  Complex coacervation, known as the liquid-liquid phase separation of
solutions with oppositely charged polyelectrolytes, has attracted substantial
interest in recent years. We study the effect of charge regulation (CR)
mechanism on the complex coacervation, by including short-range interactions
between the charged sites on the polymer chains, as well as an
association-dissociation energy parameter in the CR mechanism. We investigate
the phase diagrams of two CR models: (i)~the hopping CR model (HCR); and,
(ii)~the asymmetric CR model (ACR). It is shown that during the phase
separation, the polymers in the condensed phase are more charged than in the
dilute phase, in accord with the Le Chatelier's principle. In addition,
"secondary CR" effects also influence the change in the volume fraction of the
two phases. The latter can cause the charge difference between the two phases
to change non-monotonically as a function of the CR parameters. These
predictions are subject to future experimental verifications.
