  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.
