Star polymers: study of fluid–fluid transitions in a system with a repulsiveultrasoft-core

Abstract

We study a model for star polymers in solution which, in addition to the ultrasoftrepulsive interaction of entropic origin, has an attractive interpolymerinteraction at longer range. This attraction can arise from a suitable tuningof the solvent and solute properties. For this model we study the phasediagram using mean-field theory and two fluid-state theories, the modifiedhypernetted chain (MHNC) integral equation and the hierarchical referencetheory, and we explore star polymers with a different number of armsf(f = 12, 24, 32, 40).All three theories give the same topology for the phase diagram in thepresence of attraction. When the strength of the interaction is strong enougha fluid–fluid phase transition appears but the coexistence curve in thedensity–temperature (strength of attraction) bifurcates at a triple point into twolines of coexistence terminating at two critical points. This peculiar phasebehaviour is related to the unusual form of the repulsive contributionVrep (r):at low density and in a semidilute regime the soft-core Yukawa-like part ofVrep (r)is relevant, at higher densities the logarithmic, ultrasoft part ofVrep (r)is the relevant one. During our study we verify that the MHNC equation alsogives a very accurate description of correlations for systems with an ultrasoft-corepotential.