Numerical MSA solution for binary Yukawa mixtures

Abstract

An efficient numerical algorithm is given to find the Blum and Ho/ye mean spherical approximation (MSA) solution for binary mixtures of hard-core fluids with one-Yukawa interactions. The initial estimation of the variables is achieved by partial linearization (based on known, physical asymptotic behaviors) of the system of nonlinear equations which result from the Blum and Ho/ye method. The complete procedure is at least one order of magnitude faster than that recently outlined by Giunta et al. More importantly, it always seems to converge to the physical solution (if it exists). We delimit, for several specific mixtures, the density-temperature region where no real solution is possible. This corresponds, following Waisman’s interpretation, to thermodynamic conditions for which vapor–liquid or liquid–liquid separation occurs. The dependency of the MSA solutions on the Yukawa exponent z is studied in detail. For high values of z, adequate for generalized mean spherical approximation (GMSA) applications, we propose an accurate linear approximation, and we relate it to the solutions given by Giunta et al. For equal-sized, symmetric, equimolar binary mixtures, we show that Baxter’s factorized version of the Ornstein–Zernike equation, including the factor correlation functions, can be decoupled. We also find, for equal-sized mixtures, that one of the approximations recently proposed by Jedrzejek et al. using an effective potential method is in very good agreement with our exact (MSA) results. Finally, a theoretical analysis shows that if the Yukawa amplitudes satisfy K12=(K11K22)1/2, the coefficients Dij of the factor correlation functions outside the core are related as follows: D1i/K1i =D2i/K2i, for i=1,2.