Analytically soluble mean-spherical-approximation model of a binary mixture with phase transitions

An extension of Waisman’s model of a binary-fluid mixture is considered. In this equal-diameter mixture particles interact via a hard core for r<1 and Yukawa tail potentials $K_{\mathrm{ij}}$exp[-z(r-1)]$r^{\mathrm{-}1}$ for r>1. The symmetrical mixture consists of two species of particles, each with the same number density. For like particles $K_{11}$=$K_{22}$ and unlike particles are specified by $K_{12}$. We solve analytically the mean-spherical-approximation equations for this model and show that two kinds of phase transition may occur in it. Namely, when $K_{11}$<-$K_{12}$ a liquid-gas-type phase transition is possible whereas in the case $K_{11}$<$K_{12}$ a phase-separation-type transition may occur. The separation line between the two liquid phases is exactly a straight line in the temperature-versus-density coordinate system. The liquid-liquid transition for this system is compared with the corresponding transition for the quasilattice model. If the equation $x_1$ $K_{11}$-($x_1$/B -$x_2$)$K_{12}$-$x_2$ $K_{22}$=0 is satisfied, the equal-diameter Yukawa system for a general composition $x_i$ can also be solved analytically. Based on this finding, we propose an approximate extension of the equal-diameter Yukawa model to arbitrary values of $K_{\mathrm{ij}}$ and all compositions.