Jiawen Hu

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.

A general local composition and coordination number model for square-well fluids with variable well width and diameter ratio

A radial distribution function for attractive hard-core systems is obtained from the equilibrium of a molecular pair between local and bulk environments. With this function, a general model is established for the coordination number (CN) and local composition (LC) of square-well fluids. It meets the low-density, high-density and high-temperature limit conditions, as well as the unlike pair conservation and quasi-chemical equilibrium conditions. It also has some other features that many other models do not have: (1) its CN and LC expressions contain all pair potentials; (2) it yields temperature-dependent CN and LC for closely packed mixtures with different pair potentials; (3) its energy parameter is the difference of the total potentials of one pair in local and bulk environments, not the difference of two pair potentials. This model can accurately predict the CN, LC and compressibility factors of square-well fluids from computer simulation over a wide range of density, well width (λ = 1–2) and diameter ratio. For the case λ = 1.5, this model is better than or comparable with semi-empirical models; in other cases, it is far better than semi-empirical models. It does not need any empirical parameter for LC prediction. For the prediction of CN and compressibility factors, it only needs the smoothed radial distribution function of pure hard-sphere fluids. It also gives excellent results for lattice gases and highly nonideal lattice mixtures.