Calculation of the mean force constants of the rare gases and the rectilinear law of mean force

Abstract

The mean energies 〈U〉 and the mean force constants 〈∇2U〉 have been calculated for liquid argon and liquid krypton using the WCA perturbation theory, and for gaseous argon and krypton along the coexistence line by solution of the PY equation for the radial distribution function. Calculations have been made for the Lennard-Jones, Barker–Henderson, and Maitland–Smith potentials. There is little difference in the values of 〈U〉 and 〈∇2U〉 calculated for the three potentials. The calculated values are in good agreement with experimental data. Correlation of the calculated values of 〈∇2U〉 for the liquid and gas leads to an empirical relationship between 〈∇2U〉 and the density of the phase along the coexistence line. When the latter is combined with the law of rectilinear diameters of the density, one obtains the rectilinear law of mean force, which is in good agreement with experimental data on argon. It is shown that the scaling exponent for the mean force constant 〈∇2U〉l-〈∇2U〉g is larger than the scaling exponent of the density below the critical temperature and becomes equal to it at the critical temperature. The rational for the rectilinear law of mean force is provided by an expansion of the radial distribution function of the liquid in powers of the density and by the use of the WCA approximation to the radial distribution function.