Longuet-Higgins and Widom

Figure 2.4. Corresponding states temperature versus density phase diagram for spherical molecules calculated from the generalized van der Waals theory of Longuet-Higgins and Widom [31],...

A much more rational approach is that of Longuet-Higgins and Widom (LHW) (17) who suggested retaining Equations 37 and 42 but replacing Equation 38 by the correct hard-sphere equation of state. This leads to... 

Many generalizations of van der Waals ideas have been proposed for improving the prediction of the fluid phase behavior in a wide range of thermodynamic states and to extend the description to molecular fluids and mixtures [79]. Longuet-Higgins and Widom [80] suggested that the repulsive term Po be replaced with the accurate expressions for the pressure of hard spheres elaborated in the theory of liquids [81], such as the Carnahan-Starling approximation,[82]... 

H. C. Longuet-Higgins and B. Widom, A rigid sphere model for the melting of argon. Mol. Phys. 8, 549-556 (1964). 

Stillinger F 1973 Structure in aqueous solutions from the standpoint of scaled particle theory J. Solution Chem. 2 141 Widom B 1967 Intermolecular forces and the nature of the liquid state Sc/e/ ce 375 157 Longuet-Higgins H C and Widom B 1964 A rigid sphere model for the melting of argon Mol. Phys. 8 549... 

---