As an important category of smart materials, stimuli-responsive hydrogels are highly concerned due to their extensive application possibilities and their outstanding biocompatibilities. The ability of responsive hydrogels about significant volume change by external stimuli inspires the design of electronic devices, for example, as sensors and actuators. The modeling of the hydrogel behavior enables the optimization of corresponding applications. In the present research, on the basis of the experimentally determined material parameters, a chemo-poromechanical model was implemented in COMSOL Multiphysics® to investigate the constricted swelling of hydrogels. The swelling kinetics affected by the diffusion coefficient is discussed in detail with numerical simulations.
AcartürkAY (2009) Simulation of charged hydrated porous materials. PhD thesis, Universität Stuttgart.
2.
AlbertyRA (2001) Use of legendre transforms in chemical thermodynamics (IUPAC technical report). Pure and Applied Chemistry. Chimie Pure et Appliquee73(8): 1349–1380.
3.
AnandL (2015) 2014drucker medal paper: A derivation of the theory of linear poroelasticity from chemoelasticity. Journal of Applied Mechanics82(11): 111005.
4.
BeckAObstFGrunerD, et al. (2023) Fundamentals of Hydrogel-Based valves and chemofluidic transistors for Lab-on-a-Chip technology: A tutorial review. Advanced Materials Technologies8: 2200417.
5.
BiotMA (1941) General theory of three-dimensional consolidation. Journal of Applied Physics12(2): 155–164.
6.
BoldiniAPorfiriM (2022) On maxwell stress and its relationship with the dielectric constant in the actuation of ionic polymer metal composites. Journal of the Mechanics and Physics of Solids164: 104875.
7.
BowenRM (1980) Incompressible porous media models by use of the theory of mixtures. International Journal of Science and Engineering18(9): 1129–1148.
8.
BufaloGDPlacidiLPorfiriM (2008) A mixture theory framework for modeling the mechanical actuation of ionic polymer metal composites. Smart Materials and Structures17(4): 045010.
9.
CaseyJ (2011) On the derivation of jump conditions in continuum mechanics. In: Prof. K.R. Rajagopal’s 60th Birthday Volume (Complete). pp. 61–84.
10.
CaseyJ (2015) A remark on the conception of a body in continuum mechanics. Mathematics and Mechanics of Solids20(3): 292–300.
11.
ChanAWNeufeldRJ (2009) Modeling the controllable pH-responsive swelling and pore size of networked alginate based biomaterials. Biomaterials30(30): 6119–6129.
12.
ChesterSAAnandL (2011) A thermo-mechanically coupled theory for fluid permeation in elastomeric materials: Application to thermally responsive gels. Journal of the Mechanics and Physics of Solids59(10): 1978–2006.
13.
ColemanBDNollW (1974) The thermodynamics of elastic materials with heat conduction and viscosity. In: Noll W (ed.) The Foundations of Mechanics and Thermodynamics. Berlin: Springer. pp.145–156.
14.
CusslerEL (ed.) (2009) Diffusion: Mass Transfer in Fluid Systems, 3rd edn. Cambridge Series in Chemical Engineering. Cambridge: Cambridge University Press.
15.
DaiLXiaoR (2021) A thermodynamic-consistent model for the thermo-chemo-mechanical couplings in amorphous shape-memory polymers. International Journal of Applied Mechanics13(02): 2150022.
16.
de BoerR (2000) Theory of Porous Media. Berlin, Heidelberg: Springer.
17.
DissemondJWitthoffMBraunsTC, et al. (2003) PH-wert des milieus chronischer wunden. Der Hautarzt54(10): 959–965.
18.
DonnanFG (1924) The theory of membrane equilibria. Chemical Reviews1(1): 73–90.
19.
DrozdovAD (2015) Swelling of pH-responsive cationic gels: Constitutive modeling and structure–property relations. International Journal of Solids and Structures64–65: 176–190.
20.
