Evaluation of Transport Properties of Gases: The Bruch–McGee Potential for Helium

Abstract

The transport properties and second virial coefficient of helium have been calculated for two hybrid intermolecular potentials recently proposed by Bruch and McGee, and the results are compared with experimental values. Tables of transport collision integrals for the helium isotopes which are accurate to several parts per thousand were prepared for the temperature range 0.8–2500°K in order to adequately span the existing data. The collision integrals were computed by an exact quantum phase-shift calculation at low temperatures followed by a JWKB approximation and classical calculation at intermediate and high temperatures, respectively. The bulk properties were then evaluated using the prepared tables. The agreement with experimental measurements for the various properties at low temperatures is rather poor when compared with the results calculated using the Lennard-Jones (12–6) potential. We conclude that this is due to excessive depth of the potential well. On the other hand, the calculations above approximately 150°K agree quite well with experimental data which leads us to the conclusion that the low-energy repulsive region of either hybrid potential is a good representation of the helium–helium interaction. Since the potentials are essentially identical in this region and independent of the long-range attractive terms, it is suggested that for practical applications the Morse-VDD potential be truncated to the much simpler Morse potential with the given parameters and its region of validity restricted to temperatures above 150°K.