The fourth virial coefficient for a Lennard-Jones fluid in two dimensions

Abstract

The fourth virial and its temperature derivative are reported for a two‐dimensional Lennard‐Jones fluid. The elementary diagram is obtained by a Fourier series procedure analogous to the method proposed by Barker and Monaghan for the three dimensional case. The density expansion of the radial distribution function is also considered, and values of the first‐ and second‐order coefficients are reported. Various approximations given by the Percus–Yevick (PY) and hypernetted‐chain theories are tested and it is found that the PY–energy‐equation values are very good, especially at high temperatures. Rowlinson’s inverse‐steepness expansion is also applied and it is found that it would be reliable at reduced temperatures kT/ε greater than about 30. The critical properties are estimated. The value for the critical temperature, kT_c/ε=0.492, is in agreement with a previous estimate from the PY theory but lower than the computer simulation results.