Non-central Potential Functions

Non-central Potential Functions.—Non-central interactions can also be handled in terms of specific multi-parameter potential functions such as the Stockmayer and Kihara potentials. Although there is an extensive literature on the subject of such potentials, it is only rarely that virial coefficients are sufficiently precise or extensive to warrant their use. For this reason we will deal only briefly with the subject. 

When multi-parameter potentials are applied to mixtures, the combination rules for parameters other than e and a often follow from the model underlying the potential. For example, the Kihara spherical-core potential is based on a model in which each molecule has a molecular core of characteristic radius an. The combination rules an = (an + jj)/2 follows directly from the hard-core assumption.  

Prausnitz and Myers have used the Kihara potential for the calculation of 5j2 s for mixtures of simple molecules, and Blanks and Prausnitz employed the Stockmayer potential in studies of mixtures involving polar molecules. A variety of specific non-central interactions were included in the potentials that Lichtenthaler and Schafer employed in their analysis of their measurements of virial coefficients of Ar with polar and non-polar molecules. 

More recently, Khoury and Robinson calculated virial coefficients for ethane + hydrogen sulphide mixtures from an effective Lennard-Jones 6—12 potential that includes a contribution from the dipole-induced-dipole interaction. The parameters were evaluated by fitting their measurements on CgHg and HgS to a 6—12 potential and to a Stockmayer potential respectively. Bradley and King have used several potential functions to analyze interactions of phen-anthrene with a number of small polyatomic molecules. 

The many models used for the calculation of virial coefficients of globular molecules have been reviewed by Johnson and Spurling. They calculate B s for CH4 + CF4, CH4 + SFe, CH4 + C(CH8)4, CH4 -1- Si(CH3)4, and CF4 + SFe from the Hamann-Lambert model. In this model all atom-atom interactions are assumed to be of the Lennard-Jones type. The interaction energy is calculated by summing all pairwise atom interactions and then averaging equally over all relative orientations of the molecules. A similar approach for mixtures of globular molecules is based on interactions between spherical shells. In effect, the outer atoms of a molecule are assumed to be uniformly distributed over the surface of a sphere. 

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