Quantifying the trade-off between stiffness and permeability in hydrogels

TL;DR

This paper develops a scaling law linking the stiffness and permeability of hydrogels, validated across multiple polymer types, revealing how polymer structure influences water transport and mechanical properties.

Contribution

It introduces a simple, physics-based scaling law combining polymer theory and the Kozeny-Carman equation to quantify the stiffness-permeability trade-off in hydrogels.

Findings

The scaling law accurately predicts permeability across different hydrogels.

Polymer strand spacing governs the relationship between stiffness and permeability.

Experimental data from four polymer families confirms the model's validity.

Abstract

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.