Reexamination of Van Der Waals model for soft-core molecules

Van der Waals' assumption that the parameter a in his model is independent of density and temperature is reexamined for Lennard-Jones particles, using two different types of soft repulsive core potentials: the positive portion of the Lennard-Jones potential and the portion of the Lennard-Jones potential associated with the repulsive force. The latter core potential is found to give a nearly constant a. An analytic expression for a is given to account for the observed small density variation. It is applicable from about 25% of the triple-point density to the freezing density.