Models of free energy in lattice fluids—An excluded volume theory

Abstract

A new method of modeling free energy in a lattice fluid is developed and shown to be capable of correlating non-ideal behavior in vapor–liquid equilibria. The success of the analysis is based largely on two ideas. The first is to express the partition function as the product of two partition functions one for intramolecular bonds (internal degrees of freedom) and one for intermolecular bonds (molecular interactions) and then to treat these bond types separately in the analysis of interaction energy and configurational degeneracy. The transformation used to separate the bond types makes a molecule look like it is monatomic in the transformed lattice and significantly reduces the complexity of the analysis. It also excludes the molar cell volume associated with intramolecular bonds from the total cell volume in the transformed lattice. The second idea is that when the molecular configuration for the system being modeled is specified appropriately, strong energetic effects can be accounted for based on a random distribution. Interaction energy is modeled using a modified mean field theory in which a nearest neighbor interaction is defined to occur between the closest neighbors in line of sight. All nearest neighbor interactions separated by the same distance are assigned the same interaction energy. This allows interaction energy to depend on separation distance. Pure component models are developed and compared with experimental data for four distinct cases: (1) linear molecules (n-alkanes); (2) molecules that form clusters (water); (3) polymers and non-linear molecules (benzene); and (4) helium which exhibits quantum effects as a liquid. The simplest form of the equation of state derived is shown to be capable of predicting pure component phase equilibrium behavior in reasonably good qualitative agreement with observed behavior. The size factors in the model are shown to be well correlated with the acentric factor. A multicomponent model is developed and compared with experimental data for the non-ideal binary mixture of 1,1-difluoroethane (HFC152a) and n-butane (azeotrope formation).