Effect of a nearby charge-ordered phase on correlation functions in ionic systems

The charge–charge and number–number correlation functions are investigated using a mean-field density functional for the restricted primitive model (hard-sphere and Coulomb interactions) supplemented with short-ranged attractive forces. The system exhibits phase separation into ion-dilute and ion-dense phases, and the latter phase becomes unstable with respect to charge-ordering along the λ-line. In mean field approximation both the range and the amplitude of the charge-charge correlation function increase as (S−Sλ)−1/2 on the approach to the λ-line, where S=T*/ρ0* and Sλ is the value of S at the λ-line (T* is the reduced temperature and ρ0* is the dimensionless density). The line dividing the phase diagram into regions where the range of charge–charge correlations is longer (shorter) than the range of the number–number correlations is also determined. We argue that the large range and large amplitude of the charge–charge correlation function is consistent with the formation of aggregates (living polymers) observed in simulations of ionic systems.