The Second Virial Coefficient of Non-Spherical Molecules

Abstract

The Lennard-Jones model of molecules of spherical symmetry has been generalized to non-spherical models without sacrificing analytical integrability of the second virial coefficient. The essential generalization consists in the definition of the intermolecular distance, ρ, the intermolecular potential, U , being supposed to be a function of ρ only and \begin{aligned} U(\rho){=}U_{0}\left[\frac{m}{n-m}\left(\frac{\rho_{0}}{\rho}\right)^{n}-\frac{n}{n-m}\left(\frac{\rho_{0}}{\rho}\right)^{m}\right],\quad n{>}m{>}3. \end{aligned} As the simplest extension ρ is defined by the shortest distance between molecule cores, as which thin rods (disks) are adopted in case of prolonged (flat) molecules. Next, ρ is so defined that the model becomes an attracting spheroid. For thèse models the second virial coefficient has been integrated analytically and tabulated. The model Constants have been determined for H 2 , N 2 , C 2 H 4 and CO 2 .