Glassy-Rubbery Transition-Induced Geometry-Dependent Swelling in Gels

Gel swelling dictates the functionality of gels in biomedical, sensing, and soft robotic systems. Gels can be readily shaped, making geometry a natural parameter for tuning swelling, yet how it regulates swelling dynamics remains poorly understood. Here we show that swelling in glassy polymer gels is inherently geometry-dependent, which introduces a geometric length Λ beyond the classical Fickian diffusion length L (volume-to-surface ratio) for controlling the diffusion process. Using a three-dimensional model applicable to arbitrary geometries, we find that disks swell fastest, spheres slowest, and cylinders in between, with this trend persisting in finite cylinder and tablet-shaped gels. Geometry regulates swelling not by altering solvent diffusion but by dictating mechanical confinement arising from the glassy-rubbery transition, where a glassy core constrains the surrounding rubbery network. These findings establish a physical rather than conventional chemical mechanism for diffusion regulation, offering a new design principle for gel-based systems.