两性pH敏感凝胶瞬态溶胀问题的基本方程和数值解
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摘要
聚电解质两性凝胶的侧链有可电离的酸性和碱性基团,因其能对所处溶液环境的pH值产生响应,又可称作两性pH敏感凝胶.两性pH敏感凝胶属于超弹性材料,其变形问题涉及力学-化学耦合.同时,由于凝胶的变形伴随着溶剂分子的迁移,导致变形不能瞬间完成,故应研究两性pH敏感凝胶变形发展的全过程.由于其实用价值高,研究难度大,两性pH敏感凝胶的瞬态溶胀问题近年来引起了国内外众多研究人员的关注.本文以非线性连续介质力学理论和孔隙弹性理论为基础,结合电离平衡、唐南平衡等条件,获得了能描述两性pH敏感凝胶材料在外界激励下形变发展全过程的基本方程,探究了外加载荷、溶液pH值、盐溶液浓度等因素对两性pH敏感凝胶瞬态溶胀的影响,所得结果对该材料的应用有一定参考价值.
Amphoteric hydrogel has side chains which contain both ionizable acidic and alkaline groups. It is called amphoteric pHsensitive hydrogel because it can react to the pH value's change of surrounding environment. Amphoteric pH-sensitive hydrogel is a hyperelastic material, and its deformation involves mechanical-chemical coupling. The deformation of hydrogel occurs with the migration of solvent molecules, leading to the fact that the deformation of amphoteric hydrogel cannot be a transient process. Therefore, we should pay attention to the whole process of amphoteric hydrogel's deformation. The problem of amphoteric pHsensitive hydrogel's transient swelling attracts much attention both domestic and abroad because of its difficulty and applicability. In this paper, based on the theory of non-linear continuum mechanics and pore elasticity, we acquired the governing equations which can describe the whole process of amphoteric pH-sensitive hydrogel's deformation under external stimuli, by taking ionization equilibrium and Donnan equilibrium into consideration. In addition, we explored the influence of various factors including external loads, pH values of surrounding solutions and salt concentrations on the transient swelling of amphoteric pH-sensitive hydrogels. The results of our analysis can provide reference for the application of amphoteric hydrogels.
Amphoteric hydrogel has side chains which contain both ionizable acidic and alkaline groups. It is called amphoteric pHsensitive hydrogel because it can react to the pH value's change of surrounding environment. Amphoteric pH-sensitive hydrogel is a hyperelastic material, and its deformation involves mechanical-chemical coupling. The deformation of hydrogel occurs with the migration of solvent molecules, leading to the fact that the deformation of amphoteric hydrogel cannot be a transient process. Therefore, we should pay attention to the whole process of amphoteric hydrogel's deformation. The problem of amphoteric pHsensitive hydrogel's transient swelling attracts much attention both domestic and abroad because of its difficulty and applicability. In this paper, based on the theory of non-linear continuum mechanics and pore elasticity, we acquired the governing equations which can describe the whole process of amphoteric pH-sensitive hydrogel's deformation under external stimuli, by taking ionization equilibrium and Donnan equilibrium into consideration. In addition, we explored the influence of various factors including external loads, pH values of surrounding solutions and salt concentrations on the transient swelling of amphoteric pH-sensitive hydrogels. The results of our analysis can provide reference for the application of amphoteric hydrogels.
引文
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[15]HONG W, ZHAO X, ZHOU J, et al. A theory of coupled diffusion and large deformation in polymeric gels[J].Journal of the Mechanics and Physics of Solids, 2008, 56(5):1779-1793.
[16]ZHANGJ,ZHAOX,SUOZ,etal.Afiniteelementmethodfortransientanalysisofconcurrentlarge deformation and mass transport in gels[J]. Journal of Applied Physics, 2009, 105(9):093522.
[17]TOH W, LIU Z, NG T Y, et al. Inhomogeneous large deformation kinetics of polymeric gels[J]. International Journal of Applied Mechanics, 2013, 05(01):1350001.
[18]TOH W, NG T Y, LIU Z, et al. Deformation kinetics of pH-sensitive hydrogels[J]. Polymer International,2014, 63(9):1578-1583.
[19]TOH W, DING Z, NG T Y, et al. Wrinkling of a polymeric gel during transient swelling[J]. Journal of Applied Mechanics, 2015, 82(6):061004.
