PPT Slide
Non-additive hard spheres
In 1970 Widom and Rowlinson (WR) introduced an ingeniously simple model for the study of phase transitions in continuum fluids [13]. It consists of two species of particles 'A' and 'B', in which the only interaction is a hard-core exclusion between particle of unlike species, i.e., sab?0 and sa=sb=0. This model can be transformed (by integrating over the coordinates of one species) into a one-component model with explicit many-body interactions. A rigorous proof of the existence of a demixing transition in this model was given by David Ruelle (1971) [14]. Ruelle used a brilliant adaptation of the Landau-Peierls argument for the Ising model on a lattice that exploits the A-B symmetry. Ruelle's proof permits also a small hard core sa=sb<sqrt(3)/2*sab .
Three-dimensional non-additive hard spheres have been the object of numerous theoretical studies involving scaled particle theory [15], integral equations [16] and y-expansion [17]. The first Molecular Dynamics simulations have been carried out in 1975 for symmetric mixtures with a=0.2 [18]. Monte Carlo simulations using the Gibbs ensemble have been performed for the same system in order to determine the fluid phase boundary [19]. Critical density for the fluid-fluid demixing transition have been estimated for a mixture with a=1 by means of Monte Carlo and Molecular Dynamics technique [20].
It has been found out that when a=0.2 the fluid phase separation occurs at rcs3 = 0.415 (+0.005;-0.014). However at smaller values of non-additivity parameter the mixture might crystallize before the demixing transition takes place. This fact caused the argument that there must be some small positive value (am) of a, below which a fluid phase separation is thermodynamically impossible at any density (and molar fraction of, say, the first of components). Different value of am have been obtained theoretically and numerically: