Concurrent reaction and diffusion in photo-responsive hydrogels

A hydrogel is a polymer network dispersed in an aqueous solvent. A hydrogel with photo-reactive molecules bonded on the polymer network can change its volume in response to light. The light triggers a chemical reaction of the photo-reactive molecules, for example the photo-isomerization of spirobenzopyran, and alters the interaction parameter between the polymer network and the solvent molecules, which drives the diffusion of the solvent molecules, inducing a volumetric change of the hydrogel. The photo-response kinetics of the hydrogel is governed by concurrent reaction and diffusion. In this paper, we establish a theoretical framework to describe the constitutive behavior of photo-responsive hydrogels based on non-equilibrium thermodynamics. The framework, coupling deformation of hydrogels with diffusion of solvent molecules and reaction of photo-reactive molecules, allows us to predict the spatiotemporal response of photo-responsive hydrogels under light and in the dark. We show the significantly different photo-response kinetics, including reaction-limited, diffusion-limited, and reaction-diffusion coupling processes, with constrained and free swelling of a hydrogel thin film as examples. Particularly, we demonstrate how slow diffusion postpones the onset of post-illumination kinetic response of a photo-responsive hydrogel in the dark. This framework provides us understanding and design guidelines for photo-responsive hydrogels.