Conformations of Star-Branched Polyelectrolytes

Scaling theory describing the conformations of weakly charged star-branched polyelectrolytes in dilute and semi-dilute salt-free solutions is developed. The dependence of the star size on the number of branches as well as on the solution concentration is analyzed. It is shown that the star size increases with an increase in the number of branches, $f$, at small $f$ and tends to a constant value at large $f$. An increase in the concentration of stars in a solution results in a decrease in the star size $R$ according to the power law: $R\sim c^{-1/3}$ in the range of a moderate concentration and $R\sim c^{-1/4}$ at larger concentration. For stars with a small number of branches the behavior $R\sim c^{-1/2}$ in a certain concentration range is also predicted. The collapse transition which occurs in the polyelectrolyte star if the solvent strength decreases is considered; it is shown that the collapse of a polyelectrolyte star may be accompanied by the loss of the star spherical symmetry