Projected free energies for polydisperse phase equilibria

TL;DR

This paper introduces a robust method for simplifying the analysis of polydisperse systems by projecting their infinite-dimensional free energy onto a finite set of moments, enabling accurate phase behavior predictions.

Contribution

It presents a rational procedure for projecting infinite-dimensional free energy surfaces onto finite moments, improving phase behavior analysis in polydisperse systems.

Findings

Exact cloud, shadow, and spinodal curves when free energy depends only on chosen moments

Multi-phase regions are approximable and can be refined by adding moments

The method offers new geometrical insights into polydisperse thermodynamics

Abstract

A `polydisperse' system has an infinite number of conserved densities. We give a rational procedure for projecting its infinite-dimensional free energy surface onto a subspace comprising a finite number of linear combinations of densities (`moments'), in which the phase behavior is then found as usual. If the excess free energy of the system depends only on the moments used, exact cloud, shadow and spinodal curves result; two- and multi-phase regions are approximate, but refinable indefinitely by adding extra moments. The approach is computationally robust and gives new geometrical insights into the thermodynamics of polydispersity.