We develop a thermodynamic description of particles held at a fixed surface potential. This
system is of particular interest in view of the continuing controversy over the possibility of
a fluid–fluid phase separation in aqueous colloidal suspensions with monovalent
counterions. The condition of fixed surface potential allows one in a natural way to
account for the colloidal charge renormalization. In a first approach, we assess
the importance of the so called 'volume terms' and find that in the absence of
salt, charge renormalization is sufficient to stabilize the suspension against a
fluid–fluid phase separation. The presence of salt, on the other hand, is found to
lead to an instability. A very strong dependence on the approximations used,
however, puts the reality of this phase transition in serious doubt. To further
understand the nature of the instability we next study a jellium-like approximation,
which does not lead to a phase separation and produces a relatively accurate
analytical equation of state for deionized suspensions of highly charged colloidal
spheres. A critical analysis of various theories of strongly asymmetric electrolytes is
presented, to assess their reliability as compared to the Monte Carlo simulations.