Thermal expansion and stability limits of generalized van der Waals fluids

Generalized van der Waals equations of state can exhibit density anomalies, as characterized by a negative thermal expansion coefficient in some region of the phase diagram, when either the hard core volume, b, or the mean field attractive parameter, a, are made temperature-dependent. If b decreases as the temperature increases, negative thermal expansion occurs at all temperatures. At a given temperature, the liquid becomes anomalous when the pressure is increased; hence the P-T projection of the locus of density maxima has positive slope. The locus of density maxima extends to zero temperature when b is finite at T = 0, and it terminates at a minimum temperature if b diverges at T = 0. If, on the other hand, a increases with temperature while the core volume remains constant, generalized van der Waals fluids exhibit density anomalies that disappear at high pressure. Hence, in this case the locus of density maxima has a negative slope in the P-T plane. The liquid spinodal is re-entrant both when a increases as the temperature increases and when b increases as the temperature decreases, becoming infinite at T = 0.