We consider symmetric binary mixtures consisting of spherical particles with equal diameters interacting via a hard-core plus attractive tail potential with strengths ǫ ij , i, j = 1, 2, such that ǫ 11 = ǫ 22 > ǫ 12 . The phase diagram of the system at all densities and concentrations is investigated as a function of the unlike-to-like interaction ratio δ = ǫ 12 /ǫ 11 by means of the hierarchical reference theory (HRT). The results are related to those of previous investigations performed at equimolar concentration, as well as to the topology of the mean-field critical lines. As δ is increased in the interval 0 < δ < 1, we find first a regime where the phase diagram at equal species concentration displays a tricritical point, then one where both a tricritical and a liquid-vapor critical point are present. We did not find any clear evidence of the critical endpoint topology predicted by mean-field theory as δ approaches 1, at least up to δ = 0.8, which is the largest value of δ investigated here. Particular attention was paid to the description of the critical-plus-tricritical point regime in the whole density-concentration plane. In this situation, the phase diagram shows, in a certain temperature interval, a coexistence region that encloses an island of homogeneous, one-phase fluid.

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We study a model for star polymers in solution which, in addition to the ultrasoft repulsive interaction of entropic origin, has an attractive interpolymer interaction at longer range. This attraction can arise from a suitable tuning of the solvent and solute properties.For this model we study the phase diagram using mean-field theory and two fluid-state theories, the modified hypernetted chain (MHNC) integral equation and the hierarchical reference theory, and we explore star polymers with a different number of arms f ( f = 12, 24, 32, 40). All three theories give the same topology for the phase diagram in the presence of attraction. When the strength of the interaction is strong enough a fluid-fluid phase transition appears but the coexistence curve in the density-temperature (strength of attraction) bifurcates at a triple point into two lines of coexistence terminating at two critical points. This peculiar phase behaviour is related to the unusual form of the repulsive contribution V rep (r ): at low density and in a semidilute regime the soft-core Yukawa-like part of V rep (r ) is relevant, at higher densities the logarithmic, ultrasoft part of V rep (r ) is the relevant one.During our study we verify that the MHNC equation also gives a very accurate description of correlations for systems with an ultrasoft-core potential.

The structure factor S(q) and the direct correlation function c(q) of rare gases are expected to have a nonanalytic mod q mod 3 term at small q. This term is due, in addition to the well known long-range r-6 tail of the two-body interaction, also to the three-body Axilrod-Teller interaction. The coefficient c3 of the mod q mod 3 term of c(q) has a particularly simple state dependence, T-1 in temperature and linear in density, when the AT interaction is present. If no three-body interaction is present C3 is density independent. Therefore the experimental determination of the density dependence of c3 will give unequivocable evidence of three-body forces. On the basis of the integral equation method the authors determine that it will be easier to detect the mod q mod 3 term if the scattering data are analysed in term of c(q) and for measurements at density and temperature not far from the critical point. Under these favourable conditions scattering measurements in the range 1-4 nm-1 will give a precise determination of the mod q mod 3 term. The role of retardation, which changes the r-6 tail into r-7, on the small-q behaviour of S(q) and c(q) is also evaluated and this effect is predicted to be measurable for q<0.5 nm-1.