Bethe-lattice calculations for the phase diagram of a two-state Janus gas

TL;DR

This paper models the phase diagram of two-state Janus particles using a Bethe lattice approach, revealing how directional interactions influence phase behavior and aligning with recent simulation results.

Contribution

It introduces a lattice statistical model employing nonlinear recursion relations to analyze directional interactions in Janus particle fluids on a Bethe lattice.

Findings

Directional interactions significantly affect phase diagrams.

Model results agree with recent numerical simulations.

Recursion relations identify physical solutions on the Bethe lattice.

Abstract

We use a simple lattice statistical model to analyze the effects of directional interactions on the phase diagram of a fluid of two-state Janus particles. The problem is formulated in terms of nonlinear recursion relations along the branches of a Cayley tree. Directional interactions are taken into account by the geometry of this graph. Physical solutions on the Bethe lattice (the deep interior of a Cayley tree) come from the analysis of the attractors of the recursion relations. We investigate a number of situations, depending on the concentrations of the types of Janus particles and the parameters of the potential, and make contact with results from recent numerical simulations.