Dual Polyacrylamide-Based Ionic Cross-Linked Hydrogels: Linear Rheology and Fractional Calculus Modeling

Hydrogels are increasingly recognized as a versatile platform for applications spanning from tissue engineering to soft robotics or flexible electronics. Recent efforts have focused on enhancing and tailoring their mechanical performance to meet application-specific demands. However, the intricate viscoelastic response of hydrogels remains challenging to capture using conventional phenomenological models. In this study, we prepared a series of tough dual cross-linked hydrogels─poly(methacrylamide-co-acrylic acid)-Fe3+ and systematically tuned their mechanical properties by leveraging the salting-out effect. The viscoelastic behavior of the hydrogels was characterized under shear deformations, and a three-parameter fractional Maxwell Gel (FMG) model was constructed to quantitatively describe oscillatory shear, creep, and stress relaxation responses. The influence of salt concentration on each FMG parameter was analyzed and correlated with bulk mechanical performance. This framework provides a first step toward capturing the complex viscoelastic nature of the advanced hydrogels and lays the foundation for developing more comprehensive nonlinear constitutive models.