Thermodynamics of hard-sphere plus square-well trimer fluids. A small mystery

The aim of this work is to show that the thermodynamics of some simple fluids, composed of molecules formed by only three atoms-trimers-presents a challenge when confronted with molecular simulation results. Thermodynamic perturbation theory (TPT), coupled to statistical associating fluid theory (SAFT), has successfully accounted for the properties of quite complicated and realistic fluids, both pure and mixed. It is then surprising that simple fluids, formed by trimers with square-well (SW) and hard-sphere (HS) atoms, reveal severe limitations of such theories. TPT1 and SAFT show how to calculate the free energy of the trimer fluid involving HS and SW atoms. The reference system in TPT-SAFT is a fluid made of isolated atoms. Its free energy is dealt with by the well-known high-temperature expansion (HTE), treated here to the fourth order. The trimerization contribution according to TPT-called the chain term-accounts for the change in free energy as the atoms bind and depends on the cavity function, which is determined here by a novel and consistent procedure. We studied the SW-SW-SW and SW-HS-SW trimers. The main properties analyzed are vapor-liquid (VL) coexistence and critical points. The theory presented here accounts very well for the VL coexistence of the SW-SW-SW trimers but fails for the SW-HS-SW trimer, for which a strong disagreement appears. We analyze the cause of this flaw in the theory and introduce a successful semi-empirical correction to it. The possible cause is pointed out and is currently being investigated.