Suspensions of pairwise repulsive monodisperse spheres are believed to exist in three equilibrium phases: fluid, face-centered cubic (FCC) crystal or body-centered cubic (BCC) crystal. Experiments on charge-stabilized colloidal suspensions have revealed other states and transitions, however, including (controversial ) equilibrium liquid-vapor coexistence [35,36], reentrant solid-liquid transitions , stable voids , and metastable superheated crystals [27,38]. These are most easily explained if the colloidal pair potential includes an attractive component [sogami83,sogami84,tata92,yoshida95,yamanaka98,rajagopalan97,ito92] or if charge-stabilized suspensions develop many-body cohesions [41,42].
Metastable crystals such as the example in Fig. 2.3 are made by forcing the spheres in a low density suspension against glass walls through an as-yet-unexplained electrohydrodynamic instability . An oscillating electric field drives the spheres back and forth electrophoretically while simultaneously creating a surface-driven ion flux through electro-osmosis. Under a limited set of conditions, the interplay of hydrodynamic and electric forces drives spheres out of the bulk of the suspension and toward the walls. The volume fraction near the walls increases until several epitaxial layers of close-packed crystal form. The particular example in Fig. 2.3 consist of polystyrene sulfate spheres of radius (Catalog #5065A, Duke Scientific, Palo Alto, CA) compressed by a 10 V peak-to-peak 60 Hz signal applied across a 1 mm gap in a cell 90 thick and 1 cm wide. Created in deionized water, such compression-generated crystals can have lattice constants extending to more than 3 . The crystals should melt in a matter of seconds once the compressing field is turned off, at a rate limited by diffusion. Indeed, this is what happens  for suspensions whose ionic strength is greater than M. Crystallites in more strongly deionized suspensions, however, can persist for as long as an hour [27,38], their facets and interfacial dynamics attesting to a large stabilizing latent heat . Such metastability cannot arise from the superposition of pair-wise repulsions .
To identify how many-body correlations could induce many-body attractions, Van Roij, Dijkstra and Hansen (vRDH) expanded a charge-stabilized suspensions' free energy functional to lowest non-trivial order in the simple ions' mutual interactions [41,42]. The resulting free energy includes not only a superposition of DLVO-like repulsions but also a many-body cohesion. Failing to account for the simple ions' exclusion from the spheres' volume in this expansion yields the Sogami-Ise result. vRDH use their free energy functional to map out the macroions' phase diagram and, under conditions similar to those reported in Refs.  and , predict crystal-fluid coexistence with an exceptionally large volume fraction contrast. Comparisons with other experiments suggest comparable explanations for void formation and other anomalous bulk phenomena. Despite its apparent success, the vRDH theory is controversial, in part because of concerns regarding the convergence of the expansions involved , and in part because it does not directly explain anomalous attractions measured for confined pairs of spheres.