Abstract
Two decades ago, it has been observed experimentally that hydrogels immersed in a bath solution swells or shrinks under external stimulations (Ric̆ka et al., Macromolecules 17:2916–2921, 1984). Recently, this fact has received renewed interest, since understanding the precise mechanisms underlying that kind of behavior has the potential to tailor most sensitive drug delivery systems based on hydrogels (Segalman and Witkowski, Mater Sci Eng C 2:243–249, 1995). Here we contribute to a precise understanding of the mechanisms responsible for the hydrogels’ swelling kinetics as well as dynamics by proposing for the first time a model approach that can resolve the inherent short-range correlation effects along the hydrogel–solution interface jointly with the long-range ionic transport fields. To that end, we investigate the swelling dynamics of hydrogels, which is a moving boundary problem, by a phase field model, which couples the Nernst–Planck equation for the concentration of mobile ions, Poisson equation for the electric potential, mechanical equation for the displacement, and an equation for the phase field variable. Simulation for two-dimensional case reveals that under the chemical stimulation, the hydrogel will swell or shrink if the concentration of mobile ions inside bath solution decreases or increases. This is in agreement with the experimental results qualitatively and validates our new model approach.








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Qiu Y, Park K (2001) Environment-sensitive hydrogels for drug delivery. Adv Drug Deliv Rev 53:321–339
Kim SJ, Park SJ, Kim SI (2004) Properties of smart hydrogels composed of polyacrylic acid/poly(vinyl sulfonic acid) responsive to external stimuli. Smart Mater Struct 13:317–322
Hirotsu S, Hirokawa Y, Tanaka T (1987) Volume-phase transitions of ionized N-isopropylacrylamide gels. J Chem Phys 87:1392–1395
Kuhn W, Hargitay B, Katchalsky A, Eisenberg H (1950) Reversible dilation and contraction by changing the state of ionization of high-polymer acid networks. Nature 165:514–516
De SK, Aluru NR, Johnson B, Crone WC, Beebe DJ, Moore J (2002) Equilibrium swelling and kinetics of pH-responsive hydrogels: models, experiments, and simulations. J Microelectromech Syst 11:544–555
Ohmine I, Tanaka T (1982) Salt effects on the phase transition of ionic gels. J Chem Phys 77:5725–5729
Tanaka T, Nishio I, Sun ST, Ueno-Nishio S (1982) Collapse of gels in an electric field. Science 218:467–469
Sun S, Mak Arthur FT (2001) The dynamical response of a hydrogel fiber to electrochemical stimulation. J Polym Sci Polym Phys 39:236–246
Zourob M, Ong KG, Zeng K, Mouffouk F, Grimes CA (2007) A wireless magnetoelastic biosensor for the direct detection of organophosphorus pesticides. Analyst 132:338–343
Khaled A, George KK, Amarjeet SB (2006) Photo-responsive hydrogel for controlling flow on a microfluidic chip. In: Proc. SPIE, p 6343
Suzuki A, Tanaka T (1990) Phase transition in polymer gels induced by visible light. Nature 346:345
Houk J, Whitesides GM (1987) Structure–reactivity relations for thiol–disulfide interchange. J Am Chem Soc 109(22):6825–6836
Chatterjee AN, Yu Q, Moore JS, Aluru NR (2003) Mathematical modeling and simulation of dissolvable hydrogels. J Aerosp Eng 16:55–64
Galaev IY, Mattiasson B (1999) Smart polymers and what they could do in biotechnology and medicine. Trends Biotech 17:335–340
Luo XL, Xu JJ, Du Y, Chen HY (2004) A glucose biosensor based on chitosan–glucose oxidase–gold nanoparticles biocomposite formed by one-step electrodeposition. Anal Biochem 334:284–289
Hoffman AS (2002) Hydrogels for biomedical applications. Adv Drug Deliv Rev 54:3–12
