Constitutive model of salt concentration-sensitive hydrogel

Salt concentration-sensitive hydrogel is a material that not only has potential in novel applications of mechanical engineering, but also is very common in nature. Several theoretical studies of this type of hydrogel have been conducted in the past several years. However, existing research on the theory of salt concentration-sensitive hydrogel usually assumes the concentration of the solution to be independent of the deformation, ignoring the fact that correlations exist between them. In this study, we present a theory of salt concentration-sensitive hydrogel aiming at predicting its deformation behavior by linking the concentration of the solution with the deformation based on Donnan equilibrium and large-deformation theory. To address the difficulties raised by the process of free-energy differentiation, a mathematical method to obtain stress without the aforementioned assumption is developed. Then, two typical cases, namely a free-swelling case and a constrained-swelling case, are studied to demonstrate the usefulness of this theory. We also compare the present theory with existing ones to emphasize the suitability of the present theory for the salt concentration-sensitive hydrogel. Furthermore, because of the novel mathematical process, the present theory can be realized with the finite-element method (FEM), whose results are then compared with the analytical results. Finally, to verify the robustness of the FEM formulation, we conduct an interesting bilayer swelling experiment, which shows a reasonable agreement with the FEM result. We also compare the theoretical prediction with the experimental data that are available in the literature.