Quantifying the trade-off between stiffness and permeability in hydrogels

Hydrogels have a distinct combination of mechanical and water-transport behaviors. As hydrogels stiffen, they become less permeable. Here, we combine semi-dilute polymer theory with the Kozeny-Carman equation to develop a simple scaling law describing the relationship between hydraulic permeability and mechanical stiffness. We find that these properties are dictated by the polymer strand spacing, explained via analogy of a bowl of noodle soup. We find a remarkably close agreement between our scaling law and experimental results across four different polymer families with varied crosslinkings.