EddingtonDTBeebeDJ (2004) Flow control with hydrogels. Advanced Drug Delivery Reviews56(2): 199–210.
21.
EhrkeBErfkampJWallmerspergerT (2022) Experimental investigation of the mechanical behavior of a poly(acrylamide-co-sodium acrylate) hydrogel. Journal of Intelligent Material Systems and Structures33(2): 309–318.
22.
FloryPJ (1942) Thermodynamics of high polymer solutions. The Journal of Chemical Physics10(1): 51–61.
23.
FloryPJRehnerJ (1943a) Statistical mechanics of cross-linked polymer networks i. Rubberlike elasticity. The Journal of Chemical Physics11(11): 512–520.
24.
FloryPJRehnerJ (1943b) Statistical mechanics of cross-linked polymer networks ii. Swelling. The Journal of Chemical Physics11: 521–526.
25.
GanserMHildebrandFEKamlahM, et al. (2019) A finite strain electro-chemo-mechanical theory for ion transport with application to binary solid electrolytes. Journal of the Mechanics and Physics of Solids125: 681–713.
26.
GebhartPWallmerspergerT (2019) A general framework for the modeling of porous ferrogels at finite strains. Journal of the Mechanics and Physics of Solids122: 69–83.
27.
GerlachGArndtKF (2009) Hydrogel Sensors and Actuators: Engineering and Technology, vol. 6. Berlin, Heidelberg: Springer Science & Business Media.
28.
HolzapfelGA (2006) Determination of material models for arterial walls from uniaxial extension tests and histological structure. Journal of Theoretical Biology238(2): 290–302.
29.
HolzMHeilSRSaccoA (2000) Temperature-dependent self-diffusion coefficients of water and six selected molecular liquids for calibration in accurate 1h NMR PFG measurements. Physical Chemistry Chemical Physics: PCCP2(20): 4740–4742.
30.
HongWZhaoXZhouJ, et al. (2008) A theory of coupled diffusion and large deformation in polymeric gels. Journal of the Mechanics and Physics of Solids56(5): 1779–1793.
31.
HuangYMorozovaSMLiT, et al. (2023) Stimulus-responsive transport properties of nanocolloidal hydrogels. Biomacromolecules24: 1173–1183.
32.
HugginsML (1941) Solutions of long chain compounds. The Journal of Chemical Physics9(5): 440–440.
33.
JuHSagleACFreemanBD, et al. (2010) Characterization of sodium chloride and water transport in crosslinked poly(ethylene oxide) hydrogels. Journal of Membrane Science358(1–2): 131–141.
34.
KaessmairSSteinmannP (2018) Computational first-order homogenization in chemo-mechanics. Archive of Applied Mechanics88(1–2): 271–286.
35.
KanamalaMWilsonWRYangM, et al. (2016) Mechanisms and biomaterials in pH-responsive tumour targeted drug delivery: A review. Biomaterials85: 152–167.
36.
LeichsenringPWallmerspergerT (2017) Modeling and simulation of the chemically induced swelling behavior of anionic polyelectrolyte gels by applying the theory of porous media. Smart Materials and Structures26(3): 035007.
37.
LeronniABardellaL (2021) Modeling actuation and sensing in ionic polymer metal composites by electrochemo-poromechanics. Journal of the Mechanics and Physics of Solids148: 104292.
38.
LoretBHueckelTGajoA (2002) Chemo-mechanical coupling in saturated porous media: Elastic–plastic behaviour of homoionic expansive clays. International Journal of Solids and Structures39(10): 2773–2806.
39.
LucantonioANardinocchiPTeresiL (2013) Transient analysis of swelling-induced large deformations in polymer gels. Journal of the Mechanics and Physics of Solids61(1): 205–218.
MazaheriHBaghaniMNaghdabadiR, et al. (2016) Coupling behavior of the pH/temperature sensitive hydrogels for the inhomogeneous and homogeneous swelling. Smart Materials and Structures25(8): 085034.