Mao L, Hu Y, Piao Y, Chen X, Xian W, Piao D (2005) Structure and character of artificial muscle model constructed from fibrous hydrogel. Curr Appl Phys 5:429–428
Eddington DT, Beebe DJ (2004) Flow control with hydrogels. Adv Drug Deliv Rev 56:199–210
Roy I, Gupta MN (2003) Smart polymeric materials: emerging biochemical applications. Chem Biol 10:1161–1171
Nishizawa K, Shirose T, Itoh O (1981) Disposable diaper. United States Patent 4790836
Zrínyi M, Szilágyi A, Filipcsei G, Fehér J, Szalma J, Móczár G (2001) Smart gel-glass based on the responsive properties of polymer gels. Polym Adv Technol 12:501–505
Wu S, Li H, Chen JP, Lam KY (2004) Modeling investigation of hydrogel volume transition. Macromol Theory Simul 13:13–29
Wallmersperger T, Wittel FK, Kröplin B (2006) Multiscale modeling of polyelectrolyte gels. Smart structures and materials 2006: Electroactive polymer actuators and devices (EAPAD). In: Proceedings of SPIE, vol 6168, 61681H-1
Saunders JR, Abu-Salih S, Khaleque T, Hanula S, Moussa W (2008) Modeling theories of intelligent hydrogel polymers. J Comput Theor Nanosci 5:1942–1960
Kenkare NR, Hall CK, Khan SA (2000) Theory and simulation of the swelling of polymer gels. J Chem Phys 113:404–418
Gilra N, Panagiotopoulos AZ, Cohen C (2001) Monte Carlo simulations of polymer network deformation. Macromolecules 34:6090–6096
Schneider S, Linse P (2003) Monte Carlo simulation of defect-free cross-linked polyelectrolyte gels. J Phys Chem B 107:8030–8040
Aydt EM, Hentschke R (2000) Swelling of a model network: a Gibbs-ensemble molecular dynamics study. J Chem Phys 112:5480–5487
Lu ZY, Hentschke R (2002) Swelling of model polymer networks with different cross-link densities: a computer simulation study. Phys Rev E 66:041803–041810
Nick B, Suter UW (2001) Solubility of water in polymers—atomistic simulations. Comput Theor Polymer Sci 11:49–55
Deshmukh S, Mooney DA, McDermott T, Kulkarni S, Don MacElro JM (2009) Molecular modeling of thermo-responsive hydrogels: observation of lower critical solution temperature. Soft Matter 5:1514–1521
Flory PJ (1953) Principles of polymer chemistry. Cornell University Press, Ithaca
Kovac J (1977) Modified Gaussian model for rubber elasticity. Macromolecules 11:362–365
Anthony JG, William HB (1982) The freely jointed chain in expanded form. J Chem Phys 79:2411–2418
Erman B, Flory PJ (1986) Critical phenomena and transitions in swollen polymer networks and in linear macromolecules. Macromolecules 19:2342
English AE, Mafé S, Manzanares J, Yu X, Grosberg AY (1996) Equilibrium swelling properties of polyampholytic hydrogels. J Chem Phys 104:8713–8720
Maurer G, Prausnitz JM (1996) Thermodynamics of phase equilibrium for systems containing gels. Fluid Phase Equilib 115:113–133
Okay O, Sariisik SB (2000) Swelling behavior of poly(acrylamide-co-sodium acrylate) hydrogels in aqueous salt solutions: theory versus experiments. Eur Polym J 36:393–399
Lai WM, Hou JS, Mow VC (1991) A triphasic theory for the swelling and deformation behaviors of articular cartilage. J Biomech Eng 113:245–259
Huyghe JM, Janssen JD (1997) Quadriphasic mechanics of swelling incompressible porous media. Int J Eng Sci 35:793–802
Sun DN, Gu WY, Guo XE, Lai WM, Mow VC (1999) A mixed finite element formulation of triphasic mechano-electrochemical theory for charged, hydrated biological soft tissues. Int J Numer Methods Eng 45:1375–1402
Hon YC, Lu MW, Xue WM, Zhou X (1999) A new formulation and computation of the triphasic model for mechano-electrochemical mixtures. Comput Mech 24:155–165
