Fluid-Fluid and Fluid-Solid transitions in the Kern-Frenkel model from Barker-Henderson thermodynamic perturbation theory

TL;DR

This paper applies Barker-Henderson second-order thermodynamic perturbation theory to the Kern-Frenkel model of patchy colloids, accurately predicting phase coexistences and critical lines across a range of coverages, including regimes lacking numerical data.

Contribution

It demonstrates the effectiveness of Barker-Henderson perturbation theory in modeling fluid-fluid and fluid-solid transitions in patchy colloids, especially from full to Janus coverage.

Findings

Accurately predicts phase coexistences compared to Monte-Carlo simulations.

Provides estimates of critical lines in low-coverage regimes.

Highlights advantages over integral equation methods.

Abstract

We study the Kern-Frenkel model for patchy colloids using Barker-Henderson second-order thermodynamic perturbation theory. The model describes a fluid where hard sphere particles are decorated with one patch, so that they interact via a square-well (SW) potential if they are sufficiently close one another, and if patches on each particle are properly aligned. Both the gas-liquid and fluid-solid phase coexistences are computed and contrasted against corresponding Monte-Carlo simulations results. We find that the perturbation theory describes rather accurately numerical simulations all the way from a fully covered square-well potential down to the Janus limit (half coverage). In the region where numerical data are not available (from Janus to hard-spheres), the method provides estimates of the location of the critical lines that could serve as a guideline for further efficient numerical work at these low coverages. A comparison with other techniques, such as integral equation theory, highlights the important aspect of this methodology in the present context.