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Issue 4, 2010
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A theory of constrained swelling of a pH-sensitive hydrogel

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Many engineering devices and natural phenomena involve gels that swell under the constraint of hard materials. The constraint causes a field of stress in a gel, and often makes the swelling inhomogeneous even when the gel reaches a state of equilibrium. This paper develops a theory of constrained swelling of a pH-sensitive hydrogel, a network of polymers bearing acidic groups, in equilibrium with an aqueous solution and mechanical forces. The condition of equilibrium is expressed as a variational statement of the inhomogeneous field. A free-energy function accounts for the stretching of the network, mixing of the network with the solution, and dissociation of the acidic groups. Within a Legendre transformation, the condition of equilibrium for the pH-sensitive hydrogel is equivalent to that for a hyperelastic solid. The theory is first used to compare several cases of homogenous swelling: a free gel, a gel attached to a rigid substrate, and a gel confined in three directions. To analyze inhomogeneous swelling, we implement a finite element method in the commercial software ABAQUS, and illustrate the method with a layer of the gel coated on a spherical rigid particle, and a pH-sensitive valve in microfluidics.

Graphical abstract: A theory of constrained swelling of a pH-sensitive hydrogel

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Article information

20 Aug 2009
23 Nov 2009
First published
26 Jan 2010

Soft Matter, 2010,6, 784-793
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A theory of constrained swelling of a pH-sensitive hydrogel

R. Marcombe, S. Cai, W. Hong, X. Zhao, Y. Lapusta and Z. Suo, Soft Matter, 2010, 6, 784
DOI: 10.1039/B917211D

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