MOLECULAR PHYSICS, 1985, VOL. 56, No. 2,385-397 Validity of the high temperature approximation and influ- ence of polydispersity on the phase separation in charged colloidal dispersions by J. P. HANSEN Laboratoire de Physique Thborique des Liquides Universitb Pierre et Marie Curie, 75230 Paris Cedex 05, France, and Ecole Normale Supbrieure, 92211 Saint-Cloud, France L. REATTO and M. TAU Dipartimento di Fisica, Universit~ degli Studi, Parma, Italy and J. M. VICTOR Laboratoire de Physique Th~orique des Liquides (Equipe associbe au CNRS), Universitb Pierre et Marie Curie, 75230 Paris Cedex 05, France (Received 15 May 1985 ; accepted 22 May 1985) A recent perturbation calculation predicting a 'liquid-gas' phase separa- tion of charge-stabilized colloidal suspensions is tested against the thermody- namically self-consistent generalized mean spherical approximation. A comparison between the two calculations shows that the perturbation calcu- lation predicts a reasonably accurate critical temperature, but overestimates the critical density. These critical parameters are moreover shown to be rather insensitive to moderate degrees of polydispersity. 1. INTRODUCTION It has recently been suggested on theoretical grounds that charge-stabilized, aqueous dispersions of large colloidal particles in the presence of added salt may undergo a phase separation into a low concentration 'gas' phase and a high con- centration 'liquid' phase below some critical temperature [1, 2]. This phase tran- sition is likely to be related to the 'weak' (reversible) flocculation which has been observed experimentally [3] under conditions close to those predicted by theory. Similar transitions have been predicted to occur in weakly charged micro- emulsions [4] and have been observed in dispersions of silica particles with grafted polymer layers [22]. The phase separation predicted for colloidal dispersions is obviously closely related to the usual liquid-gas transition of simple atomic or molecular fluids. However, quite apart from the considerable difference in size (three orders of magnitude) and the fact that the colloidal phase separation takes place in an aqueous medium (treated as a continuum), there are specific features which dis- tinguish systems of interacting colloidal particles from their atomic or molecular counterparts. First, while atoms or molecules of a given chemical species are identical, colloidal particles, like polystyrene spheres, are characterized in practice