Phase equilibria of polydisperse colloids

Abstract

A set of colloidal particles (be they sterically or charge-stabilized) can never be made truly identical. They are polydisperse in their sizes (or charges), and their interactions are a function of that property. A truly polydisperse system, in the thermodynamic limit, contains infinitely many species. Therefore, calculations of phase equilibria involve infinitely many coexistence constraints (a difficulty not encountered when determining single-phase properties such as structure factors). This hampers the mathematics, and typically engenders arbitrary, uncontrolled approximations and cumbersome, system-specific results. We construct a formalism which is equally applicable to monodisperse and polydisperse systems, and use it to define a controlled expansion for slightly polydisperse colloids (i.e. those with a narrow size/charge distribution). Thus we provide a complete description of their phase equilibria. The resulting universal law of fractionation is surprisingly concise. For quantitative comparison with a real system, we have performed measurements on a colloid-polymer mixture, using both light scattering and extensive counting of transmission electron micrographs to obtain particle size distributions in coexisting phases. © Springer-Verlag 1999.