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

Abstract

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 self-consistent approximations are in reasonably good agreement with the exact calculations at all temperatures. This work has been supported by grants from the National Research Council of Canada and the U.S. Department of the Interior, Office of Saline Water. This work has been supported by grants from the National Research Council of Canada and the U.S. Department of the Interior, Office of Saline Water. Notes This work has been supported by grants from the National Research Council of Canada and the U.S. Department of the Interior, Office of Saline Water. Additional informationNotes on contributorsDouglas Henderson Alfred P. Sloan Foundation Fellow.