The gas–liquid phase-transition singularities in the framework of the liquid-state integral equation formalism

Abstract

The singularities of various liquid-state integral equations derived from the Ornstein–Zernike relation and its temperature derivatives, have been investigated in the liquid–vapor transition region. As a general feature, it has been found that the existence of a nonsolution curve on the vapor side of the phase diagram, on which both the direct and the total correlation functions become complex—with a finite isothermal compressibility—also corresponds to the locus of points where the constant-volume heat capacity diverges, in consonance with a divergence of the temperature derivative of the correlation functions. In contrast, on the liquid side of the phase diagram one finds that a true spinodal (a curve of diverging isothermal compressibilities) is reproduced by the Percus–Yevick and Martynov–Sarkisov integral equations, but now this curve corresponds to states with finite heat capacity. On the other hand, the hypernetted chain approximation exhibits a nonsolution curve with finite compressibilities and heat capacities in which, as temperature is lowered, the former tends to diverge.