Zhou X, Hon YC, Sun S, Mak AFT (2002) Numerical simulation of the steady-state deformation of a smart hydrogel under an external electric field. Smart Mater Struct 11:459–467
Wolgemuth CW, Mogilner A, Oster G (2004) The hydration dynamics of polyelectrolyte gels with applications to cell motility and drug delivery. Eur Biophys J 33:146–158
Ehlers W (2002) Foundations of multiphasic and porous materials. In: Ehlers W, Bluhm J (eds) Porous media: theory, experiments and numerical applications. Springer, Berlin, pp 3–86
Acartürk AY (2009) Simulation of charged hydrated porous materials. ISBN 3-937399-18-6, D 93. Dissertation, Universität Stuttgart
Doi M, Matsumoto M, Hirose Y (1992) Deformation of ionic polymer gels by electric fields. Macromolecules 25:5504–5511
Grimshaw PE, Nussbaum JH, Grodzinsky AJ, Yarmush ML (1990) Kinetics of electrically and chemically induced swelling in polyelectrolyte gels. J Chem Phys 93:4462–4472
De SK, Aluru NR, Johnson B (2002) Equilibrium swelling and kinetics of pH-responsive hydrogels: models, experiments, and simulations. J Microelectron Syst 11:544–555
De SK, Aluru NR (2004) A chemo-electro-mechanical mathematical model for simulation of pH sensitive hydrogels. Mech Mater 36:395–410
Chatterjee AN, Yu Q, Moore JS, Aluru NR (2003) Mathematical modeling and simulation of dissolvable hydrogels. J Aerosp Eng 16:55–64
Segalman DJ, Witkowski WR, Adolf DB, Shahinpoor M (1992) Theory and application of electrically controlled polymeric gels. Smart Mater Struct 1:95–100
Segalman DJ, Witkowski WR (1995) Two-dimensional finite element analysis of a polymer gel drug delivery system. Mater Sci Eng C 2:243–249
Brock D, Lee W, Segalman DJ, Witkowski WR (1994) A dynamic model of a linear actuator based on polymer hydrogel. J Intell Mater Syst Struct 5:764–771
Li H, Ng TY, Yew YK, Lam KY (2005) Modeling and simulation of the swelling behavior of pH-stimulus-responsive hydrogels. Biomacromolecules 6:109–120
Li H, Chen J, Lam KY (2007) Transient simulation of electric-sensitive hydrogels. Biosens Bioelectron 22:1633–1641
Wallmersperger T, Kröplin B, Gülch RW (2004) Coupled chemo-electro-mechanical formulation for ionic polymer gels—numerical and experimental investigations. Mech Mater 36:411–420
Ballhause D, Wallmersperger T (2008) Coupled chemo-electro-mechanical finite element simulation of hydrogels: I. Chemical stimulation. Smart Mater Struct 17:045011
Wallmersperger T, Ballhause D (2008) Coupled chemo-electro-mechanical finite element simulation of hydrogels: II. Electrical stimulation. Smart Mater Struct 17:045012
Emmerich H (2003) The diffuse interface approach in materials science: thermodynamic concepts and applications of phase-field models. Springer, New York, ISBN-10: 3540004165
Wheeler AA, Boettinger WJ, McFadden GB (1992) Phase-field model for isothermal phase transitions in binary alloys. Phys Rev A 45:7427–7439
Ric̆ka J, Tanaka T (1984) Swelling of ionic gels: quantitative performance of the donnan theory. Macromolecules 17:2916–2921
Acknowledgements
This work was supported by DFG SPP 1259: Intelligente Hydrogele, modeling and simulation of hydrogel swelling under strong non-equilibrium conditions using the phase-field and phase-field crystal methods. Daming Li is also supported by National Sciences Foundation of China (Young Scholars; Grant No. 10701056) and Chinese Ministry of Education (No. 108056).
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Li, D., Yang, H. & Emmerich, H. Phase field model simulations of hydrogel dynamics under chemical stimulation. Colloid Polym Sci 289, 513–521 (2011). https://doi.org/10.1007/s00396-011-2381-4
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DOI: https://doi.org/10.1007/s00396-011-2381-4