Combinatorial Entropy and the Statistical Mechanics of Polydispersity

Abstract

A new method to treat statistical mechanics in a polydisperse system is described, applicable when the nonideal part of the free energy depends only on a few moments of a size distribution. A simple entropic contribution to the free energy is identified from combinatorial considerations. Although approximate in the general case, the method obtains the exact spinodal curve, critical points, cloud curve, and shadow curve. Polydisperse Flory-Huggins theory is treated as an example.