Ternary Mixtures of Hard Spheres and Their Multiple Separated Phases

We study the liquid phase behavior of ternary mixtures of monodisperse hard spheres in solution. The interactions are modeled in terms of the second virial coefficient and can be additive hard sphere (HS) or non-additive hard sphere (NAHS) interactions. We give the set of equations that defines the phase diagram for mixtures of three components. We calculate the theoretical liquid-liquid phase separation boundary for two-phase separation (the binodal) and, if applicable, the three-phase boundary, as well as the plait points and the spinodal. The sizes of the three components are fixed. The first component (A) is the smallest one, the second component (B) is four times the size of the smallest component, and the third (C) component is three times the size of the smallest one. The interaction between the first two components is fixed, and this AB sub-mixture shows phase separation. The interactions of component C with the other two components are varied. Component C can be compatible or incompatible with components A and B. Depending on the compatibility of the components, the phase diagram is altered. The addition of the third component has an influence on the phase boundary, plait points, stability region, fractionation, and volume ratio between the different phases. When all sub-mixtures (AB, AC, and BC) show phase separation, a three-phase system becomes possible when the incompatibility among all components is high enough. The position and size of the three-phase region is dependent on the interactions between the different sub-mixtures. We study the fractionation off all components depending on specific parent concentrations.