The mixing rule estimates of the radial distribution functions g(alpha
beta)(r), from the van der Waals one-fluid and mean density approxima
tions for Lennard-Jones fluid mixtures, are examined by comparing with
Monte Carlo simulations. In addition, these mixing rule estimates of
g(alpha beta)(r) are used to calculate the Helmholtz energy for Lennar
d-Jones homonuclear chain mixtures based on the thermodynamic perturba
tion theory (TPT). Two simplifying modifications of these mixing rules
are proposed for the TPT mixture model. The accuracy of these simplif
ied rules is examined and found to give accurate representation of the
theoretically derived Helmholtz energy over a wide range of densities
and temperatures.