The effect of polydispersity on colloidal phase transitions

A polydisperse mixture of hard spheres with a continuous range of sizes is a simple model of many colloidal suspensions. A well-known example [1] is poly(methyl methacrylate) (PMMA) stabilised by a thin polymeric layer of poly(12-hydroxystearic acid) and dispersed in a good solvent such as decalin. The colloidal particles in this suspension interact via a short-range repulsion, which is well represented by a hard-sphere interaction. While many of the properties of uniform hard spheres have been known for at least 30 years our understanding of polydisperse mixtures is much less developed. Most of the theoretical e€ort to date has concentrated on exploring the consequences of polydispersity for scattering [2]. In contrast, virtually no theoretical work on polydisperse phase diagrams has been reported (until recently [3±9]) despite the fact that many industrial products are frequently very polydisperse. It is, however, clear that as soon as a suspension is allowed to enjoy a signi®cant degree of polydispersity several interesting new phenomena arise. First, increasing polydispersity can suppress certain phase transitions. For instance, the ̄uid±crystal phase transitions reported in dispersions of latex particles of PMMA are only found if the particles have a narrow range of sizes. Pusey reported [1] that while PMMA spheres with a polydispersity, r, of about 0.075 displayed a ̄uid± crystal transition similar to that reported for identically sized hard spheres, on increasing r to about 0.12 no crystallites were found even after several months of observation. Second, those transitions which still remain in polydisperse systems are frequently accompanied by a fractionation of the particle size distribution between coexisting phases [7]. Finally, polydispersity can induce new transitions, not found for monodisperse systems [8]. Despite both the practical importance and the potential richness of polydisperse phase behaviour, the mathematical complexity of treating a mixture with essentially an in®nite number of components makes a ®rst-principles determination of a polydisperse phase diagram a formidable task. We examine a simple model for a system of polydisperse hard spheres with the aim of developing some generic insight into the thermodynamics of polydisperse transitions. We calculate the phase Progr Colloid Polym Sci (2000) 115 : 137±140 Ó Springer-Verlag 2000 POLYMER COLLOID AND SOLID PARTICLES