Poroelastic swelling kinetics of thin hydrogel layers: comparison of theory andnbspexperimentPoroelastic swelling kinetics of thin hydrogel layers: comparison of theory andnbspexperimentPoroelastic swelling kinetics of thin hydrogel layers: comparison of theory andnbspexperimentPoroelastic swelling kinetics of thin hydrogel layers: comparison of theory andnbspexperimentPoroelastic swelling kinetics of thin hydrogel layers: comparison of theory andnbspexperimentPoroelastic swelling kinetics of thin hydrogel layers: comparison of theory andnbspexperimentPoroelastic swelling kinetics of thin hydrogel layers: comparison of theory andnbspexperimentPoroelastic swelling kinetics of thin hydrogel layers: comparison of theory andnbspexperimentPoroelastic swelling kinetics of thin hydrogel layers: comparison of theory andnbspexperimentPoroelastic swelling kinetics of thin hydrogel layers: comparison of theory andnbspexperimentPoroelastic swelling kinetics of thin hydrogel layers: comparison of theory andnbspexperimentPoroelastic swelling kinetics of thin hydrogel layers: comparison of theory andnbspexperimentPoroelastic swelling kinetics of thin hydrogel layers: comparison of theory andnbspexperimentPoroelastic swelling kinetics of thin hydrogel layers: comparison of theory andnbspexperimentPoroelastic swelling kinetics of thin hydrogel layers: comparison of theoryand experimentJinhwan Yoon,aShengqiang Cai,bZhigang Suo*band Ryan C. Hayward*aReceived 26th May 2010, Accepted 12th August 2010DOI: 10.1039/c0sm00434kThin poly(N-isopropylacrylamide) (PNIPAM) hydrogels were allowed to swell under two conditions:as freestanding layers and as substrate-attached layers. Through a combination of particle tracking anddefocusing methods, the positions of beads embedded within the gels were monitored over time viafluorescence microscopy, providing a convenient method to track the kinetics of swelling for layers withthicknesses of the order 100 mm. These data are compared with the predictions of linear poroelastictheory, as specialized for polymer gels. This theory, along with a single set of material properties,accurately describes the observed swelling kinetics for both the freestanding and substrate-attachedhydrogels. With the additional measurement of the substrate curvature induced by the swelling of thesubstrate-attached hydrogels, these experiments provide a simple route to completely characterize thematerial properties of the gel within the framework of linear poroelasticity, using only an opticalmicroscope.IntroductionA network of covalently crosslinked polymers may imbibea larger quantity of a solvent, resulting in a polymer gel. The gelbehaves as an elastic solid due to the presence of the polymernetwork, yet can transport matter due to the mobility of thesolvent. These combined solid and liquid attributes lead tounique properties that make gels ubiquitous in nature andengineering. Gels constitute many biological tissues and are usedin diverse applications, such as carriers for drug delivery,1,2actuators and sensors,3,4tissue engineering matrices,5,6andpackers in oilfields.7,8In a polymer gel, deformation of the network and transport ofthe solvent are concurrent processes. While polymer gels arecapable of large deformations that require a non-linear theory toanalyze fully,9–13linear theories have met with remarkablesuccess in describing even moderately large deformations. Onesuch linear theory for polymer gels is due to Tanaka and co-workers.14,15Owing to the assumption of negligible fluiddisplacements, this theory fails to capture some of the mostsalient experimental observations.16–18It has been appreciatedthat concurrent deformation and transport in gels can bedescribed using Biot’s theory of linear poroelasticity, which doesnot suffer from the same limitations.19–25Meanwhile the theoryof Tanaka and co-workers, despite its inadequacies, remains thedominant theory in the literature to describe swelling kinetics ofpolymer gels.26–34This situation stems at least partially from thefact that relatively little work has been done to compare thepredictions of linear poroelastic theory to experiments onswelling kinetics.20In the current article, we seek to fulfill three objectives. First,we reproduce the derivation of Biot’s theory explicitly in terms ofpolymer gels, yielding a set of differential equations that repre-sent a straightforward route to model swelling kinetics for gelswith arbitrary geometries and boundary conditions. Second, weshow that the theory, along with a single set of materialparameters, accurately describes the experimentally measuredswelling kinetics of a poly(N-isopropylacrylamide) (PNIPAM)hydrogel under the two conditions shown in Fig. 1, namely,a thin gel layer undergoing swelling either freely in 3D (subject tono external constraints) or only in 1D due to the constraintimposed by attachment to a rigid substrate. Both of these caseshave previously been analyzed separately in terms of Tanaka’stheory,26–34though we are unaware of any cases where they havebeen considered side-by-side on the same material system toprovide a more stringent validation of the theory. Finally, weshow that these two experiments, combined with a measurementof the substrate curvature induced in the case of 1D swelling,provide a straightforward route to completely characterize thematerial properties of the gel within the framework of linearporoelasticity, yielding the modulus, Poisson’s ratio, andpermeability of the gel. Thus, in addition to establishing theFig. 1 A schematic illustrating the two geometries considered experi-mentally and theoretically here: free three-dimensional swelling andconstrained one-dimensional swelling of thin gel layers (H ¼ 76–504 mm).aDepartment of Polymer Science & Engineering, University ofMassachusetts, Amherst, MA, 01003, USA. E-mail: [email protected]; Tel: +1 413-577-1317bSchool of Engineering and Applied Sciences, Kavli Institute, HarvardUniversity, Cambridge, MA, 02138, USA. E-mail: [email protected]; Tel: +1 617-495-37896004 | Soft Matter, 2010, 6, 6004–6012 This journal is ª The Royal Society of Chemistry 2010PAPER www.rsc.org/softmatter | Soft MatterDownloaded by Harvard University on 30 December 2010Published on 17 November 2010 on http://pubs.rsc.org | doi:10.1039/C0SM00434KView Onlineadequacy of linear poroelasticity to describe swelling kinetics ofpolymer gels, we anticipate that our approach will providea useful tool to