Phase diagram of symmetric binary fluid mixtures: First-order or second-order demixing

Binary fluid mixtures of 1:1 concentration can demix in a phase transition of first order or of second order. We analyze the two scenarios in density-concentration space and relate them to the structure of the line at which the demixing coexistence surface cuts the liquid-vapor coexistence surface. These scenarios help us to decide between first and second order for a model of a symmetric Lennard-Jones mixture. An optimized reference hypernetted chain integral equation method is employed for calculating the correlation functions and from there the pressure and chemical potentials. We conclude that demixing of a 1:1 mixture is of first order in the whole range of parameters that we have investigated. We did not find a critical point in the 1:1 concentration plane.