Critical charge and density coupling in ionic spherical models

Near-Critical Phase Behavior in Polyelectrolyte Solutions: Effect of Charge Fluctuations

The critical behaviors in polyelectrolyte (PE) solutions are studied by a renormalized Gaussian fluctuation theory. PEs are fully charged linear wormlike chains. The electrostatic interactions are considered in a continuum solvent while ignoring other interactions. The effects of temperature on the criticality are explored in a salt-free polyanion solution, and the effects of salt are explored in a symmetric mixed solution of polycation and polyanion. An unphysical phase coexistence (UPPC), in which a metastable dense phase coexists with an unstable dilute phase, always exists in the phase diagram. In the near-critical region, the UPPC could interfere with the real phase coexistence. The classical critical point is replaced by a "critical line", giving a flat top for the phase diagram. These behaviors are due to the effect of charge fluctuation in the near-critical region. Our results explain why the mean field approach overestimates the critical salt density by about 10% to experimental data in the study of coacervation between oppositely charged PEs.