A nonequilibrium thermodynamics approach to the transient properties of hydrogels

Abstract

A polymer network can imbibe copious amounts of water and swell, and the resulting state is known as a hydrogel. In many potential applications of hydrogels, such as ionic cables, stretchable conductors, and fire resistance materials, the properties of hydrogels may change in response to the environment stimuli. However, existing researches about the transient properties of hydrogels usually treat different physical processes (mass diffusion, heat transportation, electric conduction, etc.) separately, ignoring the fact that there exist correlations between them. In the present work, from the point of view of nonequilibrium thermodynamics, the coupled non-linear governing equations for the transient properties of hydrogels are derived. Instead of writing the free energy of hydrogels as a combination of the stretching of polymer networks and mixing with solvent, we derive the free energy in the form of swelling of hydrogels plus stretching of the swollen hydrogels, which is a function of water content and stretch ratio of hydrogels under external forces or constraints. Chemical potential and total deformation of polymer networks are the fundamental parameters to characterize hydrogel states in many previous research. These are hard to determine, and we are less interested in these parameters. The new form of free energy is more suitable to be used in the laboratory or for the application of hydrogels in real situations, and its physical meaning is clearer. At last, a numerical simulation of the drying process of a hydrogel film attached on a substrate is carried out based on the governing equations and free energy. The transient water content distribution, temperature profile and stress field are investigated, which may provide a guide to the diverse applications of hydrogels.