Model intermolecular potentials and virial coefficients determined from the speed of sound

Abstract

A simple procedure is given for determining model two- and three-body intermolecular potential energy functions from precise measurements of the speed of sound in the gas phase. The method is applied to the pure gases argon, methane and nitrogen and results are considered for propane and the mixture (methane + propane) obtained recently by similar methods. For the pair potential, the four-parameter model proposed by Maitland and Smith is used while the consequences of three-body forces were generally assumed to be represented adequately by the triple-dipole dispersion potential of Axilrod and Teller. The effect of including additional dispersion and exchange terms in the three-body potential was investigated for argon; each of these terms is significant but their effect on the third virial coefficient may be absorbed accurately in an effective triple-dipole potential. Three or, in some cases, all four of the parameters in the pair potential were optimized, together with the triple-dipole dispersion coefficient, in fits to the acoustic data. Ordinary second and third virial coefficients have been calculated from the model potential and the former are shown to be in excellent agreement with directly measured values. In the case of the third virial coefficient, some small discrepancies are noted; the resolution of these differences could have important implications for our understanding of many-body forces. The values of the dilute-gas viscosity predicted by the model pair potentials are examined also and, in the case of argon, found to be in good agreement with experimental values; for the other systems differences of several per cent were noted.