Re-entrant phase behavior for systems with competition between phase separation and self-assembly

In patchy particle systems where there is a competition between the self-assembly of finite clusters and liquid-vapor phase separation, re-entrant phase behavior can be observed, with the system passing from a monomeric vapor phase to a region of liquid-vapor phase coexistence and then to a vapor phase of clusters as the temperature is decreased at constant density. Here, we present a classical statistical mechanical approach to the determination of the complete phase diagram of such a system. We model the system as a van der Waals fluid, but one where the monomers can assemble into monodisperse clusters that have no attractive interactions with any of the other species. The resulting phase diagrams show a clear region of re-entrance. However, for the most physically reasonable parameter values of the model, this behavior is restricted to a certain range of density, with phase separation still persisting at high densities.