A Deformation-Diffusion-Coupled Constitutive Theory for Hydrogels by Considering the Preparation Conditions

Hydrogels are excellent soft materials that can absorb large amounts of water and have applications ranging from biocompatible sensors to soft robots. Experiments have demonstrated that the equilibrium swelling state of hydrogels strongly depends on their preparation and external conditions, such as the as-prepared water content, cross-linking density, and temperature. However, traditional theories based on Flory's work have failed to capture these dependence effects. In particular, these theories ignore the existence of solvents in the as-prepared state of hydrogels, making them unable to characterize the sensitivity of the swelling and mechanical behaviors to the as-prepared water content. In this study, we propose a constitutive theory that considers the preparation conditions based on statistical thermodynamics. Our theory can precisely predict the swelling ability of hydrogels under diverse preparation conditions and capture the phase transitions of temperature-sensitive hydrogels. We further derived the governing equations for large deformations and solvent diffusion considering their strong coupling effects. Based on our theory, the inhomogeneous deformation-induced solvent migration and delayed fracture of hydrogels were investigated. From theoretical investigations, we revealed the underlying mechanism of these interesting hydrogel behaviors. The theoretical results were further used to guide the design of diverse intelligent structures that can be applied as soft actuators, flexible robots, and morphing the growth of plants.