Global crossover equation of state of a van der Waals fluid

A global crossover equation of state that incorporates the classical van der Waals behavior (including the ideal-gas limit and the high-density hard-sphere limit) far away from the critical point and the singular behavior near the critical point has been developed. It is based on a transformation derived from the renormalization-group theory of critical fluctuations to the classical van der Waals equation of state. The crossover van der Waals equation contains only one non-universal system-dependent parameter associated with the range of intermolecular forces and it shows how the density fluctuations affect all thermodynamic properties more and more significantly when the fluid approaches the critical point. In particular, the critical compressibility factor which for the classical van der Waals equation is Zc=0.375, becomes suppressed to a more realistic value of 0.26–0.29 as is typical for simple fluids.