Note on the Perturbation Equation of State of Barker and Henderson

Abstract

Perturbation theory of equation of state due to Barker and Henderson is reformulated. This new formulation makes it possible to calculate the Helmholtz free energy of a fluid system analytically by perturbation relations of Barker and Henderson, without use of any approximation or need of any numerical table for the hard-sphere reference system other than the original Percus–Yevick approximations. The results are compared with the calculation of Barker and Henderson, and it is shown that the two agree with each other at all the temperatures which are compared, while the present method produces compressibilities slightly closer to the experimental and machine-calculated data. The results of the present method, based on average Percus–Yevick hard-sphere compressibilities, are also compared with the result of other theories of equation of state of simple fluids, molecular dynamics, and Monte Carlo calculations.