  We study the effects of charge-regulated acid/base equilibrium on the
swelling of polyelectrolyte gels, by considering a combination of the
Poisson-Boltzmann theory and a two-site charge-regulation model based on the
Langmuir adsorption isotherm. By exploring the volume change as a function of
salt concentration for both nano-gels and micro-gels, we identify conditions
where the gel volume exhibits a discontinuous swelling transition. This
transition is driven exclusively by the charge-regulation mechanism and is
characterized by a closed-loop phase diagram. Our predictions can be tested
experimentally for polypeptide gels.
