Isomorphism in fluid phase diagrams: Kulinskii transformations related to the acentric factor

For a wide class of molecular fluids, the temperature-density phase diagrams exhibit two prominent generic properties: a nearly linear locus, termed the Zeno line, along which the compressibility factor, Z = P/ρRT = 1 (same as an ideal gas), and the widely arching border of the vapor-liquid coexistence region, termed the binodal curve, with gas and liquid branches meeting at the critical point. The Zeno and binodal loci have been known for more than a century, yet only during the past two decades were striking empirical correlations between them recognized. Recently, Kulinskii introduced a remarkably simple projective transformation, wherein the linearity of the Zeno line and its relation to the binodal curve are geometrical consequences of an approximate isomorphism of the fluid with a venerable theoretical model, the lattice gas (equivalent to the Ising spin model). Here we show the Kulinskii transformation is significantly improved in accuracy and scope by using as input, in place of the lattice gas, the original van der Waals equation or simulation results for the Lennard-Jones potential. Moreover, the key parameters in these transformations can be expressed in terms of the acentric factor, introduced by Pitzer to extend corresponding states.