Thermodynamics of phase equilibrium for systems containing gels

A gel is a three-dimensional cross-linked elastic polymer. When a gel is immersed into a liquid, it can swell, similar to a sponge. If the surrounding liquid is a solute-containing solution, a solute partitions between the gel and the surrounding liquid. This work derives the fundamental equations of phase equilibrium for such systems. These equations take into account the elastic properties of the gel. Criteria are given for the distribution of solutes between a gel and a coexisting liquid phase. Criteria are also presented for calculating three-phase equilibria where a swollen gel and a collapsed gel coexist with the surrounding liquid. Attention is given to a slightly ionized gel (polyelectrolyte) surrounded by a dilute aqueous electrolyte solution. The equations of equilibrium show that, when Donnan equilibria are taken into account, the pH inside the gel is not equal to that of the surrounding aqueous solution. The discussion presented here may be useful for design of gels used in medicine, pharmacy and biotechnology.