Closed-loop phase equilibria of a symmetrical associating mixture of square-well molecules examined by Gibbs ensemble Monte Carlo simulation

A closed loop of liquid-liquid immiscibility for a simple model binary symmetrical mixture of square-well monomers with a single short-ranged interaction site has been recently observed using the Gibbs ensemble Monte Carlo technique [L. A. Davies, G. Jackson, and L. F. Rull, Phys. Rev. Lett. $82,$ 5285 (1999)]. This model system has unfavorable mean-field interactions between unlike components which leads to phase separation at intermediate temperatures; the addition of a directional bonding site leads to association and miscibilty of the system at low temperatures. In this work we present a detailed study of the effect of a variation in pressure and of the strength of the bonding interaction on the phase equilibria of such a model system by Gibbs ensemble simulation. The phase diagram is dominated by regions of liquid-liquid immiscibility which are bounded at high temperatures by an upper critical solution temperature and by a lower critical solution temperature (LCST) for specific values of the pressure and association strength. This closed-loop region is seen to increase in size as the pressure of the system is increased. For weak bonding interaction strengths the system does not possess a LCST and is seen to exhibit regions of two-phase vapor-liquid coexistence which are separated from the region of liquid-liquid immiscibility by a three-phase line. The phase equilibria of the same model system is also determined using the statistical associating fluid theory as adapted for potentials of variable range; the theory provides a good description of the closed-loop immiscibility and other features of the phase diagram.