Independent characterization of the elastic and mixing free energy of density of swellable polymer networks

Despite decades of research, it remains challenging to develop accurate constitutive models for swellable polymer networks. The major hurdle here is that the constitutive model of a polymer network involves various physical mechanisms and it is difficult to independently characterize their effects. Then when a constitutive model fails, it is unclear which part of the model should be adjusted. When an adjustment works, it is unclear if it reflects real physics or is merely an overfitting with additional parameters. Here we developed a novel experimental procedure to independently characterize two physical mechanisms that are involved in the swelling of any polymer networks: the elasticity of stretching the polymer chains and the mixing between the polymer and solvent. We used polyacrylamide hydrogel as the model system and showed that the mixing part is accurately described by the classical Flory-Huggins model while the elastic part deviates significantly from the neo-Hookean model or the Flory-Rehner model. Our measurements disprove the common belief that the Flory-Huggins model is responsible for the error of existing constitutive models and points to the new direction to correct the elastic part for swellable polymer networks.