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 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.