Discrete potential fluids in the supercritical region

Supercritical fluids are an interesting area of research because their use in industrial processes has environmental benefits. Since their processes are low energy consumption they are considered as green solvents of the future. However, the study of the supercritical region remains a controversial issue, particularly, the possibility to find three different regime: gas-like, liquid-like and a mixture of them. The existence of a line (Widom line) or a region (delta Widom) that delimit this behavior is still under discussion. In this work we assume that this border is a line, like a continuation of a vapor-liquid saturation curve in the pressure-temperature plane. The Widom line is defined by the locus of points of maximum correlation length. Taking advantage of the relation that exists between the correlation length with the response functions and scalar curvature in the vicinity of the critical point, we build the Widom line with the locus of extrema of response functions and scalar curvature, and use the coincidence of these curves to determine the end of the Widom line. The Widom lines for Square-Well of variable range and Hard-Core Lennard-Jones systems are obtained using analytical equations of state. We propose a quantitative criterion to determine the end of this line. Besides, we give a new and alternative way of determining this line using the locus of the pressure inflection points (obtained in the density-pressure plane) and look for the coincidence of these points with the locus of the maxima of the isothermal compressibility in the temperature-pressure plane.