Phase Behaviors of Binary Hard-Sphere Mixtures Using Simple Analytical Equations of State

Abstract

Recently, we have proposed a unified analytical equation of state (EOS) for solid–liquid–vapor states of matter, and have examined the thermodynamic properties of argon, carbon dioxide, and methane, as well as binary mixtures of methane and carbon dioxide. Also it has been demonstrated that the EOS can be applied for the solid–fluid transition of hard spheres, by eliminating the attractive part of the EOS. The present work is an extension of the earlier calculations for identical hard spheres, and here we examine the phase behavior of binary hard-sphere mixtures. The hard-sphere EOS employed in this study is $$P = \frac{{RT}}{{V - b}}\left( {\frac{{V - d}}{{V - c}}} \right)^k ,$$ where k = 1 or 2, and k = 0 [or c = d = 0] as a special case. b, c, and d are proportional to a hard-sphere volume, and their mixing rule is a quadratic form in mole fraction x, with a mixing parameter l ij (l ij = l ji and l ii = 0). The b parameter is given by $$b = \sum\limits_{i,j = 1}^2 {\frac{{\left( {b_i + b_j } \right)}}{2}} \left( {1 - 1_{ij} } \right)x_i x_j .$$ Similar mixing rules are applied to c and d. It is shown that various fundamental phase-transition behaviors can be described: ideal or near ideal, azeotropic (maximum and minimum), eutectic, eutectoid, monotectic, peritectic types, and stable fluid–fluid de-mixings without becoming metastable due to the interference of solid–liquid phase transitions. Rather complicated phase diagrams with a combination of various types are also predicted. The present study is a starting point and is useful for understanding the global topology of solid–liquid–vapor phase transitions of binary mixtures.