Ab initio study of the vapour-liquid critical point of a symmetrical binary fluid mixture

A microscopic approach to the investigation of the behaviour of a symmetrical binary fluid mixture in the vicinity of the vapour-liquid critical point is proposed. It is shown that the problem can be reduced to the calculation of the partition function of a 3D Ising model in an external field. For a square-well symmetrical binary mixture we calculate the parameters of the critical point as functions of the microscopic parameter r measuring the relative strength of interactions between the particles of dissimilar and similar species. The calculations are performed at intermediate ($\lambda=1.5$) and moderately long ($\lambda=2.0$) intermolecular potential ranges. The obtained results agree well with the ones of computer simulations.