Liquid-liquid phase separation has emerged as one of the important paradigms
in the chemical physics as well as biophysics of charged macromolecular
systems. We elucidate an equilibrium phase separation mechanism based on charge
regulation, i.e., protonation-deprotonation equilibria controlled by pH, in an
idealized macroion system which can serve as a proxy for simple coacervation.
First, a low-density density-functional calculation reveals the dominance of
two-particle configurations coupled by ion adsorption on neighboring macroions.
Then a binary cell model, solved on the Debye-H\"uckel as well as the full
nonlinear Poisson-Boltzmann level, unveils the charge-symmetry breaking as
inducing the phase separation between low- and high-density phases as a
function of pH. These results can be identified as a charge symmetry broken
complex coacervation between chemically identical macroions.Comment: 11 pages, 7 figure