Phase coexistence in the hard-sphere Yukawa chain fluid with chain length polydispersity: High temperature approximation

High temperature approximation (HTA) is used to describe the phase behavior of polydisperse multi-Yukawa hard-sphere chain fluid mixtures with chain length polydispersity. It is demonstrated that in the frames of the HTA the model belongs to the class of ``truncatable free energy models'', i.e. the models with thermodynamical properties (Helmholtz free energy, chemical potential and pressure) defined by the finite number of generalized moments. Using this property we were able to calculate the complete phase diagram (i.e., cloud and shadow curves as well as binodals) and chain length distribution functions of the coexisting phases.Comment: 18 pages, 13 figure

Two- and three-phase equilibria in polydisperse Yukawa hard-sphere mixture. High temperature and mean spherical approximations

Phase behavior of the Yukawa hard-sphere polydisperse mixture with high degree of polydispersity is studied using high temperature approximation (HTA) and mean spherical approximation (MSA). We have extended and applied the scheme developed to calculate the phase diagrams of polydisperse mixtures described by the truncatable free energy models, i.e., the models with Helmholtz free energy defined by the finite number of the moments of the species distribution function. At high degree of polydispersity, several new features in the topology of the two-phase diagram have been observed: the cloud and shadow curves intersect twice and each of them forms a closed loop of the ellipsoidal-like shape with the liquid and gas branches of the cloud curve almost coinciding. Approaching a certain limiting value of the polydispersity index, the cloud and shadow curves shrink and disappear. Beyond this limiting value, polydispersity induces the appearance of the three-phase equilibrium at lower temperatures. We present and analyze corresponding phase diagrams together with distribution functions of three coexisting phases. In general, good agreement was observed between predictions of the two different theoretical methods, i.e., HTA and MSA. Our results confirm qualitative predictions for the three-phase coexistence obtained earlier within the framework of the van der Waals approach.Comment: 15 pages, 4 figure

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 $\lambda$-line with the liquid-vapour binodals and by the appearance of the closed- loop liquid-liquid immiscibility with upper and lower critical solution temperatures.Comment: 11 pages, 5 figure

Second-order Barker-Henderson perturbation theory for the phase behavior of polydisperse Morse hard-sphere mixture

We propose an extension of the second-order Barker-Henderson perturbation theory for polydisperse hard-sphere multi-Morse mixture. To verify the accuracy of the theory, we compare its predictions for the limiting case of monodisperse system, with predictions of the very accurate reference hypernetted chain approximation. The theory is used to describe the liquid-gas phase behavior of the mixture with different type and different degree of polydispersity. In addition to the regular liquid-gas critical point, we observe the appearance of the second critical point induced by polydispersity. With polydispersity increase, the two critical points merge and finally disappear. The corresponding cloud and shadow curves are represented by the closed curves with 'liquid' and 'gas' branches of the cloud curve almost coinciding for higher values of polydispersity. With a further increase of polydispersity, the cloud and shadow curves shrink and finally disappear. Our results are in agreement with the results of the previous studies carried out on the qualitative van der Waals level of description.Comment: 13 pages, 4 figure