Temperature-driven volume transition in hydrogels: Phase-coexistence and interface localization

• The study address the modeling of thermally-driven volume transition in hydrogels accounting for the temperature-depending pattern of the interaction parameter which is known from the literature for both NIPA hydrogels and aqueous solutions of uncrosslinked PNIPAM, and shows a very different dependence on temperature in the two cases.
• The study aims to address the sensitivity of thermally-driven volume transition on the two different pattern.
• Moreover, the study also proposes a detailed analysis aimed to establish the ranges of both temperature and traction (supposed to act on the hydrogel) which allow for the coexistence of two different phases (swollen and shrunken) in the hydrogel. The analysis is developed with reference to a one-dimensional problem.
• Finally, for the values of temperature and traction ensuring phase coexistence, the study also presents a gradient model and localizes the interface position between the shrunk and the swollen phase, on one hand by means of a phase space analysis, previously developed by some of the authors, on the other developing proper finite element numerical calculations.

We study volume transition phenomenon in hydrogels within the framework of Flory–Rehner thermodynamic modelling; we show that starting from different models for the Flory parameter different conclusions can be achieved, in terms of admissible coexisting equilibria of the system. In particular, with explicit reference to a one-dimensional problem we establish the ranges of both temperature and traction which allow for the coexistence of a swollen and a shrunk phase. Through consideration of an augmented Flory–Rehner free-energy, which also accounts for the gradient of volume changes, we determine the position of the interface between the coexisting phases, and capture the connection profile between them.