A constitutive model that couples light propagation direction and deformation for photo-responsive polymers and polymeric gels

Light serves a pivotal function in polymer systems, creating a dynamic interplay with the materials. It initiates various photochemical processes such as polymerization, phase transitions, photo-isomerization, photo-ionization, etc, endowing the polymers with diverse functionalities. Concurrently, as these materials undergo the changes, their shape and optical properties evolve, which also change the light behaviors in terms of reflection, refraction, and propagation. This mutual interaction is intricate and can lead to novel phenomena. Understanding this complex coupling is crucial for generating new insights and paves the way for innovative design possibilities. In this study, we combine principles of geometrical optics with a nonlinear chemomechanical theory to investigate the interdependent effects of light direction and polymer behavior, including reactions and deformations. We apply this framework to a photo-responsive hydrogel, comparing simulation with experimental results to extract necessary material properties and using the calibrated model to propose a new design of an optical fiber actuator through simulations. This example highlights how the interaction between light direction and the hydrogel’s photo-induced swelling governs actuation, and we discuss strategies to leverage this understanding for enhanced control and functionality of such devices. Additionally, we employ the model to analyze the growth morphology of the photo-responsive hydrogel, offering a detailed examination of how these interactive forces contribute to the gel’s photo-induced morphological evolution.