MATHEMATICAL DOUBLE POINTS ACCORDING TO THE SIMPLIFIED-PERTURBED-HARD-CHAIN THEORY

Critical curves of a binary fluid mixture are usually plotted as a fun ction of pressure and temperature (p, T projection), temperature and c omposition (T, x projection) or as a function of the reduced densities of the two components (y1, y2 projection). In these three ways of rep resentation, we will show the structure of the critical curves around a mathematical double point. Moreover, it will be shown that mathemati cal double points can conveniently be divided into two groups: the (me ta)stable and unstable mathematical double points. To date, the (meta) stable mathematical double points have not been investigated with a pr essure-explicit equation of state. In this paper, it will be shown how the two types of mathematical double points can be calculated. We wil l digress on the thermodynamic conditions to be obeyed for the calcula tion of the two types of mathematical double points.