Concentration regimes in solutions of polyelectrolyte stars

We present a scaling theory for solutions of star-branched polyclectrolytes in different concentration regimes. We distinguish between two cases of counterion distribution around the star arms and describe differences in the structure of stars with and without counterions condensed on the arms. Above the overlap concentration c*, the size of stars decreases with increasing concentration in such a way that the stars remain at the onset of overlap in a wide range of concentrations. This regime of compaction (which we call the overlap regime) continues until the length of the star arms decreases either to the value determined mainly by the intra-arm repulsion or to the Gaussian size of a linear chain in a semidilute solution. At higher concentrations, stars interdigitate and the solution structure resembles that of a semidilute solution of linear chains. Added salt screens the electrostatic interactions within the star if salt concentration is higher than the concentration of counterions which are not condensed on the arms.