Characterizing hydrogel behavior under compression with gel-freezing osmometry

Hydrogels are particularly versatile materials that are widely found in both Nature and industry. One key reason for this versatility is their high water content, which lets them dramatically change their volume and many of their mechanical properties – often by orders of magnitude – as they swell and dry out. Currently, we lack techniques that can precisely characterize how these properties change with water content. To overcome this challenge, here we develop Gel-Freezing Osmometry (GelFrO): an extension of freezing-point osmometry. We show how GelFrO can measure a hydrogel’s mechanical response to compression and shrinkage in response to an applied osmotic pressure, while only using small, $O$ ($100\mu$L) samples. Because the technique allows measurement of properties over an unusually wide range of water contents, it allows us to accurately test theoretical predictions. We find simple, power-law behavior for both mechanical and osmotic responses, while these are not well-captured by classical Flory–Huggins theory. We interpret this power-law behavior as a hallmark of a microscopic fractal structure of the gel’s polymer network, and propose a simple way to connect the gel’s fractal dimension to its mechanical and osmotic properties. This connection is supported by observations of hydrogel microstructures using small-angle X-ray scattering. Finally, our results motivate simplifications to common models for hydrogel mechanics, and we propose an updated hydrogel constitutive model.