In this study, it will be shown that in binary mixtures, type VI phase behavior, according to the classification of van Konynenburg and Scott [Philos. Trans. R. Soc. London, Ser. A 298,495 (1980)], can be obtained from a simple, semitheoretical equation of state. The applied equation of state was derived from the simplified-perturbed-hard-chain theory (SPHCT). In literature, there are no known examples of type VI phase behavior being obtained from a simple equation of state. In addition, the systematic changes in phase behavior from type I via type V towards type VI will be discussed in this contribution. Surprisingly, a new type of phase behavior was found that was foreseen by Schneider [Ber. Bunsenges. Phys. Chern. 70, 497 ( 1966) ]. It is proposed to call this new phase behavior type VIII.

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

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The equation of state that results from the simplified-perturbed hard-chain theory ͑SPHCT͒ has been used to calculate phase diagrams for binary fluid mixtures and to classify these phase diagrams in accordance with the system of van Konynenburg and Scott. For molecules with equal or similar sizes, the global phase diagrams are similar to the ones obtained with the van der Waals, Redlich-Kwong, and Carnahan-Starling-Redlich-Kwong equation of state. In addition to the types I-V, one can calculate also types VI, VII, and VIII with the SPHCT equation. For molecules with large size differences two new, main types of phase behavior have been discovered. We propose to call them type IX and X.

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