as a function approximator and its application in solving differential Eq.s, Appl. Math. Mech.-Engl. Ed., 40, 237-248 (2019) · Zbl 1416.65060 |
| [47] | Lu, L.; Meng, X. H.; Mao, Z. P.; Karniadakis, G. E., DeepXDE: A Deep Learning Library for Solving Differential Eq.s, SIAM Rev, 63, 208-228 (2021) · Zbl 1459.65002 |
| [48] | A.D. Drozdov, Equilibrium swelling of core-shell composite microgels, 50 (2015) 1579-1592, doi:10.1007/s11012-015-0107-2. · Zbl 1329.76363 |
| [49] | Herrmann, F.; Wurfel, P., Light with nonzero chemical potential, Am. J. Phys., 73, 717-721 (2005) |
| [50] | Hong, W.; Zhao, X.; Suo, Z., Large deformation and electrochemistry of polyelectrolyte gels, J. Mech. Phys. Solids, 58, 558-577 (2010) · Zbl 1244.82089 |
| [51] | Huggins, M. L., A Revised Theory of High Polymer Solutions, 86, 3535-3540 (1964) |
| [52] | Afroze, F.; Nies, E.; Berghmans, H., Phase transitions in the system poly(N-isopropylacrylamide)/water and swelling behaviour of the corresponding networks, 554, 55 (2000) |
| [53] | Mazaheri, H.; Baghani, M.; Naghdabadi, R., Inhomogeneous and homogeneous swelling behavior of temperature-sensitive poly-(N-isopropylacrylamide) hydrogels, J. Intel. Mat. Syst. Str., 27, 324-336 (2016) |
| [54] | Ricka, J.; Tanaka, T., Swelling of ionic gels: quantitative performance of the Donnan theory, 17, 2916-2921 (1984) |
| [55] | Dulkeith, E.; Niedereichholz, T.; Klar, T. A.; Feldmann, J.; Von Plessen, G.; Gittins, D. I.; Mayya, K. S.; Caruso, F., Plasmon emission in photoexcited gold nanoparticles, 70 (2004) |
| [56] | Richardson, H. H.; Carlson, M. T.; Tandler, P. J.; Hernandez, P.; Govorov, A. O., Experimental and Theoretical Studies of Light-to-Heat Conversion and Collective Heating Effects in Metal Nanoparticle Solutions, 9, 1139-1146 (2009) |
| [57] | Kang, B.; Dai, Y. D.; Shen, X. H.; Chen, D., Dynamical modeling and experimental evidence on the swelling/deswelling behaviors of pH sensitive hydrogels, Mater. Lett., 62, 3444-3446 (2008) |
| [58] | Seelenmeyer, S.; Deike, I.; Rosenfeldt, S.; Norhausen, C.; Dingenouts, N.; Ballauff, M.; Narayanan, T.; Lindner, P., Small-angle x-ray and neutron scattering studies of the volume phase transition in thermosensitive core-shell colloids, J. Chem. Phys., 114, 10471-10478 (2001) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
