A simple approach to the equilibrium statistical mechanics of two-dimensional fluids

Abstract

A simple statistical mechanical theory previously developed for three-dimensional hard spheres is applied to a system of two-dimensional hard disks to obtain analytical equations for activity and pressure. The first order result, based on only the third virial coefficient, fits the molecular dynamics data for fluid disks significantly better than the seven-term virial series, but (unlike the case in three dimensions) not so well as the scaled particle theory. The second order result, involving the fourth virial coefficient, is the equal of the Padé approximant (3,4) with seven correct virial coefficients built in, and is significantly better than the scaled particle theory. The simple theory is surprisingly accurate even for the hard disk crystal. A simple theory of the two-dimensional Lennard-Jones fluid is obtained by incorporation of attractive wells with a hard core of temperature-dependent diameter. Comparison of the theory with the 17 high-density, supercritical pressures obtained by Fehder using molecular dynamics shows deviations averaging only 3 1/2%. Agreement with the high-density, low-temperature data obtained by Tsien and Valleau using Monte Carlo techniques is not so good. Calculations for the Lennard-Jones 6–12 potential are compared with calculations for the 6–12–3 potential, proposed as more suited than the 6–12 for adsorbed gases.