Core-shell separation of a hydrogel in a large solution of proteins

Upon absorption of large oppositely charged electrolytes such as proteins, polyionic hydrogels are frequently observed to separate into dense shell-swollen core states. We have developed a theory that in a detailed way takes into account the inhomogeneous swelling and distribution of the protein within such a core-shell separated gel. With this we investigated whether the core-shell separation can be an equilibrium state or if it must be understood as a dynamical phenomenon. Restricting ourselves to spherical gels with an unlimited supply of protein, we found that as an intermediate between a swollen and a collapsed gel the core-shell state can indeed be the one of lowest free energy but this state is not stable. In such cases where formation of a shell could occur spontaneously there was no further thermodynamic barrier to complete collapse of the gel (but possibly dynamical ones). The core-shell separation was favourable in systems of high charge and low ionic strength and was explained, within our theory, by the fact that the energy gain in packing proteins and polyions closely together outweighs the entropy loss of the uneven distribution.