Statistical mechanics in polydisperse systems

Phase coexistence in polydisperse systems is studied far the case when the excess thermodynamic functions depend on only a few moments of a size distribution. A method is devised in which moment densities may be treated as independent thermodynamic density variables. Cloud curves, shadow curves, and thermodynamic stability criteria (spinodals, critical points, etc) are recovered exactly, although the full phase behaviour is inexact. The method gives an interesting geometric insight into the nature of phase separation in polydisperse systems. Polydisperse Flory-Kuggins theory is treated as case study.