Non-ideal effects in highly asymmetric ionic mixtures at moderate coupling

A binary mixture of hard-sphere polyions and point-size counterions is considered using the hypernetted-chain equation and the symmetric Poisson–Boltzmann equation. It is shown that such non-ideal effects as the polyion–polyion attraction, counterion association near the polyion surface, and the polyion charge inversion that were noticed mainly in strongly coupled systems with multivalent counterions can appear also at moderate coupling with monovalent counterions. It is proposed to use the change of the sign of the polyion surface potential as an indicator for the polyion charge inversion. Both theories demonstrate the latter effect at moderate coupling. In the case of monovalent counterions, the counterion association appears at higher total ion concentration than the polyion–polyion attraction does. In the case of multivalent counterions, these two effects appear in the opposite order.