Vapor Pressures of 36Ar and 40Ar. Intermolecular Forces in Solid and Liquid Argon

Abstract

The vapor pressures of ³⁶Ar and ⁴⁰Ar have been measured in the temperature range 62–102°K. Measurements in the liquid agree quantitatively with the previous measurements of Clusius et al. which cover the limited range 84–88°K. A significant difference is found between our equilibrium measurements, which have a precision of 0.5% in the logarithm of the vapor pressure ratio, and dynamic measurements of the isotope fractionation in solid–vapor systems. The reduced partition functions of the solid and liquid are calculated from the observed vapor pressure ratios. The reduced partition ratio of the solid can be represented by the equation $T^2\ln {\text{(fs\hspace{0.17em}/\hspace{0.17em}fg)\hspace{0.17em}=\hspace{0.17em}63.39\hspace{0.17em}±\hspace{0.17em}0.34\hspace{0.17em}−\hspace{0.17em}(0.124\hspace{0.17em}±\hspace{0.17em}0.005)T\hspace{0.17em}−\hspace{0.17em}(95\hspace{0.17em}/\hspace{0.17em}63)(63.4\hspace{0.17em}−\hspace{0.17em}0.124T)}}^2{\mathrm{\hspace{0.17em}/\hspace{0.17em}T}}^2$ . The experimental values of $\ln \mathrm{(fs\hspace{0.17em}/\hspace{0.17em}fg)}$ are in good agreement with calculations from the improved self‐consistent phonon theory of an anharmonic lattice with a 13–6 potential. Since the quantum effect is small, ${\mathrm{〈\nabla }}^2\mathrm{U〉}$ is obtained directly from the reduced partition functions. In the liquid range the experimental results agree quantitatively with previous estimates based on 12–6 potential, with calculations from molecular dynamics and with the Rowlinson correlation function. It is shown that the reduced ${\mathrm{〈\nabla }}^2\mathrm{U*〉}$ is the same for neon and argon both in the liquid and solid. The change in ${\mathrm{〈\nabla }}^2\mathrm{U〉}$ on melting is discussed in terms of the change of the number of nearest neighbors on melting and the “significant structure theory of liquids.”