Bonded hard-sphere (BHS) theory for the equation of state of fused hard-sphere polyatomic molecules and their mixtures

Abstract

The bonded hard-sphere (BHS) approach originally developed for diatomic and triatomic molecules is generalized to hard-sphere polyatomic models which are formed by bonding together their constituent hard spheres. The thermodynamic properties of the polyatomic fluid are obtained from the known properties of a corresponding multicomponent mixture of different sized hard spheres with bonding sites. In the limit of complete bonding, hard-sphere polyatomic molecules are formed. As well as the general expressions for polyatomic molecules and their mixtures, the equation of state of hard-sphere chain molecules, which are simple models of homologous series such as the alkanes, perfluoroalkanes, etc., is presented. More specifically, the chain molecules are formed from two different types of hard spheres 1 and 2. Spheres of type 1 make up the backbone of the chain and, in this case, would represent the carbon atoms; spheres of type 2 represent the substituents, i.e., the hydrogen or fluorine atoms. Although the BHS theory is only strictly valid for molecules of tangent spheres, the theory can also be applied to fused hard-sphere (FHS) molecules with overlapping spheres. The latter are more realistic models of actual molecules. In the spirit of the semiempirical scaled particle theories (SPT), the properties of the FHS molecule can be related to those of an equivalent BHS molecule of tangent spheres with the same parameter of nonsphericity, α. When dealing with large polyatomic molecules, α does not need to be calculated numerically as is the case with the usual SPT approach. As an approximation one may use the analytical values of α for the diatomic segments making up the molecule. This simple approach turns out to be quite successful. The BHS equation of state has been compared with ‘‘exact’’ computer simulation data for homonuclear and heteronuclear FHS systems of diatomics, linear and nonlinear triatomics, and tetrahedral pentatomics, as well as mixtures of FHS molecules. Good agreement is found for all of these systems. In general, the BHS approach is more rigorous and easier to extend to larger polyatomic molecules and their mixtures than SPT.