Thermodynamics of star polymer solutions: A coarse-grained study

We consider a coarse-grained (CG) model with pairwise interactions, suitable to describe low-density solutions of star-branched polymers of functionality f. Each macromolecule is represented by a CG molecule with (f + 1) interaction sites, which captures the star topology. Potentials are obtained by requiring the CG model to reproduce a set of distribution functions computed in the microscopic model in the zero-density limit. Explicit results are given for f = 6, 12, and 40. We use the CG model to compute the osmotic equation of state of the solution for concentrations c such that Φ_p=c∕c^*≲1, where c^* is the overlap concentration. We also investigate in detail the phase diagram for f = 40, identifying the boundaries of the solid intermediate phase. Finally, we investigate how the polymer size changes with c. For Φ_p≲0.3, polymers become harder as f increases at fixed reduced concentration c∕c^*. On the other hand, for Φ_p≳0.3, polymers show the opposite behavior: At fixed Φ_p, the larger the value of f, the larger their size reduction is.