[20]HONG W, LIU Z, SUO Z. Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load[J]. International Journal of Solids and Structures, 2009, 46(17):3282-3289.
[21]EDWARDS S F, VILGIS T. The effect of entanglements in rubber elasticity[J]. Polymer, 1986, 27(4):483-492.
[2]DING Z, LIU Z, HU J, et al. Inhomogeneous large deformation study of temperature-sensitive hydrogel[J].International Journal of Solids and Structures, 2013, 50(16-17):2610-2619.
[3]YANH,JINB.EquilibriumswellingofapolyampholyticpH-sensitivehydrogel[J].EuropeanPhysical Journal E, 2013, 36(3):27-33.
[4]HONG W, ZHAO X, SUO Z. Large deformation and electrochemistry of polyelectrolyte gels[J]. Journal of the Mechanics and Physics of Solids, 2010, 58(4):558-577.
[5]HONG S, SYCKS D, CHAN H F, et al. 3D Printing of highly stretchable and tough hydrogels into complex,cellularized structures[J]. Advance Materials, 2015, 27(27):4035-4040.
[6]JAHRENSL,BUTLERMF,ADAMSS,etal.Predictivemodellingoftheswellingbehaviourof polyelectrolytic chitosan hydrogels[J]. Carbohydrate Polymers, 2011, 86(2):769-773.
[7]MARCOMBE R, CAI S, HONG W, et al. A theory of constrained swelling of a pH-sensitive hydrogel[J].Soft Matter, 2010, 6(4):784-793.
[8]BAEKS,SRINIVASAAR.Modelingofthep H-sensitivebehaviorofanionicgelinthepresenceof diffusion[J]. International Journal of Non-Linear Mechanics, 2004, 39(8):1301-1318.
[9]TANAKAT,FILLMOREDJ.Kineticsofswellingofgels[J].TheJournalofChemicalPhysics,1979,70(3):1214-1218.
[10]WALLMERSPERGERT,KELLERK,KR?PLINB,etal.ModelingandsimulationofpH-sensitive hydrogels[J]. Colloid and Polymer Science, 2011, 289(5-6):535-544.
[11]DROZDOVAD.Swellingofp H-responsivecationicgels:constitutivemodelingandstructure-property relations[J]. International Journal of Solids and Structures, 2015, 64-65:176-190.
[12]YANH,JINB.InfluenceofenvironmentalsolutionpHandmicrostructuralparametersonmechanical behavior of amphoteric pH-sensitive hydrogels[J]. European Physical Journal E, 2012, 35(5):36.
[13]YAN H, JIN B, GAO S, et al. Equilibrium swelling and electrochemistry of polyampholytic pH-sensitive hydrogel[J]. International Journal of Solids and Structures, 2014, 51(23-24):4149-4156.
[14]YI C, ZHANG X, YAN H, et al. Finite element simulation and the application of amphoteric pH-sensitive hydrogel[J]. International Journal of Applied Mechanics, 2017, 1750063.
[15]HONG W, ZHAO X, ZHOU J, et al. A theory of coupled diffusion and large deformation in polymeric gels[J].Journal of the Mechanics and Physics of Solids, 2008, 56(5):1779-1793.
[16]ZHANGJ,ZHAOX,SUOZ,etal.Afiniteelementmethodfortransientanalysisofconcurrentlarge deformation and mass transport in gels[J]. Journal of Applied Physics, 2009, 105(9):093522.
[17]TOH W, LIU Z, NG T Y, et al. Inhomogeneous large deformation kinetics of polymeric gels[J]. International Journal of Applied Mechanics, 2013, 05(01):1350001.
[18]TOH W, NG T Y, LIU Z, et al. Deformation kinetics of pH-sensitive hydrogels[J]. Polymer International,2014, 63(9):1578-1583.
[19]TOH W, DING Z, NG T Y, et al. Wrinkling of a polymeric gel during transient swelling[J]. Journal of Applied Mechanics, 2015, 82(6):061004.
[20]HONG W, LIU Z, SUO Z. Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load[J]. International Journal of Solids and Structures, 2009, 46(17):3282-3289.
[21]EDWARDS S F, VILGIS T. The effect of entanglements in rubber elasticity[J]. Polymer, 1986, 27(4):483-492.