Criterion for determining crossover phenomenon in volume-translated equation of states

Volume translation is widely adopted in cubic equation of state (CEOS) to achieve more accurate density predictions for pure compounds and mixtures. Previous research reveals that a temperature-dependent volume-translated EOS could result in crossing of pressure-volume isotherms for a pure compound, which leads to an anomalous behavior that the predicted molar volume for a pure component can possibly be lower at a higher temperature at an isobaric condition. Such crossover phenomenon fails to consistently predict the thermodynamic properties of a pure compound, e.g., giving a negative isobaric thermal expansivity. In this study, we develop a concise criterion to judge whether a volume-translated EOS will result in crossover issues, and if so, the extent of the temperature and pressure range over which the crossover phenomenon occurs. The recently proposed volume translations are evaluated on the basis of the developed criterion. For the various types of temperature-dependent volume translations, we obtain the specific temperature/pressure conditions over which there is certainly no crossover phenomenon.