Simulation-based equations of state for the Lennard-Jones fluid: Apparent success and hidden failure

In this work, we utilize concepts from bifurcation theory to pinpoint hidden defects in accurate multiparameter simulation-based equations of state for the Lennard-Jones (LJ) fluid. The proposed bifurcation diagrams track the evolution of volume roots as temperatures vary at constant pressure. We critically evaluate four distinct types of LJ-based equations of state: modified Benedict-Webb-Rubin equation (with three different parameter sets), Kolafa and Nezbeda, Mecke et al, and Thol et al. For each model, we mainly construct two bifurcation diagrams at subcritical and supercritical isobars. The unphysical behaviors associated with the studied equations involve spurious two-phase separation regions, distorted volume-temperature behavior, unphysical branches, unphysical turning points, and multiplicity in volume roots. Our proposed bifurcation diagram provides a reliable and simple technique to pinpoint hidden defects in equations of state-based merely on temperature, volume, and pressure without the need of their partial derivatives or thermodynamic potentials.