Two-patch colloidal model with re-entrant phase behaviour

We propose a second-order thermodynamic perturbation theory for a hard-sphere patchy colloidal model with two doubly bondable patches of type A and B. AB bonding results in the formation of a three-dimensional network of the particles and AA and BB bonding promotes chain formation. The theory is applied to study the phase behaviour of the model at different values of the potential model parameters. Competition between network and chain formation gives rise to a re-entrant phase behaviour with upper and lower critical points. The model with an additional van der Waals type of interaction may have a re-entrant phase diagram with three critical points and two separate regions of the liquid-gas phase coexistence. We analyze our results in terms of the fractions of the particles in different bonding states and conclude that re-entrant phase coexistence can be seen as a coexistence between a gas phase rich in chain ends and a liquid phase rich in branch points.