Star polymers: study of fluid fluid transitions in a system with a repulsive ultrasoft-core

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 Vrep (r): at low density and in a semidilute regime the soft-core Yukawa-like part of Vrep (r) is relevant, at higher densities the logarithmic, ultrasoft part of Vrep (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.