Theoretical prediction of the coordination number, local composition, and pressure-volume-temperature properties of square-well and square-shoulder fluids.
By assuming a Boltzmann distribution for the molecular equilibrium between local and bulk environments, a general model is derived for the prediction of coordination numbers and local compositions of square-well and square-shoulder fluids. The model has no empirical parameter fitted from the data of square-well and square-shoulder fluids, but is valid from the low-density limit to the high-density limit. The applicable width of well or shoulder covers the commonly used range varying from 1.0 to 2.0. The model can accurately predict the coordination numbers of pure square-well and square-shoulder fluids, so the equation of state derived from it is superior to other equations of state based on the existing coordination number models. The model also accurately predicts the local compositions of mixtures in wide ranges of density and size ratio (1.0-8.0), as well as the configuration energy of lattice gases and highly nonideal lattice mixtures. It is remarkable that the model correctly predicts temperature-dependent coordination numbers and local compositions for both equal- and unequal-sized mixtures at close packing, which cannot be predicted by the existing coordination number models. Our derivation demonstrates that the energy parameters in local composition models should represent the potential difference of a molecule between the local and bulk environments, not the pair-interaction potential, and depend on the system conditions and different kinds of pair-interaction parameters. This result is very useful for the development of local composition and activity coefficient models and the mixing rules of equations of state.