Charged-stabilized colloidal suspensions:: counterion condensation and phase diagrams

The theoretical possibility of fluid-fluid phase separation in systems of charged colloidal suspensions has been previously explored by several researchers. Here we expand upon a previous treatment using the methods of density functional theory, and finding a one-body volume term in the free energy, which affects the system's phase behaviour. We consider the effects of including correlational terms at the level of the local density approximation, and recover the correct limiting behaviour. We find that we may draw connections with the use of McMillan-Mayer electrolyte theory, which elucidates the physical meaning of the volume term. We further consider the effect of explicitly allowing for charge condensation of counterions on the colloids. The resulting state-dependent effective charge of the polyions has a dramatic effect on the resultant phase behaviour, and we predict fluid-fluid phase separation under experimentally accessible conditions.