Dependence of stiffness on water content in hydrogels: A statistical mechanics-based framework

Hydrogels are polymers that can uptake large amounts of water within their molecular network. Thanks to their physical, chemical, and mechanical properties, which are close to those of biological materials, hydrogels can be conveniently employed in a variety of fields, ranging from soft robots to biomedical applications. The microstructure of dry hydrogels comprises chains that are chemically cross-linked and interact with one another through intermolecular hydrogen bonds. In the present paper, we derive a model that describes the influence of water content on the overall stiffness of hydrogels. Broadly, water uptake in a hydrogel has three main consequences: (1) the presence of (compliant) liquid which softens the gel, (2) the stretching of the chains to accommodate water molecules leads to entropic stiffening, and (3) water molecules dissociate intermolecular bonds, resulting in entropic gain and significant softening. In this work, we derive a microscopically motivated model that accounts for these three effects and captures the influence of water molecules on the stiffness of hydrogels. To validate the model, we perform compression tests on superabsorbent polymers that swell to >100 times in volume and employ Hertzian contact theory to determine the stiffness. The model is in agreement with the experimental findings. To enable one to control the mechanical properties, we employ the model to investigate the role of pertinent microscopic quantities such as chain length and the number of intermolecular hydrogen bonds on the overall stiffness. The findings from this work pave the way to the microstructural design of hydrogels with tunable water content dependent stiffness.