Delayed oscillation of light-responsive hydrogel layers bonded to a rigid substrate under periodic illumination

The effects of static illumination on light-responsive hydrogels have been widely explored, and understanding their dynamic behavior under periodic illumination is essential for achieving time-programmed functionalities in applications such as soft robotics and controlled drug release. In this work, the dynamic oscillatory behaviors of hydrogel layers bonded to a rigid substrate under periodic illumination are systematically investigated for the first time by theoretical modeling and numerical calculations. Based on the dynamic coupling mechanism of photochemical reaction and solvent diffusion, a nonequilibrium thermodynamic model is established to reveal the influence laws of chemical potential gradient, light intensity distribution and material parameters on the periodic oscillation of hydrogel layer. Numerical results indicate that under periodic illumination, the thickness of the hydrogel layer exhibits periodic variations with a noticeable phase delay relative to the light stimulus, primarily governed by solvent diffusion kinetics. Meanwhile, the effects of material parameters and illumination conditions on the amplitude and equilibrium position of the hydrogel layer are further investigated. Under periodic illumination, the swelling force and hydrogel thickness exhibit synchronized oscillations. By tuning illumination parameters such as intensity, illumination period and illumination time rate, along with material properties like crosslinking density and photosensitive content, it is possible to precisely control the amplitude, equilibrium position, and response time. This study provides a theoretical framework and parametric design strategy for designing light-controlled soft actuators, smart sensors and energy conversion systems.