Mean spherical approximation algorithm for multicomponent multi-Yukawa fluid mixtures: Study of vapor–liquid, liquid–liquid, and fluid–glass transitions

Abstract

An efficient algorithm is given to find the Blum and Ho/ye mean spherical approximation (MSA) solution for mixtures of hard-core fluids with multi-Yukawa interactions. The initial estimation of the variables is based on the asymptotic high-temperature behavior of the fluid. From this initial estimate only a few Newton–Raphson iterations are required to reach the final solution. The algorithm consistently yields the unique thermodynamically stable solution, whenever it exists, i.e., whenever the fluid appears as a single, homogeneous phase. For conditions in which no single phase can appear, the algorithm will declare the absence of solutions or, less often, produce thermodynamically unstable solutions. A simple criterion reveals the instability of those solutions. Furthermore, this Yukawa-MSA algorithm can be used in a most simple way to estimate the onset of thermodynamic instability and to predict the nature of the resulting phase separation (whether vapor–liquid or liquid–liquid). Specific results are presented for two binary multi-Yukawa mixtures. For both mixtures, the Yukawa interaction parameters were adjusted to fit, beyond the hard-core diameters σ, Lennard-Jones potentials. Therefore the potentials studied, although strictly negative, included a significant repulsion interval. The characteristics of the first mixture were chosen to produce a nearly ideal solution, while those of the second mixture favored strong deviations from ideality. The MSA algorithm was able to reflect correctly their molecular characteristics into the appropriate macroscopic behavior, reproducing not only vapor–liquid equilibrium but also liquid–liquid separations. Finally, the high-density limit of the fluid phase was determined by requiring the radial distribution function to be non-negative. A case is made for interpreting that limit as the fluid–glass transition.