42.
MooneyM (1940) A theory of large elastic deformation. Journal of Applied Physics11(9): 582–592.
43.
MorlandLW (1972) A simple constitutive theory for a fluid-saturated porous solid. Journal of Geophysical Research77(5): 890–900.
44.
NarayanSAnandL (2022) A coupled electro-chemo-mechanical theory for polyelectrolyte gels with application to modeling their chemical stimuli-driven swelling response. Journal of the Mechanics and Physics of Solids159: 104734.
45.
NguyenVKLeeJWYooY (2007) Characteristics and performance of ionic polymer–metal composite actuators based on nafion/layered silicate and nafion/silica nanocomposites. Sensors and Actuators B Chemical120(2): 529–537.
46.
NinanNForgetAShastriVP, et al. (2016) Antibacterial and anti-inflammatory pH-responsive tannic acid-carboxylated agarose composite hydrogels for wound healing. ACS Applied Materials & Interfaces8(42): 28511–28521.
OkayODurmazS (2002) Charge density dependence of elastic modulus of strong polyelectrolyte hydrogels. Polymer43(4): 1215–1221.
49.
RayNRuppASchulzR, et al. (2018) Old and new approaches predicting the diffusion in porous media. Transport in Porous Media124(3): 803–824.
50.
RichterAPaschewGKlattS, et al. (2008) Review on hydrogel-based pH sensors and microsensors. Sensors8(1): 561–581.
51.
RivlinRS (1948) Large elastic deformations of isotropic materials IV. further developments of the general theory. Philosophical Transactions of the Royal Society of London. Series A: Mathematical and Physical Sciences241(835): 379–397.
52.
RossiMNardinocchiPWallmerspergerT (2019) Swelling and shrinking in prestressed polymer gels: An incremental stress–diffusion analysis. Proceedings of the Royal Society A475(2230): 20190174.
53.
RossiMWallmerspergerTNeukammS, et al. (2017) Modeling and simulation of electrochemical cells under applied voltage. Electrochimica Acta258: 241–254.
54.
ShiYWallmerspergerT (2022) A finite strain chemo-poro-mechanical framework for the chemically stimulated permeation of fluid in polymer gels. Journal of Intelligent Material Systems and Structures33(20): 2564–2577.
55.
SobczykMWiesenhütterSNoennigJR, et al. (2022) Smart materials in architecture for actuator and sensor applications: A review. Journal of Intelligent Material Systems and Structures33(3): 379–399.
56.
SteinmannP (2011) Mechanics and Electrodynamics of Magneto– and Electro-elastic Materials. In: Ogden RW and Steigmann DJ (eds.) CISM International Centre for Mechanical Sciences, vol. 527. Vienna, NY: Springer Vienna. pp.181–230.
57.
TruesdellCNollW (1965) The non-linear field theories of mechanics. In: Antman SS (ed.) The Non-linear Field Theories of Mechanics / Die Nicht-Linearen Feldtheorien der Mechanik. Berlin, Heidelberg: Springer. pp.1–541.
58.
TuranEÇaykaraT (2007) Swelling and network parameters of pH-sensitive poly(acrylamide-co-acrylic acid) hydrogels. Journal of Applied Polymer Science106(3): 2000–2007.
59.
VogelFBustamanteRSteinmannP (2012) On some mixed variational principles in electro-elastostatics. International Journal of Non-Linear Mechanics47(2): 341–354.
60.
WuJWeiWWangLY, et al. (2007) A thermosensitive hydrogel based on quaternized chitosan and poly(ethylene glycol) for nasal drug delivery system. Biomaterials28(13): 2220–2232.
61.
YanN (2017) Ion Transport in Crosslinked AMPS/PEGDA Hydrogel Membranes. Austin: University of Texas at Austin.
62.
ZiaRKPRedishEFMcKaySR (2009) Making sense of the legendre transform. American Journal of Physics77(7): 614–622.
