Mean spherical approximation algorithm for multicomponent fluid mixtures withmulti-screened Coulomb plus power series interactions

Abstract

An efficient algorithm is presented to find the Blum–Høye mean spherical approximation(MSA) solution for mixtures of hard-core fluids interacting through multi-screenedCoulomb plus power series (multi-SCPPS) potentials. The solution for hard-spheremixtures is used as an initial estimate of the variables. From this initial estimate only a fewNewton–Raphson iterations are required to reach the final solution. The algorithm is alsoable to reflect correctly their molecular characteristics into the appropriate macroscopicbehaviour. All MSA thermodynamic properties are presented analytically. Ouranalysis will be applicable to a large variety of fluid mixtures because any smooth,realistic isotropic potential can be well reproduced by the multi-SCPPS closure witharbitrary accuracy. Demonstrations of the power of the algorithm are made for twobinary-component systems of Lennard-Jones particles. One is composed of particles withnearly the same sizes, while the other mixture with widely different sizes. We havestudied their thermodynamic stabilities based on the compressibility and theisotherms of virial and energy equations of state, and further from microscopicviewpoints in connection with radial distribution functions. The present method isable to detect vapour–liquid transitions and perhaps liquid–glass transitions.The multi-SCPPS closure includes the multi-Yukawa closure as a special case.