Wertheim perturbation theory: thermodynamics and structure of patchy colloids

TL;DR

This paper critically examines Wertheim's perturbation theory applied to patchy colloids, demonstrating its effectiveness in predicting phase diagrams and structural properties of complex associating fluids with a focus on self-assembling colloidal suspensions.

Contribution

The study extends Wertheim's theory to complex patchy colloids, establishing its consistency and providing analytical expressions for structural properties and phase behavior.

Findings

The theory offers a stable and consistent description of patchy colloids.

A new analytical expression for the structure factor is proposed.

The valence from thermodynamics matches structural predictions in the one-site case.

Abstract

We critically discuss the application of the Wertheim's theory to classes of complex associating fluids that can be today engineered in the laboratory as patchy colloids and to the prediction of their peculiar gas-liquid phase diagrams. Our systematic study, stemming from perturbative version of the theory, allows us to show that, even at the simplest level of approximation for the inter-cluster correlations, the theory is still able to provide a consistent and stable picture of the behavior of interesting models of self-assembling colloidal suspension. We extend the analysis of a few cases of patchy systems recently introduced in the literature. In particular, we discuss for the first time in detail the consistency of the structural description underlying the perturbative approach and we are able to prove a consistency relationship between the valence as obtained from thermodynamics and from the structure for the one-site case. A simple analytical expression for the structure factor is proposed.