A thermodynamically-consistent large deformation theory coupling photochemical reaction and electrochemistry for light-responsive gels

Abstract Gels are composed of crosslinked polymer network and solvent molecules. When the main chain network is incorporated with functional groups that can undergo photo-chemical reaction upon light irradiation, the gel becomes light-responsive. Under irradiation, the photosensitive groups may undergo photo-ionization process and generate charges that are attached to the main chain or diffuse into the solvent. The newly generated ions disturb the osmotic balance of the gel medium. As a result, water molecules and mobile ions will be driven into or out of the network to compensate the osmotic imbalance, which will eventually lead to macroscopic swelling or shrinking of the gel. In this work, we develop a rigorous nonequilibrium thermodynamic framework to study the coupled photo-chemo-electro-mechanical responses of the photo-ionizable gels. We first discuss the mathematical descriptions of the light propagation and photo-induced chemical reactions inside the gel, as well as the equations governing the kinetics of the photo-chemical reactions. We then explore the consequences of the fundamental laws of thermodynamics in deriving the governing equations of the photo-ionizable gels. The continuous light irradiation drives the gel system towards a new thermodynamic stationary state that is away from equilibrium and is accompanied by energy dissipation. Next, we focus on the photo stationary state of the gel and explore the consequences of the continuous irradiation on the mechanical response of the gel in both optically thin and optically thick configurations. In the optically thin cases, we quantitatively compare the theoretical prediction with experimental data available in the literature. In one example, we show that the model can quantitatively capture the photo-tunable volume-phase transition of the Poly(N-isopropylacrylamide) (PNIPAM) gel grafted with photo-responsive triphenylmethane leucocyanide groups. In another example, we show that the model can quantitatively study the effect of salt concentration and pH value of the external solution on the photo-induced swelling of the polyacrylamide gels incorporated with triphenylmethane leucohydroxide groups. Finally, for the optically thick gels, we develop a finite element code to study their inhomogeneous deformations due to the light attenuation. This work will be of great importance for precise control and optimal design of photo-ionizable gels in future applications.