  We study phase equilibria in a minimal model of charge-regulated polymer
solutions. Our model consists of a single polymer species whose charge state
arises from protonation-deprotonation processes in the presence of a dissolved
acid, whose anions serve as screening counterions. We explicitly account for
variability in the polymers' charge states. Homogeneous equilibria in this
model system are characterised by the total concentration of polymers, the
concentration of counter-ions and the charge distributions of polymers which
can be computed with the help of analytical approximations. We use these
analytical results to characterise how parameter values and solution acidity
influence equilibrium charge distributions and identify for which regimes
uni-modal and multi-modal charge distributions arise. We then study the
interplay between charge regulation, solution acidity and phase separation. We
find that charge regulation has a significant impact on polymer solubility and
allows for non-linear responses to the solution acidity: re-entrant phase
behaviour is possible in response to increasing solution acidity. Moreover, we
show that phase separation can yield to the coexistence of local environments
characterised by different charge distributions and mixture compositions.
