A thermodynamic model of phase transition of poly(N-isopropylacrylamide) hydrogels in ionic solutions

Submerged in an aqueous solution of sodium chloride (NaCl), a poly(N-isopropylacrylamide) (PNIPAM) hydrogel can be in one of two phases: swollen phase and collapsed phase. We measure the equilibrium volume of the hydrogel as a function of temperature T and ionic concentration y. The hydrogel is in the swollen phase when T and y are low, and is in the collapsed phase when T and y are high. We develop a thermodynamic model in which the free energy is a function of volume, temperature, and ionic concentration. The free energy also contains several adjustable parameters, which we best-fit to the experimental data of volume as a function of T and y. For a given pair of T and y, the free energy is a function of volume. This function has a single minimum for some pairs of (T, y), but two minima and a maximum for other pairs of (T, y). In the former, the single minimum corresponds to either a swollen or a collapsed state. In the latter, the lower minimum corresponds to a state of equilibrium, the higher minimum corresponds to a metastable state, and the maximum corresponds to an unstable state. When the two minima are equal, the hydrogel undergoes phase transition. The condition of phase transition is represented as a curve on the (T, y) plane. The thermodynamic model represents the experimental data well.