Effective pair potentials in fluids in the presence of three-body forces. II

Abstract

Earlier calculations are extended to the second order in density thus providing the n0n-additive contributions to the fourth virial coefficient in the presence of a weak three-body force given by the triple-dipole dispersion potential of Axilrod and Teller. We compare the Percus-Yevick approximations of Rushbrooke and Silbert and of Rowlinson at the level of the fourth virial coefficient and find that the former is more accurate. We also compare our calculations of the effective pair potential of liquid argon with the results of Mikolaj and Pings obtained from X-ray diffraction measurements.

Thermophysical Properties of Gaseous CF4 and C2F6 from Speed-of-Sound Measurements

“…(The HCLJ potential worked better than the Maitland-Smith potential with the present data.) For each intermolecular potential, we calculated the classical second and third virial coefficients and their temperature derivatives [14,15]. The calculation of the third virial coefficient requires inclusion of three-body contributions.…”

Comment on “An equation of state for gaseous argon determined from the speed of sound”

“…Whereas it is sensible to omit 4-body contributions D 4 to D ¼ D 2 þ D 3 þ D 4 [5], Ref. [1]'s approximation to the 3-body part obtained by discarding all terms with more than one 3-body f-function f ijk :¼ e ÀbU ijk À 1 (in the usual diagrammatic notation [1,6,7] symbolized by a shaded triangle), is unnecessary and inconsistent. [8,9] also for weak triple-dipole potentials as employed in Ref.…”

“…(2), actually inspired by the assumption of insignificant 3-body interactions [1,6,7,13], results in a significant overestimation of these interactions in a fourth-order virial EOS. (For illustration, this overestimation goes roughly like 1.46 Â 10 7 e À8.15T cm 9 mol À3 for the ab initio potentials.…”

“…(A choice of fixed functional forms for 2-and 3-body potentials U ij and U ijk is a limitation that cannot be avoided.) Whereas it is sensible to omit 4-body con-[1]'s approximation to the 3-body part obtained by discarding all terms with more than one 3-body f-function f ijk :¼ e ÀbU ijk À 1 (in the usual diagrammatic notation [1,6,7] symbolized by a shaded triangle), is unnecessary and inconsistent.For b = 1/k B T > 0, f ijk ? 0 if and only if U ijk ?…”

“…[1]'s approximation to the 3-body part obtained by discarding all terms with more than one 3-body f-function f ijk :¼ e ÀbU ijk À 1 (in the usual diagrammatic notation [1,6,7] symbolized by a shaded triangle), is unnecessary and inconsistent.…”