Hydrogels swell when immersed in water, yet existing theories often fail to quantitatively explain experimental observations. This limitation is particularly evident in copolymer hydrogels, which exhibit unusually large swelling ratios far exceeding predictions from the rule of mixtures.
Here, we define this phenomenon as 'hyper-swelling' and quantitatively explain its origin by incorporating counterion condensation and finite stretch limits into an ideal elastomeric gel model. Using osmometry and swelling-dependent shear modulus measurements, we show that increasing the ionic polymer fraction strengthens counterion condensation while reducing the stretch limit of polymer strands. These effects suppress ionic osmotic pressure while enhancing elastic stress during swelling.
Our model captures the hyper-swelling behavior of copolymer hydrogels and provides a quantitative basis for designing hydrogels with programmable swelling properties.