Quantifying the trade-off between stiffness and permeability in hydrogels

Hydrogels have a distinct combination of mechanical and water-transport behaviors. As hydrogels stiffen when they de-swell, they become less permeable. Here, we combine de Gennes' semi-dilute polymer theory with the Kozeny-Carman equation to develop a simple, succinct scaling law describing the relationship between mechanical stiffness and hydraulic permeability where permeability scales with stiffness to the -8/9 power. We find a remarkably close agreement between the scaling law and experimental results across four different polymer families with varied crosslinkings. This inverse relationship establishes a fundamental trade-off between permeability and stiffness.