Virial expansion for the radial distribution function of a fluid using the 6 : 12 potential

Abstract

The radial distribution function can be expressed in a virial expansion. Using the 6 : 12 potential the second-order density coefficient, g 2(r), is numerically calculated for a wide range of temperatures and intermolecular separations. These results are used to calculate the second-order density coefficient, c 2(r), in the expansion of the direct correlation function and to calculate the fourth virial coefficient, B 4. In addition, approximate results for g 2(r), c 2(r), and B 4 are calculated on the basis of the Percus-Yevick, hypernetted chain, and the self-consistent approximations of Hurst and Rowlinson. These approximate results are compared with the exact results. The Percus-Yevick theory is in good agreement with the exact results at high temperatures but is unsatisfactory at low temperatures. The hyper-netted-chain approximation is in fair agreement with the exact results at high temperatures, is in poor agreement at intermediate temperatures, but is in good agreement at low temperatures. The sel...