A Simple Relation between Stiffness and Swelling of a Hydrogel*

From pasta to biological tissues to contact lenses, gel and gel-like materials inherently soften as they swell with water. In dry, low-relative-humidity environments, these materials stiffen as they de-swell with water. We use semi-dilute polymer theory to develop a simple power-law relationship between hydrogel elastic modulus and swelling. From this relationship, we can predict hydrogel stiffness or swelling at arbitrary relative humidities. This predictive capability can enable more rapid material discovery and selection for hydrogel applications in varying humidity environments.