Weakly polydisperse systems: Perturbative phase diagrams that include the critical region

TL;DR

This paper develops a perturbative approach to analyze the phase diagrams of weakly polydisperse systems, accurately capturing critical behavior and explaining the proximity of critical points to cloud and shadow curve maxima.

Contribution

It introduces a generalized perturbative method that remains well-behaved near critical points, improving understanding of polydisperse phase equilibria.

Findings

Perturbative approach accurately predicts phase behavior near critical points.

Explains the location of the critical point near maximum cloud and shadow curves.

Provides qualitative insights into polydisperse phase diagrams.

Abstract

The phase behaviour of a weakly polydisperse system, such as a colloid with a small spread of particle sizes, can be related perturbatively to that of its monodisperse counterpart. I show how this approach can be generalized to remain well-behaved near critical points, avoiding the divergences of existing methods and giving access to some of the key qualitative features of polydisperse phase equilibria. The analysis explains also why in purely size polydisperse systems the critical point is, unusually, located very near the maximum of the cloud and shadow curves.