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Closed-loop liquid-liquid immiscibility in mixture of particles with spherically symmetric interaction

Thermodynamic perturbation theory for central-force (TPT-CF) type of associating potential is used to study the phase behavior of symmetric binary mixture of associating particles with spherically symmetric interaction. The model is represented by the binary Yukawa hard-sphere mixture with additional spherically symmetric square-well associative interaction located inside the hard-core region and valid only between dissimilar species. To account for the change of the system packing fraction due to association we propose an extended version of the TPT-CF approach. In addition to the already known four types of the phase diagram for binary mixtures we were able to identify the fifth type, which is characterized by the absence of intersection of the $λ$-line with the liquid-vapour binodals and by the appearance of the closed- loop liquid-liquid immiscibility with upper and lower critical solution temperatures.