Thermodynamics of Hydrogels for Applications to Atmospheric Water Harvesting, Evaporation, and Desalination

Most thermodynamic modeling of hydrogels focused on predicting their final volumes in equilibrium with water, built on Flory's theories for the entropy of mixing and rubber elasticity, and Donnan's equilibrium conditions if polyelectrolyte polymer and mobile ions are involved. This work will focus on water and ions in and outside hydrogels, which are of interests in solar interfacial water evaporation for desalination and waste water treatment, atmospheric water harvesting, and forward osmosis. Via a reformulation of Flory's classical hydrogel thermodynamic model by considering a combined system consisting of the hydrogel and its ambient, some confusions in previous work will be clarified. The reformulated thermodynamic model shows clearly the high pressure state of water in hydrogels and the coupling between the osmotic pressure and the Donnan potential. The model is applied to study thermodynamic properties of both pure and salty water in non-electrolyte and electrolyte hydrogels such as (1) the latent heat of evaporation, (2) the ability of hydrogels to retain water and to absorb water from the atmosphere, (3) the use of hydrogels for desalination via solar or forward osmosis, (4) the antifouling characteristics of hydrogels, and (5) melting point suppression and boiling point elevation, and solubility of salts in hydrogels. The reformulated thermodynamic framework will also be useful for understanding polymer electrolytes and ion transport in electrochemical and biological systems.