Distribution functions and equations of state of sticky hard sphere fluids in the percus-yevick approximation

Abstract

The dependence of the different distribution functions (DF) on molecular separation is evaluated for sticky hard sphere (SHS) fluid mixtures in the Percus-Yevick (PY) approximation. The conclusions are generalized to an arbitrary cut-off potential of molecular interactions. Making use of the expression for the DF, the different routes to obtain the equation of state, the gas-liquid equilibrium properties and the critical parameters in SHS fluids are examined. In particular, a new equation of state is derived by the use of a recent generalization to the zero-separation (ZS) theorem. It is found that the ZS equation of state is comparable to the energy and the compressibility equations of state (the virial equation does not describe a gas-liquid equilibrium), although for hard spheres (HS), the ZS equation of state is inferior to all other routes, and thus it is recommended to further investigation. We show that the PY theory is consistent with the usual conditions of the thermodynamic stability of an arbitrary binary mixture (with any potential of molecular interactions). The physically admissible states and the critical properties of two binary SHS systems of special type are considered carefully,. It is found that the critical locus of the mixture with a strong attraction between unlike molecules goes first through a temperature and subsequently through a pressure maximum, resembling thus the van der Waals fold theory. For mixtures where one of the components might be described by the HS model (e.g. helium containing mixtures), the pressure-temperature projection of the critical line beginning at the critical point of the less volatile component, immediately tends to higher temperature and pressures.